Topicalization, Scrambling, and Argument Scope in German: Integrating Semantic and Syntactic Information

Journal oj Semantics 11:311-363 © N.I.S. Foundation (1994)

ANATOLI STRIGIN Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 Max-Planck Research Group 'Structural Grammar', Berlin

Abstract The paper proposes an explanation of some argument scope phenomena in German in terms of interaction of syntactic and semantic information. On the assumption that lexical semantics of a verb induces a hierarchical ordering on its arguments, it is proposed that this hierarchy together with the mapping of the hierarchy to syntactic structure define a basic scope configuration. The mapping is controlled both by syntactic and by semantic information. Another hypothesis proposes that changes in the syntactic structure caused by topicalization and scrambling extend the mapping by assigning a specific role to the traces of the moved DPs. The traces can either have the semantic type of DPs or the type of individuals. This typing ambiguity yields two options: either the DP is semantically reconstructed into its original argument position, or the domain of the mapping of verbal arguments is extended. The options correspond to the narrow and the wide scopes of an argument, scope being expressed at the level of Discourse Representation Structures. This treatment of German facts is more restrictive than the ones based on Cooper storage, Logical Form, or Flexible Type Assignment,

o INTRODUCTION: SCOPE ASSIGNMENT AT THE LEVEL OF SEMANTIC FORM

o. 1 A brief review of the subject matter The phenomenon of scope in natural language as it is understood in this paper is due to dependencies between mental constructs—semantic representations. The dependencies which are of interest in this sense reflect dependencies of verifiability conditions for representations corresponding to propositional structures. In other words, they define what may be called truth-conditional scope. The main aim of the paper is to provide a technical outline of a theory of how argument scope is computed in this framework for a small fragment of German. An argument in the context of this paper is simply a determiner phrase (DP) which is assigned a 0-role by some syntactic constituent. The term argument scope refers to the dependencies in propositional representations introduced by arguments; that is to say, in the case, of some first order sentence of the form predicate (a, b) with two individual constants a and b, possible 312 Topicalizarion, Scrambling, and Argument Scope in German interpretations of b can be required to depend on those of a inasmuch as any mapping of [a, b) to a model which is allowed to vary in letting b denote different individuals must observe some fixed interpretation of a, but a can vary irrespective of b, e.g. if it is required that for every embedding/ of a into some model M there must be an embedding £ oft into M with the additional requirement that£ should agree with/wrt. a. I take this to be the core case of

argument scope, and the question usually asked in this connection is which Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 factors determine it. There are a number of treatments of argument scope, both in model theoretic semantics, e.g. Cooper (1983), Hendriks (1990), and in representational theories, e.g. May (1977, 1985). There is also a recent proposal in the framework of Discourse Representation Theory, DRT, by Reyle (1993); Frank & Reyle (1992). This introduction is devoted to motivating yet another attempt to formulate mechanisms and principles of argument scope assignment. Since both semantic means and syntactic factors of scope assignment are reasonably well understood, the emphasis of any such attempt should be on the ways these two aspects are interrelated. To explain where exactly the emphasis of the present proposal lies, I will start by briefly reviewing some theories, beginning with the representational theory which has the widest currency: May's theory of scope determination at the level of Logical Form with the rule of Quantifier Raising (May 1977, 1985, 1991). According to May (1991), any language has its logical form—the representation of the form of the logical terms of a language. May characterizes logical terms as those expressions of the language which have, in some sense, invariant meanings. Their fixed meanings (i.e. those aspects of their meanings which are not lexical) arise from their being interpreted by general semantic rules. Thus, the rules for quantifiers have pattern-matching preconditions for their application which require the distinction between a sentence and a sentential function. This requires, in turn, that the mechanisms of interpretation be able to dis- tinguish free occurrences of variables from bound occurrences, hence the notion of binding. Binding requires the notion of scope, so scope in the sense of May is the domain of binding. A logical form is then a representation of those formal properties which are required to ensure proper application of the general semantic rules. A level of linguistic representation will be (a representation of) logical form only if it manifests these properties. May argues that there is a syntactic level of representation, LF, and his central claim, an empirical discovery, is that the part of the grammar which deals with the syntax provides enough structure at LF for general semantic rules to use in the truth definition. This makes introduction of any other representational means for the purpose superfluous. Argument scope is defined at LF by the c-command configuration of syntactic representations of arguments arising after the application of the rule of Quantifier Raising (QR), which is a particular instance of the syntactic Anatoli Strigin 313 rule known as 'move a'. The configuration of c-command between arguments is claimed to provide enough information for the application of the recursive rules. Thus the sentence Everyone admires someone is claimed to be scope ambiguous due to the fact that (i)

(1) [s someone; [s everyonej [s e-t admires ?;]]]

is a structure of symmetrical c-command between the two quantified deter- Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 miner phrases someone and everyone which permits different orderings of the iterative application of the semantic quantifier clauses. Both DPs have been moved from their respective positions by the rule QR, and adjoined to an S node (bracketed expressions are used to denote uninterpreted syntactic structures). Note that binding here is effected by syntactic constituents. Similarly, domains of binding, as well as sentential functions and free variables, are syntactically defined. If, however, Logical Form is equipped with ^.-abstraction, and semantic types as in Williams (1977) (I am not quite sure about Williams 1986), I prefer to consider these proposals at a level of semantic representation rather than at a purely syntactic level which is subject to semantic constraints. In other words, I consider semantically motivated types of expression and the presence of a semantic binding operation (like ^.-abstraction or some equivalent of it) to be jointly characteristic of a semantic rather than a syntactic level of representation, though inasmuch as the word 'semantic' does not refer to any object of a non-representational character in this context, some researchers see it as more appropriate to consider any such representation level as syntax. There are arguments against the syntactic level of LF (see Berman & Hestvik 1991 for a recent critical survey of arguments for and against LF). In particular, it was claimed that the rule QR is not the right device to produce the relevant configurations. For example, QR presumably also predicts scope ambiguities in

(2) many cellists played few variations which it does not seem to show. Such behaviour is typical of quantified DPs based on determiners which differ in their logical properties from someone or everyone. LF is too permissive here. Furthermore, some authors (e.g. Frey 1993) have argued that argument scope in German is implicitly represented at S-structure (see also Diesing 1992), and claimed that LF predictions for German are incorrect in a number of cases. The qualification 'implicitly' indicates that relative scope of quantifiers must be calculated from S-structure in German, and is not described by a simple pattern. Inasmuch as this claim is supported, the role of LF as a language-inde- pendent level of representation is dubious. The work of Frey will be reviewed in more detail later. 314 Topicalization, Scrambling, and Argument Scope in German

Objections against QR, and against LF, in general stimulated the search for alternative means to represent relative scope of quantified DPs. One of the best known is the device of quantifier storage (Cooper 1983), which is a purely semantic means of dealing with the problem. Purely semantic here is meant to characterize any approach which assumes no special level of representation for scope, no syntactic ambiguity to reflect scope ambiguity, and in general no constraining influence of syntax on scope configuration over and above provid- Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 ing some constituent structure, but which tries to manipulate model theoretic constructs. The version developed in Cherchia (1988) makes provisions for some syntactic constraints. It should be noted that quantifier storage produces an impression of being not quite as explanatory as Logical Form. The following illustration is the one adapted from Chierchia (1988). The essence of Cooper's technique is a discontinuous operation of variable binding using a special information structure which stores interpretations of quantified phrases and their binding indices. Storing-in a quantified phrase amounts to freezing its interpretation until some point later than the application position for this phrase determined by syntactic structure, and simultaneously recording this application position by introducing a variable co-indexed with the interpretation in this place. At the point where the correct scope is reached1 the interpretation is stored-out, e.g. (4), which is the derivation of the semantics of (3). Syntactic structures need not be ambiguous, and there is no separate level expressing logical form. Note how the NP a man is translated as a variable plus a stored-in binder giving its content. (3) every cat loves a man

(4) Constituent Translation Store Operation

[a manjNp x3 (XP3y[man'(y) A P(y)],3) store-in [loves a man]vp love'(x3) (XP3y[man'(y) A P(y)],3) every cat loves a man Vx[cat'(x) -»love'(xj)(x)] (XP3y[man'(y) A P(y)],3) Result every cat X.P3y[man'(y) A P(y)] 0 loves a man Xx3Vx[cat'(x) - Iove'(x3)(x)] store-out Storing-out the phrase a man binds the corresponding variable. As already mentioned, Chierchia suggested that this device has to be supple- mented by some means of using syntactic information, arguing that a sig- nificant amount of agreement phenomena involved in quantification have no adequate purely semantic treatment. His proposal amounts to encoding scope as a sequence of indices at the top node of clausal syntactic structure, and using the kind of slash notation depicted in Gazdar et al. (1985), Unking the operations of storing-in and storing-out to rules both eliminating and introducing slashed categories. The basic semantic mechanism remains that of quantifier Anatoli Strigin 315 storage. And since it is so, both proposals complicate (model-theoretic) semantic structures (cf. Landman & Moerdijk 1983). Recendy, a different semantic technique has been proposed by Hendriks (1990) (see also van Benthem 1991 and Dekker 1991). Q-Store is not really necessary and its effect—delayed binding—can be simulated by providing elements in the lexicon, e.g. verbs with different possible scopings. Hendriks

(1990) presents a semantic treatment of scope which is based on the systematic Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 semantic ambiguity of the syntactic expressions of the language. The ambiguity is termed flexible type assignment (another word is polymorphism). Syntactic expressions are assigned one basic type as lexical entries, but there are rules assigning (a large number of) derived types by performing transformations on the denotations of the expression. If flexible typing is allowed, the effect of delayed binding can be achieved by semantic operations, and the following example shows how the application of such a semantic operation, Rule 1, allows two different readings for any two quantifiers which are arguments to the verb find. The vector notation (a,,, p) abbreviates (o^, (.. .(an, ($))), i.e. a functional type mapping n arguments of types j to the value of type; t is the type of truth values. Rule 1: Type: (a, flj, (%, t))) => (a,J((p, t), t), (% t))) Semantic operation: X.PX3yc.y(Xjc.Paxc) where P is of the appropriate type to match the argument sequence. Below, the operation is applied to die two-place individual predicate Xxy.FINDxy. The correspondence of the variables of the predicate to the variable sequences of the scheme of Rule 1 is shown to the right of the deriva- tions in the example. As it varies, different results are obtained.

(5) Xxy.FINDxy b — x, c — y ^xy.FINDxy a — x, b — y XyT.T(fcx.FINDxy) b-y,c-T XxT'.T'(ty.FINDxy) b-x,c-T XTT'.T'(Xy.(T.(XjcFINDxy))) The hierarchy of ^.-prefixes is preserved in both cases. But Rule 1 over- generates combinatorially in two respects. First, since a, b and c are allowed to be of any type, there is an infinity of possible transformations, and it should be proved that they produce logically equivalent results. Second, it presumably assigns two readings to (2), which is undesirable. In general, this rule is too permissive as well, since it postulates at least n! readings for « quantifiers—a prediction which is not borne out, e.g. for German under one set of prosodic conditions, as will be seen in a moment. Possible amendments are to constrain either the rule, or its applicability, or both. In particular, there is evidence that such rules should be linked to syntactic structure in a more subtle way. A 316 Topicalization, Scrambling, and Argument Scope in German thorough assessment of syntactic factors relevant to scope determination for German was given by Frey (1993). In particular, Frey claims that, although quantifier scope is a genuine semantic phenomenon, there are some syntactic factors which either allow for a reading with a particular relative scope of arguments or prohibit it He also lists conditions which determine ambiguous scope readings in German. Scope is considered by him to be a two-term

relation SCOPE(A, B), intended to mean 'A can have scope over B' where A is Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 called a scope-inducing element, and B is called a scope-sensitive element. The notion of a scope-inducing element is, in my view, a semantic notion, not an S-structural one: it does not seem plausible that syntax would single out the class of all scope-inducing elements by marking, e.g. modal verbs [+scope bearer] (Frey does not restrict his theory to argument scope alone). Therefore SCOPE(A, B) is either defined on S-structure using some information from semantics, or Frey's theory can rather be thought of as establishing syntactic factors of scope, not scope itself, which simply means that an algorithm computing scope from S-structure for German must be given which conforms to the generalizations by Frey. Cases where SCOPE(A, B) and SCOPE(B, A) for two quantifiers A and B hold simultaneously on one S-structure give rise to scope ambiguity. Thus, SCOPE is a modalized relation, i.e. A is allowed to have scope over B if SCOPE(A, B); in symmetric cases there is a choice, but according to Frey no syntactic ambiguity underlies argument scope ambiguity. Frey's theory gives no explication o( the phenomenon of scope, reserving this for semantic theories, e.g. for the Discourse Representation theory (Kamp & Reyle 1993). In the rest of this section I will briefly review Frey's theory as I understand it. There are two subcases of SCOPE. (6) SCOPE(A,B)inTiff (i) the L-head of the chain headed by A c-commands the foot of some chain headed by some member of the movement sequence of B in T, or (ii) There is a congruence chain (I, a,) where a, is the foot of the chain headed by A, and I (the head of I-projections) c-commands the foot of some chain headed by a member of the movement sequence of B in T.

This definition is tailored to the needs of German, so the theory in this version should be tested against German facts. It contains two basic ingredients: (a) the hypothesis that for every scope-inducing element there is a domain with a special property where this element gets its scope computed wrt any relevant elements, and (b) the hypothesis that the relevant elements are those which are to be interpreted in this domain. The notion of the local head (L-head) of a chain is essential in determining the domain, and the notion of movement sequence of an element is responsible for determining if this element is going to be Anatoli Strigin 317 affected. The complexity of the definition actually reflects the complexity of German facts. Instead of expanding the definition itself, I will introduce some German facts and point out which portions of the definition account for them. I will concentrate on (6) (i) in this paper, and disregard (ii). It follows from (6)(i), that SCOPE is unique in S-structures without displaced constituents, where L-heads are DPs themselves, and their movement

sequences are trivial. Frey assumes that this unique SCOPE is determined by the Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 lexical properties of verbs, and mainly by the basic word order they define in a sentence. Thus, (7) and (9) are scope ambiguous, whereas (8) and (10) are not (words in capitals are stressed, the translation is given below).

(7) DASS er mindestens ein Gemalde; fast jedem Gast t( zeigte that he at-least one picture-ace almost every guest-dat showed (8) DASS er fast jedem Gast mindestens ein Gemalde zeigte that he almost every guest at-least one picture showed (9) DASS er fast jedem Test,- mindestens einen Bewerber t{ unterzog that he almost (to) every examination-*/^ at-least one applicant-acc submitted (10) DASS er mindestens einen Bewerber fast jedem Test unterzog that he at-least one applicant (to) almost every examination submitted The linear order of the case forms of the DPs is different in these pairs. Frey's explanation is that sentences with unique readings reflect differences in basic unmodified orders for the two verbs here, whereas the ambiguous sentences are examples of scrambling, i.e. are a result of a structure which is modified wrt. the basic one. In (7) the accusative DP has been scrambled over the dative one, producing the configuration in which the accusative DP is the local head of its chain, and c-commands the only element of the movement sequence of the dative DP. The same structure is in (9), only this time the dative DP has been scrambled over the accusative one. The notion of the movement sequence is needed to account for more complicated examples like (11) and (12). The sentence (11) is less acceptable than (12),2 but it is nevertheless claimed to show scope ambiguity, in contrast to (12). (11) "fast jedem Besucher gezeigt HAT Hans mindestens ein Gemalde almost every \iskor-dat shown has Hans at-least one picture-acc (12) ?mindestens ein Gemalde gezeigt HAT Hans fast jedem Besucher at-least one picture-dec shown has Hans almost every visitor-dat To determine the basic word order Frey appeals to the notion of the maximal focus potential (Hohle 1991): the basic word order configuration is claimed to occur in most contexts. This configuration can display scope ambiguities, if the respective constituent is focused. To avoid focusing it, the finite verb or the complementizer can be stressed (the so-called VERUM-focus, producing the 318 Topicalizarion, Scrambling, and Argument Scope in German

effect of an explicit confirmation of the truth of the utterance; this focus is reflected by putting the verb or the complementizer in capitals in the examples). Under these conditions relative scope is unique. Using these means of ensuring the uniqueness of scope seems to suggest that it is not really the serial order which constitutes a factor in the theory of scope, although it must be something related to it. Moreover, this factor can be over-

ridden in German as witnessed by topicalizarion, scrambling or focusing. Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 Another assumption which seems to be justified by these observations is that the best way to integrate syntactic factors is to cause semantic mechanisms to be licensed by syntactic structures. This suggestion has already been made, e.g. by Pereira (1990), and will be explored in detail in this paper. Let us see what predictions Frey's theory makes for (1 i)-(i2). The assumed basic word order for zeigen is NOM > DAT > AKK, with NOM having the widest scope, c-commanding one DP, and a trace of a member of the movement sequences of the other one in both sentences. There is only one relative scope of the complement DPs in (12), because the topicalized VP (the one to the left of HAT) is not a scope inducing element, presumably, therefore, the accusative DP is its own L-head, and its scope potential has not been extended. On the other hand, (11) shows an alternative: the accusative DP can have scope over the dative DP because it c-commands the foot of the chain headed by a member of the movement sequence of die dative DP. The dative DP is its own L-head, because its local domain is the whole clause, and it c-commands a member of the movement sequence of the accusative DP, creating the second reading. Frey argues that this and structurally similar sentences are marginal, because the trace of the scrambled accusative is not c-commanded by its antecedent, but they are clearly comprehensible and display scope ambiguities. This raises the question of how to define chains in German, but the general idea seems to be clear. Part (6)(ii) of the conditions on scope is meant to account for ambiguities with unaccusative verbs, e.g. for (13) and (14), both of which are claimed to show scope ambiguities. (13) wenigstens ein Film 1ST fast jedem meiner Freunde entgangen at-least one film-MOW(has ) almost every of-my friends-dat escaped-notice (14) fast jedem meiner Freunde 1ST wenigstens ein Film entgangen The basic order is DAT < NOM. This accounts for the wide scope of the dative DP in (13), where it c-commands the trace of the topicalized nominative DP. The latter c-commands the dative DP, hence the ambiguity. But to account for the ambiguity in the second case, Frey assumes that the nominative DP forms a congruence chain with 1°, and 1° c-commands the trace of the dative DP (i.e. nominative can always have wide scope). Frey's theory seems to make a number of correct predictions for complicated Anatoli Strigin 319

cases, but it does leave the effects captured in the definition (6) unexplained. In particular, there is no a priori significance in the word order, and it is simply postulated that there is a basic word order for every verb which unambiguously determines argument scope under some prosodic conditions. Frey's dieory has in part been implemented in Frank & Reyle (1993) and surveyed in Reyle (1993). While I cannot render full justice to their work, I

would like to make some remarks on the relation of their algorithm to the ideas Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 of this paper. The algorithm of Reyle (1993) and Frank & Reyle (1992) exploits the assumptions that there is a basic order of arguments for every verb in German, and that this order can be uniquely mapped on to a c-command hierarchy which determines scope. By (recursively) comparing the list of arguments in basic order with the list of their order in a given sentence, the algorithm establishes which scope information can be simply retained (the order in the sentence fits the order on the basic list) and which should be modified. As far as I understand it, it works on the assumption that if an argument is displaced, it additionally gets scope over the elements it c-commands, since left to right order is assumed to correspond to c-command in German. Therefore it does not work on topicalized VPs as in (12), which is unambiguous, but where the order of argument is not the basic one. However, there are suggestions how to extend it (Frank, personal communication). (12) ?mindestens ein Gemalde gezeigt HAT Hans fast jedem Besucher at-least one picture-acc shown has Hans almost every visitor-dat The algorithm of Frank & Reyle uses systematically underspecified structures to represent scope ambiguities, but this part of the algorithm is a separate issue.

0.2 Theproposal There are some conclusions which I think can be drawn from the above discussion. First, May's theory has no explanation for the dependence of possible scope configurations on lexical properties of verbs noted by Frey for German, neither have the theories of Cooper, Chierchia or Hendriks. Of course, a different interpretation of the facts about the unique readings of basic word orders observed by Frey might be possible, but if that is accepted something should be revised in the theories to accommodate the role of the lexicon. The general impression is that the assumption about the default case of scoping as 'everything goes' should be revised, and I will explore Frey's alternative which assumes that there always is a basic scope configuration for the arguments of a predicate. Second, scope configurations in German obviously depend on syntactic structure, but it is no longer the dependence envisaged by May. It is possible to postulate syntactic rules like quantifier lowering or VP-reconstruction for 320 Topicalization, Scrambling, and Argument Scope in German

German in order to regain the basic predicate-argument structure in the syntax, or to provide for some modified syntactic level where scope can be read off, but then such a purely syntactic theory of scope has to be differendy argued for, and has to confront the lexical challenge again. My conclusion is that the contribution of syntactic structure need not consist in providing some pattern which is amenable for interpretation by semantic rules, but which might be more

intricate and simple at the same time. Just how intricate it can be is a language- Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 specific question. Third, semantic theories of scope can be expected to produce better results if provided with possibilities for using syntactic information. At least the complexity or necessity of semantic operations used can be perhaps reduced. So the treatment of this paper is based on the assumption that it is an inter- play between syntax and semantics which determines scope configurations, but which is not merely some syntactic pattern which happens to be interpretable by general semantic rules or simply semantic polymorphism of linguistic expressions, but is the licensing of semantic operations both by syntactic structures and by semantic types. This general assumption is made precise by adopting the following hypothesis as a basis which seems to account for the lexical facts in German: I will assume that (a) every semantic representation of a predicate defines a semantic prominence hierarchy of its arguments. The arguments must be related to their syntactic positions. I maintain that for every semantic representation of a lexical entry which is a predicate there is a function mapping its prominence hierarchy into the syntactic structure of asymmetric c-command, the least prominent argument being the lowest c-commander of the predicate, and having the narrowest scope. This is the basic scope configuration; it is always recoverable. And it can be subject to lexical change, in accordance with the fully lexicalist position on lexicon assumed here. (b) every syntactic change of the basic configuration involves some semantic operation extending the basic mapping of the arguments to syntactic structure. In other words, semantic operations are licensed by syntax. The extended mapping is a potential source of scope ambiguity, since the basic configuration is always recoverable. This is a particular combination of the ideas on type-driven translation3 and type coercion as a weak (and controlled) form of polymorphism of semantic operations. I shall substantiate these observations by considering two phenomena in German as an example: topicalization and scrambling. This choice implies that I will be concerned with the overt manifestations of scope ambiguity phenomena, leaving factors which influence argument scope without being visible in the syntactic structure, e.g. prosody, for another occasion. Anatoli Strigin 321

As a matter of technical detail I will assume that representations as I introduce them can be interpreted as programs computing scoped semantic representations, which I will take to be discourse representation structures, DRS, introduced in Kamp (1981), and developed in Kamp & Reyle (1993). There are two reasons for constructing the framework in this way: it allows one to speculate on the nature of mental representations as information structures, and to be more specific in some decisions, such as postponing pronominal Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 binding for the DR part of the theory, where, I think, it should belong. The structure of the paper is as follows: in the first section I will introduce a particular version of the notion of Argument Structure which will be used to define the mapping from semantic representations to syntactic structures, and to formulate the scope assignment hypothesis. In the second section I will provide a description of some syntactic structures in German; in the third I will apply the hypothesis to some simple scope ambiguity facts in German. In the fourth section I will extend the coverage to somewhat more complex cases of VP topicalization, and in the fifth section describe how to construct discourse structures from semantic representations relevant in determining scope. A summary and an appendix where the relevant rules are collected into a rule summary conclude the paper.

1. SEMANTIC FORM AND ARGUMENT STRUCTURE

1.1 Semantic Form Manfred Bierwisch has argued in a series of papers (Bierwisch 1989a, 1989b, 1990) for a sentential semantic representation level placed between some relevant syntactic structure (S-structure or Logical Form, for example) and a more fully interpreted semantic representation, e.g. discourse representation. He calls this level S(emantic) F(orm), SF. One motivation for assuming this level was to be able to isolate those aspects of the semantic structure of the constituents which characterize their essential combinatorial potentials, and their basic contribution to interpretation, leaving their full semantic interpretation to the general conceptual system (of the brain). Another motivation was to attain the place where syntactic combinatorial properties of constituents are related to their semantic combinatorial properties. This is done basically in the lexicon at a place called Argument) S(tructure), AS, and then the structure of constituents is paired at a relevant level with the rules interpreting it in terms of the SF of the constituents. The language of SF is lambda-calculus with constants (see Hindley & Seldin 1986 for the formal basis). The constants were intended to stand for semantic primitives. However, since there is little agreement on the question of existence of such primitives, let alone their exact properties, the constants used in the sequel are best treated as abbreviations of 322 Topicalizarion, Scrambling, and Argument Scope in German complex expressions containing such SF primitives. The version of X-calculus recurring in the works cited is typed. The basic types are o (for propositions) and i (for individuals). There is also the standard operation of functional type formation, denoted by (,), i.e. (a, P) is the type of functions from objects of type a to objects of type p. Although claims about the role of SF as a distinct level may be fairly con- sequential, they will not be discussed here (see the papers by Bierwisch, and also Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 Zimmermann 1992), except for the following two brief remarks. The first concerns the relation of SF to model-theoretic semantics: even if model theoretic semantics is claimed to suffice for providing an interpretation for natural language discourse, there is still the question of how the knowledge of semantic interpretations in the model-theoretic sense should be represented, regardless of how platonic the interpretation itself is. Secondly, levels of semantic interpretation are a source of controversy in theoretical linguistics, so putting them to work helps to make their claims more concrete. Its controversial status should not therefore preclude the use of SF in a semantic theory. The technical role of SF in the paper will be to provide programs which compute structures serving as raw material for discourse representations of isolated sentences. In particular, it should provide control structures for such programs. The syntactic analysis trees will be translated as trees showing application of functions to arguments. In other words, an object of SF will be some expression evaluated according to the rules of X-calculus. The result of the evaluation will be a structure which should contain at least the necessary information delimiting the semantic contribution of the sentence in discourse—a prefab discourse representation. To sum up these technicalities, given a sentence S, its semantic form ||S|| is a program in functional notation, i.e. a functional expression which will be evaluated. The value will be a structure which is very near to a discourse consisting of one sentence. Later, an algorithm will construct for any given context (discourse background) a new discourse representation, updating the context with the information contained in the structure obtained as the result of the evaluation. The evaluation itself will be split in two parts.

Evaluate(||S|D => Execute(Evaluate([[S|D) => UPDATE(Context,Execute(Evaluate(l|S|D)). Evaluate(||S|D yields the first stage of the structure containing the discourse contribution of the sentence, transforming syntactic information into control structures. Execute(Evaluate(||SD) yields an almost complete DR for S. Evalua- tion is considered separately from execution to allow for the possibility of experimenting with different DR-construction algorithms, like bottom-up or Anatoli Strigin 323 top-down, etc., and execution is considered in isolation from updating mainly for ease of exposition. Taken together, they form the interpretation algorithm whose input is the syntactic structure of sentence S, and the SF of its lexical nodes. These are expressions of type o standing for the core semantics of lexical units. Assumptions about the content of the expressions should be justified, but whenever they are not essential for illustrating the workings of the theory, they Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 will be merely explained, and the reader will be referred to their origin. Let us look at the SF of two verbal forms, as they leave the lexicon (according with a fully lexicalist point of view). The first is the German shown, i.e. the past participle of zeigen, and it has the same SF as the infinitive. The typing state- ments will be of the form expression-.Type. Some normal bracketing conventions are employed to improve readability, constants are in capitals, variables are small letters. (16) gezeigt ((INST(((SHOWx)y)z))(e)):o The SF of this verb can be paraphrased as 'some event is structured (instantiated) so as to be an event e of x being showed to y by z\ This method goes back to Davidson's theory of action sentences, except for the two-place INST predicate, which is used by Bierwisch in the papers cited and can be considered in the context of this paper as merely a syntactic sweetener which can be dispensed with. SHOW is three-place, as can be guessed; the arguments, including e, are of type 1. Let us turn to an abbreviated version of the SF of the auxiliary verb haben (have) in the 3rd person singular present. (17) hat v(e):o This verb makes a very vague claim that some event e has the property v, leaving it to its complement VP to specify both. Actually, the role of this verb is not seen here because temporal information is not considered. The particulars of the two semantic forms are from Bierwisch (1990). Lexical units have some internal syntactic and semantic structure in accordance with the strict lexicalist view of the lexicon, reflected, for instance, by the morphology ofgezeigt, but only the SF of the whole form is shown here. In fact, the examples are not meant to be serious analyses, but they will suffice for the purposes of the exposition. What matters for the discussion to follow is the fact that whenever a lexical unit has more than one argument its arguments are hierarchically ordered, and this ordering is used by AS. 324 Topicalization, Scrambling, and Argument Scope in German

1.2 Argument Structure AS—Argument Structure in the sense of Bierwisch—is a mapping from this (lexical prominence) hierarchy4 to a syntactic structure assigning to (some) arguments their syntactic positions. This pairing, called 0-grid due to its connections to the notion of 0-role assignment in the current generative litera- ture, observes only the prominence hierarchy and no other characteristics of Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 the variables. Factors determining the pairing constitute the theory of argument structure. Note that there are two empirical hypotheses at work here: there is a semantically defined linear ordering of arguments, and the interface between syntax and semantics is sensitive only to the order and not to the content of the arguments. Both hypotheses can be formulated in frameworks different from X,-calculus. I will use very simple examples. Lexical entries (LEs) will be represented using feature structures. The content of the latter follows Bierwisch (1989a). Formally, each LE is a feature structure with four features, Fi: Fi: P(honological) F(orm), F2: Grammatical) F(rame), F3: A(rgument) S(tructure), F4: S(emantic) F(orm), which will be taken up in turn. Phrasal categories will have one feature less in their feature structures.5 PF: FiflLE) is a data structure specifying phonological properties of lexical entries. No further use will be made of it, except indicating what words are being talked about. GF: F2(LE) contains a structure of grammatical features which characterize the syntactic properties of the lexical entry, and its contribution to syntactic structure. I assume a fully lexicalist position, which insists that words exit the lexicon fully specified in all relevant aspects. This feature is not a subcategorization frame, but a categorial specification. Part of what usually constitutes subcategorization frames is put into F3. At this point there is no point in taking a stand on the question of whether subcategorization frames should lead a life of their own. AS: FifLE) is the Argument Structure of lexical entries. Its basic function is to relate the addresses of the semantically relevant parts of a lexical entry to its syntactic combinatorial properties. It seems adequate to treat AS as a function. Thus, AS is an n-tuple of pairs (xj, gf) consisting of a structure of grammatical features gf and a typed variable. The semantic type of the variable is defined by the type theory of SF. However, it is natural to view gf as a kind of grammatical variable- typing, with types defined by the syntax, and with the possibility of letting the type of the variable be an ordered pair of a grammatical type and an SF type, AS Anatoli Strigin 325 being a function from variables to type pairs. Technically, this function can be implemented as X.-prefix of an SF expression with X-hierarchy coding relative prominence. The variables of die prefix acquire two kinds of types, a semantic type and a syntactic type, thus ensuring that a variable is related to a correct syntactic constituent determining its interpretation. Both types will be checked before applying functions to arguments. Therefore, what F3 actually contains is

the X-prefix with double typed variables, and this notation will be used for all Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 syntactic constituents, saving one feature compared with the lexical entries. SF: is an expression of type o in a type system (o, 1 (,)) with constants, standing for the core semantics of lexical units, as indicated. That the basic semantics of lexical entries is in the propositional format might appear restrictive, and it is an intriguing question whether this assumption is appropriate, but we will adhere to it here, obtaining as a consequence the fact that the SF of almost all lexical or phrasal constituents has the form (...,(..., o)).6 The Argument Structure encodes that there is a hierarchy of arguments of the non-finite form of the verb and relates it to some morphosyntactic properties. The least prominent argument of the verb form is assumed to be marked either ACC (for accusative), or by DAT (for dative), in general, and ACC for the verb zeigen. This case-form is kept for the perfect participle and checked during the process of assigning the arguments to their syntactic positions, as will be seen presently, in the same way in which semantic types are checked. It is not suggested that this linking theory is sufficient for German in general, but it suffices for the present purpose. The event argument will be ignored. The hierarchy of the arguments in the SF of the verb is reflected in the ordering of the prefixes in the AS sequence. The value of F3 is just a sequence, and that of F4 is a X-expression, but with all variables free. Since all other rules will later use the format of X.-calculus, a special rule must prefix F3 to F4. The feature F2 will be exemplified in Section 2.1 after introducing some syntactic terminology.

(18) gezeigt Fi — /gezeigt/ F3 - (x , y:

(19) hat Fi - /hat/ F3 - (v:

Two more provisional simplifying assumptions will be made. The determiner phrases, DP, are represented by ||DP||, without specifying their internal structure for a while. The SF type of ||DP|| is ((i ,o),o). And I will sometimes use a dummy adverb bekanntermafien (translated as is known) just to fill the topic position in a sentence without considering its SF at all. Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 i. 3 Lexical scope hypothesis As already noted, it is assumed that the prominence hierarchy of a lexical entry defines one basic argument scope configuration, with the least prominent argument having the narrowest scope. Therefore, it is the hierarchy jointly with the syntactic range of its AS that partly determine the way in which syntax constrains all possible scope configurations. The hypothesis that Argument Structure determines one basic relative scope configuration will be called Lexical Scope Hypothesis for obvious reasons.

(20) LSH: for every n-place lexical predicate in a sentence there is a basic relative scope of its arguments which is a monotone mapping of the argument hierarchy of the predicate to some relation of the syntactic structure. The mapping is uniquely determined by the Argument Structure with the least prominent argument having the narrowest scope.

According to this hypothesis any other scope configuration must be derived. Factors determining what constitutes a derived configuration in this sense can vary from language to language. This hypothesis has a natural motivation, as the following considerations show. The SF of the syntactic tree node dominating the LE of zeigen which will be fed into the SF computing machinery is Xjcyz.SHOW xyz. The simplest Argument Structure is a mapping relating SF-arguments to syntactic positions ordered by the relation of minimal c-command,7 which is induced by semantic requirements similar to type coercion, and based on the (intended) interpretation of the syntactic trees as application trees.8 The mapping can be rendered in (21) in this simple case by connecting lines. The least prominent argument has the narrowest scope and is the lowest DP in the tree in this configuration, since die X.-prefix hierarchy is monotonically mapped to the c-command structure. Anatoli Strigin 327

(2!) Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021

Xxyz. SHOWxyz II

Evidently, in languages using this simple form of argument structure, changing the relative scope of the DPs can involve 'moving' the DP whose scope must be extended, and that relative argument scope ambiguity is then due to the presence of the 'trace' of this DP. The scare quotes mean that the terminology is not intended to refer to specifically derivational versions of principles-and-parameters theories, but just to indicate that this is a syntactic source of the ambiguity, and moreover the one which is 'visible' in phonological terms. An example of such a tree where scope ambiguity is to be expected is (22).

(22)

Axyz. SHOWxyz J| 328 Topicalization, Scrambling, and Argument Scope in German

Scope ambiguity can now be claimed to be the result of a slight ambiguity in the interpretation of the trace, assuming it is semantically rendered as a variable, which is due to the tension in the assignment of semantic types: it can be typed I to conform to the requirements of the predicate, or ((i, o),o) to conform to the requirements of the antecedent. This potential type ambiguity explains, e.g. () Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 (23) fastjedes Gemdldei hat er mindestens einem Besucher t{ gezeigt almost every picture has he at-least one visitor shown which is claimed to be scope ambiguous yielding either (i) or (ii): (i) there was at least one visitor to whom he has shown almost all the pictures (ii) he has shown almost every picture to some visitor or other This ambiguity is claimed not to be present in (24)

(24) dafi er mindestens einem Besucher fastjedes Gemalde gezeigt hat that he at-least one visitor almost every picture shown has which can be assumed to conform to the basic scope and minimal c-command configuration, and does not contain the trace. This simple version of argument structure will be made more precise now, clarifying the role of type coercion. Continue to assume that the SF type of determiner phrases is ((1 ,o),o), i.e. they take a property and return a proposition. Given this, the tree (25)

tayz. SHOWxyz is not well formed: since the typing of the predicate is (1,1,1,0) (I use association to the right to drop some brackets), there is a type mismatch at the lowest application node, and the basic assumption about interpreting syntactic structures is that a binary branching node of syntactic structure yields an application node of SF. The daughters of such a node are considered unordered, since there is no convention to determine which daughter is the functor and Anatoli Strigin 329 which the argument, except only by reference to the SF types of the two expressions. Now the argument structure of the verb must determine which X,-abstracted variable is associated with which determiner phrase. It can be done by means of an operation which I will call assignment (Assign) to invoke the notion of 0- role assignment, and which will resolve the type mismatch. The operation

needed to satisfy these requirements leaves one X-abstracted variable available Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 for the DP, and extracts the rest. Thus, it is essentially functional composition (26) (Assign) X£(( 1 ,o),o)Xg:( 1,..., o)Xi:!.f(Xx: 1 .gxz) In this formula g is an n-place predicate, x its first and hierarchically lowest argument, and the vector notation for z abbreviates the remaining n — 1 arguments, all of them of the type 1 of individuals. It hides the fact that Assign is a polymorphic function, i.e. a function which is defined for a number of types. In order not to enter into the complexities of polymorphism in this paper, it can be treated as a family of closely related functions. Applying Assign to the lowest DP in (25) as its first argument, and the SF of the verb as its second argument, we get (27).

(27) Xyx.||DP||()tw.SHOWwyz) with the result that there is a type match for the first DP, since the expression in parentheses now has the type (1,0). This procedure is repeated once again, but this time a function extracting only one abstraction is used. The result is the tree (28), where the variable w was replaced by x, in order to show similarities with (21).

Ax. SHOWxyz

Remember that nodes of a tree are translated to SF as application nodes, so this tree is represented in (29) in linear notation.

(29) ||DPS{Xz|DP||(Xy|DP|KXx.SHOWxyz))) 33O Topicalizarion, Scrambling, and Argument Scope in German

To derive the basic scope we can assume that scoping is an effect of the dependencies which are introduced when |DP|| operates on its argument constructing a DR, or to provide an interpretation of this structure directly in a model. Thus, assuming the explication of AS in the sense of Bierwisch and the fairly standard typing of DPs requires the introduction of the assignment operation

or something similar. Assumptions about the role of SF elements in con- Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 structing DR in conjunction with this operation lead to basic scope configurations. If the basic argument order of a verb corresponds to the standard hierarchy, then we have an explanation of the relevance of word order in German. Now if the tree (22) is to be interpreted, it is natural to assume that the trace of the moved DP is interpreted as a variable which is abstracted over the node where the DP resides. If the variable is of the DP type, the DP can be X- converted into its base position yielding its basic scope; if the variable is of the type 1 we have functional composition which extends the scope of the DP. Although the idea is simple, the whole situation is not quite so simple for German, as will become evident when some elements of German syntax are introduced. I would like to side-step the issue of German grammar here and use as simple syntactic structures as possible. In particular, I will assume that some simple rules for German syntax can be reconstructed from the analyses given below, and the conventions to them which follow.

2 SOME SYNTACTIC STRUCTURES OF GERMAN

2.1 Preliminaries Assume that the syntactic analyses are binary trees labelled by feature structures similar to those of Pollard & Sag (1987), which are sets of features. However, in order to be as general as possible, I will not talk in terms of features structures themselves but in terms of their types.9 This will allow me not only to doubly type variables as SF, but also to speak of any constituent as having both syntactic and SF types. A feature structure is typed syntactically according to the rules in (3O). (30) Typing rules 1 and 2 TRi: if a feature structure r has feature F with the value of type O, it belongs to the type of feature structures which have at least this feature with the value of type O (written r: [F:a], a positive type statement). TR2: if a feature structure r does not have feature F with the value of type 0, it belongs to the type of feature structures which do not have at least this Anatoli Strigin 331

feature with the value type O (written r:[\F:o], a negative type statement). There is a natural subtype relation < on the types of fs. Informally, O ^ o' iff elements of a contain at least the information elements of a' contain, i.e. if it is at least as informative as o'. In other words, the type expression of 0 contains at least the same positive and negative type statement as o', the value of types of which stand in the relation to the value types of the corresponding type Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 statement of o', i.e. (31) Typing rule 3 TR3: [..., F,:a, , Fn:O, ] ^ [F,:o',, , Fno'n], where O{ < o'{. We postulate now that whenever r:0, and O ^ o', then r:O'. This is the requirement of subsumption. Thus every feature structure (fs from now on) will have many types. Primi- tive types are needed to provide the basis for typing. There is a special type Unit, with the only value nil. Any feature with the value of this type is a unique feature-value pair and can be used as if it were a feature without any value, keeping in mind, however, that it is actually a unary feature, so that, if we assume such a feature, e.g. FIN, then [\FIN] is the type of fs with no feature FIN, for instance that of non-finite verbs. Among the primitive types are True and False with + and — as respective inhabitants. Let now, e.g. NOMINAL and VERBAL be features, the value of NOMINAL be '+', and that of VERBAL '-'. A type statement for fs r = (NOMINAL — +, VERBAL = —) is then a positive type statement r: [NOMINAL:True, VERBAL:False]. I shall use linguistic abbreviations writing values of binary features as + or — before labels for features. Thus the type statement above becomes r: [+ N, — V], characterizing a verbal constituent. The labels of the tree nodes are chosen to subsume as many types as possible, and are assumed to contain three fss: PHON (phonological information), SYN (syntactic information), and SFM (expressions of Semantic Form). As a first example of this syntactic notation, here are the missing features F2 of (18) and (19). The verb zeigen (show) is in the perfect participle form. This is reflected in the feature F2 by the absence of the feature FIN, by the presence of the special morphological property GE, and by the requirement that this should not be a passive participle PAS. The verb hat is a third person singular (past tense, not reflected) auxiliary. Its subcategorization information is stated as a syntactic type of its complement. In the same mode, cases of complement DPs in F3 of (18') are subcategorized information, too. The unit type case features here are type expressions, too. (18') gezeigt Fi —/gezeigt/ F2 - r: [+V, -N, \FIN, GE,\ PAS] 332 Topicalization, Scrambling, and Argument Scope in German

F3 - (x:

I would like to assume a version of X-bar theory which distinguishes between Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 lexical (or X°) and non-lexical categories (XP) on the one hand, referring to them summarily as X1, and between maximal and non-maximal categories, on the other hand. Obviously, lexical categories can sometimes be maximal, e.g. adverbs. I assume here that categories are [MAXIMAL] when they are sisters to X°-projections. An important convention concerns the use of'silent' information. Let Y' be a type. To allow the information about some missing (or 'moved', in the current terminology) constituents in the tree with the mother node m to be present in the fs label of this node rm, the device which resembles slash categories in GPSG (see Gazdar et al. 1985) will be used. The fact that the information about such subtrees in rm is really about a missing constituent and has no phonetic realiza- tion is indicated by postfixing ':' to the left bracket of the type expression characterizing the missing constituent, e.g. Y'[:X>] denotes the type Y1 of fs, but fss with some feature F containing a fs of type exactly like X* except for the phonological information, which is absent, i.e. the expression [:Xi] is a short- hand for F: [X>, \PFM]. The name of this feature F is irrelevant so it can be ignored, but to know which information it contains there must be some way of referring to it. I will use [:X*] itself to refer to this feature F within another fs. The notation [:X>] standing on its own without any label prefixed will be used to denote exclusively type of records without the PF feature which label terminal nodes, i.e. of what is usually called e(mpty) c(ategorie)s. If it is explicitly required that a tree with the root r is not to have a displaced constituent of type [:...], diis is stated by [\:...]. I shall also use node identification indices, mostly to mark ecs in the form of subscripts written either outside or within square brackets, and consider empty categories uniquely characterizable, i.e. a node labelled with an fs which has no PFM feature carries information about exactly one constituent, hence the prohibition (denoted by *) of structures like (32), describing some moved constituent dominating another moved constituent, i.e. think of (32) as a filter on fs.

(32) •[•Xfc [-YJ] This singles out the empty categories, since, e.g. ZP[[:XJ, [:Yj]] is a possible non- empty constituent with two subconsrituents missing. Empty categories are always connected to some antecedent in this fragment of the German syntax, i.e. they are traces. Thus, we need structures like (3 3). The Anatoli Strigin 333 equalities in (33) can be treated as admissibility conditions of Gazdar et al. (1985), but in terms of types of constituents.

(33) (i) Y*[:XPk]:- [:XPk] [] (ii) YPpCPj :- XPj Y>[:XPk], where i * k (iii) VPJMAXIMAL, [:DPk]] := [:DPk] VPi[:DPk] Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 An empty constituent should be at once registered at its mother node, as (33)(i) requires, whereas (33)(ii) allows this information to be passed on if no antecedent is encountered. (33)(iii) says that one intermediate DP trace can be adjoined to a node of VP category with the feature MAXIMAL (Chomsky 1986). The information about a displaced constituent is identified in the rules via die node identification index. This index could be the value of some feature, say POINTER INDEX to give it a name, but more interesting theories of indexing are conceivable, using agreement features, case, etc. What matters is diat the displaced constituent will have the same index as its trace. No categories of type X'[[:Yi], [:Y>]], i.e. having two copies of the same feature, occur.

2.2 German declarative sentences A German clause comes mostly in two varieties: verb last and verb second.

Verb-last structures The first type is a subordinate clause, as a rule. There are many controversial issues in German syntax; therefore I will try to remain as neutral as possible. If INFL (or AGR) projections10 are ignored, the verb-last sentential structure in German is something like (34). 334 Topicalizarion, Scrambling, and Argument Scope in German

(34) CP

0 a

dass VP[FIN, EXT, MAX]

A. Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 / \ DP 1 VP er \ VP[\FIN,\EXT, V[FIN] MAX]/\ \ hat DP / VP

mindestens /* \ einem DP V[\FIN] Besucher I I fast jedes gezeigt Gemalde

that he to at-least one visitor-rfaf almost every picture-acc shown has

The DP which is set apart in (35) as the only argument dominated by the topmost VP node is the external argument of the verb, and it causes the feature EXT to be assigned by C, the remaining arguments being naturally internal. This is because only VfMAXIMAL; FIN] can have the external argument realized, and not VfMAXIMAL, \FIN], infinitives tending to go without subjects nowadays.

Verb-second structures The second type of sentence structure, and one of interest in connection with the aims of the paper, begins with some maximal constituent which is related to its trace somewhere in the sentence. Such a constituent is referred to as topicalized. It is followed by a displaced finite verb which is related to its trace, too. Since I ignore the issue of inflexional projections (thus, there is neither a separate NFL node, nor any of its projections), I assume that the finite verb is followed by a maximal verbal projection. The topicalized constituent may be one of the verb arguments, e.g. the external argument, as in (35), or (one of) the internal arguments), as in (36). In both cases the relevant traces are denoted by [:DP]. I will side-step the exact structure of C/V and drop this label altogether in subsequent examples. Anatoli Strigin 335

""DP A, I er C/V VP

I Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 hat [:DP] VP

/ VP [: V, FIN]

DP VP / mindestens

einem DP V[\FIN] Besucher 1 1 fast jedes gezeigt Gemalde

he has to at-least one visitor-dat almost every picture-acc shown

(36)

DP C' I fast jedes r/v vp Gemalde W

hat DP VP I er VP [:V,FIN]

DP VP

mindestens

einem [.Dp] V[\RN] Besucher 1 gezeigt almost every picture-acc has he at-least one visitor-daf shown 336 Topicalization, Scrambling, and Argument Scope in German

It is possible to topicalize a non-finite verb (37), and even (accompanied by wildly varying acceptability judgements) a non-finite verb with one of its internal arguments, but not with the external argument (at least not in the northern German dialects), e.g. (38).

(37) Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021

V?[\FIN] I gezeigt

mindestens fast einem jedes Besucher Gemalde [:V?,\FIN] [: V, FIN]

shown has he at-least one visitor almost every picture

(38)

DP VP

mindestens VP einem Besucher [:DP i] V [\FIN] [:VP k] [:V, FIN] fast jedes Gemalde

gezeigt

at-least one visitor showed has he almost every picture The question mark in (37) is not a misprinc one of the difficult questions of German syntax is the status of the topicalized V-constituent in (37). Two solutions have been proposed: it is a V°, or it is a verb phrase, VP. The controversy is related to what is usually called scrambling within VP and to the structure of VP itself. The position of the paper on both issues is given below. Anatoli Strigin 337

Verb phrase A verb projection of this fragment has either a determiner phrase (perhaps ari empty category) as its left constituent or a verbal projection containing the non- finite verb together with its internal arguments; its right daughter is then some verb projection, in particular V°. Naturally, if the left daughter is an ec, then

information about it should be present at its mother node, but it will be Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 suppressed in the examples in order not to clutter up the trees. I will assume that the left daughter ofV in the verbal cluster consisting of two verbal categories may only be a maximal verbal projection, also a silent one, provided it is non-finite.

Scrambling within VP To accept V° in the topic position seems to be unpalatable for quite a number of syntacticians. Webelhuth & den Besten (1987) suggested that even a single non- finite verb in the topic position is actually a VP. This provokes the question as to where all the arguments have gone. Webelhuth's answer is that they have been scrambled out (of the smallest VP, if I understand him correctly). Scrambling is claimed to be characteristic of structures like (39).

(39)

mmdestens DP/ einem / \ Besucher / DP VP fast 1 / N jedes \ Gemalde ein Unbekannte/r / \ VP V[FIN] /\ \ / \ hat [:DP i] VP /^ \ / \ [:DPj] V[\FIN] I gezeigt that at-least one visitor-

This kind of operation can strip the verb of its arguments, leaving traces, and this bare verb VP can be moved to the topic position in (37), giving the impression of a single verb. In this case the prediction is that (37) is always scope ambiguous.

Case assignment Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 I will make a very simple assumption about how Case is assigned in German. There is the EXT feature which is assigned by C, and which means that the nominative case is assigned by (or realized by) C.'1 The other cases, like dative and accusative, are assigned (or realized) freely within VP, freely, of course, from the point of view of phrasal syntax. In other words, the German phrasal syntax does not specify any basic order of verbal complements in terms of Case, this being the domain of lexically given argument structure (the structural genitive of DPs is not considered here). With this sketch of German syntax at hand we can now turn to the construction of semantic forms of German sentences.

3. BUILDING UP SEMANTIC FORM AND DP TOPICALIZATION

3.1 Basic configuration The construction rules are used to calculate an expression of SF at a node of S-structure, i.e. the value of the feature SFM (cf. Section 2.1), in terms of its daughters. I will use some abbreviations to indicate the reference to syntactic structure. Instead of writing SFM([X]) to mean 'the value of the feature SFM of some record of syntactic type [X]', I will write the syntactic information within ||.. .|| to state the syntactic conditions. The expression obtained as the result of computing the ||.. | function for the mother node at S-structure will be either an applicative expression showing the application of a functor to an argument (this will be called application node, application denoted by @ or by juxta- position), or an expression to be evaluated itself. Thus, (40) (40) ||C| = |A| @ p| is to be read 'compute the SFM of the node of syntactic type C by applying the SFM of one of its daughters of syntactic type A or B to the SFM of the other daughter'. Then |C| is the result of the application of either ||A|| to |[B||, or the other way round, since the application nodes are unordered, relying on the fact that the functor-argument structure is determined by the types of the daughters of the application nodes. This is a difference to the LF level of representation, where order is carried over from the syntax. Anatoli Strigin 339

Since the functional application is not enough to construct new SFMs, and at least functional composition will be needed in addition to accommodate the assignment of argument, any such additional operation will be shown superimposed on the basic format of an applicative node.12 The application sign will be dropped whenever possible. The presentation of the rules begins with specifying what information is to

be put into the SFM feature of a terminal node dominating some lexical entry. Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 This is done by the lexical rule which is simply abstraction that uses the X-prefix of F3 and the expression of F4. It is always assumed that the abstraction operates as desired, binding exactly the desired variables, i.e. this is a non-explanatory solution under which the hierarchy of the Bierwisch hypothesis is simply postulated.

(41) ||X|| = XF3(LE).F4(LE) where X dominates LE

Thus, the SFM feature of the terminal nodes dominating LE always contains X- expressions of the form to the right of the equality sign, and the computation of the SFM features of all phrasal nodes can proceed along the lines of X-calculus.13 Now, take for example (42), and its S-structure (43),

(42) bekanntermafien hat er mindestens einem Besucher fast jedes Gemalde gezeigt as-is-known has he shown at-least one visitor almost every picture

(43) CP

bekanntermaBen C

hat VP

er VP [:V,FIN]

VP DP

V[\FIN] mindestens DP 1 einem Besucher 1 1 fast gezeigt

• j__ jedes Gemalde 340 Topicalization, Scrambling, and Argument Scope in German and start formulating the rules bottom up. The lexical rule (41) provides us with the expression Xxyz.SHOWxyz for the non-finite verb. Hence, the lowest VP node dominates ||DP|| and the expression he (1, [ACC]) \y. (1, [DAT]) Xz: (1, [EXT]).SHOWxyz. In accordance with the proposals of the first section die assignment function is used to interpret complementation structures. The syntactic type of the first variable of the X,-prefix is [ACC]. Since the

syntactic types of the two expressions match, but there is a semantic type Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 mismatch, we apply the Assign operation at the next step of SF computation. Therefore, we formulate the rule of SF construction which uses both the syntactic match and the semantic mismatch, and consists of the application of the (typed version) of Assign first to ||DP||, and then to ||V||. (44) (XQ:«I,O),O))J>

Remember that the empty category of type [AUX] is of type (o, o), ||VP|| is of type (..., (..., o)), and hence the variables Q and P are of these types, respectively. As it stands, the rule has drawbacks: the free variable (translating [AUX; FIN]) in the expression JVP[AUX; FIN]j is somewhat disturbing, and the rule itself seems to be inessential, and although it can be developed in a more explicit fragment of German, e.g. with tense, I will return to this point later and reconsider it in Section 3.2, after discussing example (54). For now, the Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 result of its application is (46') with the variable v rendering the [AUX]-trace. (46') X.w[EXT].v(|pP|Xu.|pP||(Xx.SHOWxuw)) Combining these results with ||er|| simply creates an application node, since we have not yet specified how determiner phrases operate on their arguments. Now we abstract on the verbal variable using rule (47), which is also provisional, due to the misgivings about the free variable. Of course, since VP[:V[AUX]] records the trace of AUX, the variable which is abstracted can be established uniquely. (47) ||C'[\:V[AUX]]|| - ||C|| @ (Xv:[AUX].|[VP[:V[AUX]|O

Applying the lexical rule to hat produces XXJC (or I, for identity). Since bekanntermafien is a dummy filling the topic position, the resulting SF is (48). The fact that the subject ||er|| is not in the scope of/ should not lead to the conclusion that it is out of scope of a possible tense operator, this will be clear when discussing alternatives to rule (46). (48) 5efcj«ntemiflj8e«(I(Xv.|er)|Xw.v(|pP[DAT]||Xu.||DP[ACC]||(Xx.SHOWxuw))))

Reducing (48) via ^.-conversion yields (49) (when / is X-converted, its argument is of type o). (49) bekanntermafien (||er||Xw.|pP[DAT]||Xu.|pP[ACC]|(Xx.SHOWxuw))

The prediction is that the scope relations in (43) are unique, and it is borne out under standard intonation.

3.2 Changed scope: topicalization and scrambling German allows to topicalize one maximal14 constituent, i.e. it allows, e.g. an argument DP (or a non-finite VP), to be the sister of C (i.e. in the C-specifier position, cf. (36) below). In the first case exemplified by (36) and repeated below, scope ambiguity must be expected according to the assumptions of Section 1 about the role of DP traces of movement Indeed, this scope ambiguity is claimed to be present between the two complements of the verb zeigen if the 342 Topicalizarion, Scrambling, and Argument Scope in German topicalized DP is in the accusative, but not if it is in the dative (50), or if the subject in the nominative has been moved, as in (51). The effect is claimed to be observed under the VERUM-focus on hat.

(36) CP

DP Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 I fast VP Gemalde c/v

hat DP VP I er VP [: V FIN]

DP VP

mindestens einem [:DP] V[\FIN] Besucher I gezeigt

(5O) CP

DP I mindestens VP einem HAT Besucher

DP VP

VP [:V,FIN] er

[:DF» DAT] VP

DP V[\RNJ I gezeigt fast jedes Gemalde Anatoli Strigin 343 (SO

mindestens ein Besucher Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021

ihm

fast jedes Gemalde

There are three subtasks to be carried out to explain this. First we need an interpretation of the trace of the topicalized DP; evidently, it must be related to the basic scope hypothesis. Second, the problem is to explain the wide scope of the topicalized DP in (36), and the absence of the wide scope reading for the topicalized DP in (50) and (51), and the third problem is to explain the narrow scope reading of the topicalized DP in (36). I will start with (36) by making the simplest assumptions, and modify them if the need arises.

The role of traces A DP trace will be rendered by a free variable of the (SF) type 1. It constitutes, then, a legitimate argument of the predicate, and can be X-converted into the position of the first argument, i.e. we have w.i, and applying the predicate we get Xyz.(SHOWwyz). The Assign operation (type coercion) will be applied once, taking care of the DP[DAT] and the trace of [AUX] and DP[EXT] will be processed as before. On reaching the C node, a rule interpreting the elimination of the silent information could be postulated which simply abstracts the new individual variable. The result will be the expression below. ||fast jedes Gemaelde|| @ Xw.(|er|| Xz.(||mindestens einem Besucher|| @ Xy.SHOWwyz)) 344 Topicalization, Scrambling, and Argument Scope in German

The typing and the indexing could ensure that the abstraction picks up the correct variable. Then we would have a case of a simple syntactically bounded functional composition. Its introduction takes care of the wide scope of the topicalized DP and of its trace. Yet this solution does not explain the narrow scope of the topicalized DP (i.e. no scope ambiguity is predicted), and it creates a problem with the limits of extended scope compared with the movement

range, since topicalization is unbounded in the dialects where extraction out of Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 finite clauses is allowed but scope assignment is more local, at least for arguments. This problem is illustrated by (52).

(52) fastjedes Gemalde, sagte Hans (zu)jedem Mitarbeiter, hatte er mindestens einem Besucher gezeigt almost every picture told Hans every colleague had he at-least one visitor shown

The scope offast jedes Gemaelde is here narrower than that ofjedem Mitarbeiter, which would contradict the prediction of the treatment which simply intro- duces ^-abstraction at the sister node of the topicalized constituent. This problem was noticed by Frey, who suggested that the scope of the topicalized constituent in German is always limited roughly to the domain in which all the 0-roles assigned by its predicate are realized. Realizing a ©-role makes use of syntactic information. In particular, if a predicate has an external argument, then its 0-role is realized under the EXT assignment. According to Frey, this makes CP the scope domain of topicalized arguments of such a predicate. If a predicate does not have an external argument, the domain of scope is merely VPfMAXIMAL], since all its 0-roles are realized there. Let us turn to the problem of ambiguity first. Let us pose the question about the role of the connection between a displaced DP and its trace in the framework which postulates traces. We have seen its one side: triggering functional composition. I would like to suggest here that scope ambiguity is an ambiguity of interpretation of this connection. The second side of the interpretation is that it indicates the original position of the displaced DP under the basic configuration of 0-role assignment. This suggestion is a kind of recoverability constraint. So I assume (53).

(53) Changing basic scope configuration is only possible if it is recoverable

This requirement is related to the projection principle of Chomsky (1981). Thus, basic lexical information is preserved. And if this information is preserved, it can be used, too. This possibility creates argument scope ambiguity. To reflect the two interpretations of the connection I will use a simple device of SF type variable to type the trace (the variable by which the trace is translated, Anatoli Strigin 345 to be more precise). The Greek letter in the rule interpreting traces is a type variable. To specify the type value of the DP type-variable T means to determine the relative scope of the argument which is the antecedent of the trace. The value of x will be either the type of |DP||, i.e. ((1, o), o) or the type 1, which is the type of the verb arguments.

(54)|[:DP,]|-xi:T Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 If the abstraction of this variable is performed now, there are two possibilities of assigning a type to the abstracted variable. If the type is 1, the topicalized DP has its wide scope: if the type is ((1, o), o), the DP is X-converted into its basic scope position, obtaining its original scope. Hence, the problem of argument scope ambiguity can be solved. But how should the SF of the node dominating such a variable be computed in this case? One solution is to treat type variables simply as abbreviations for 'either the one, or the other possibility', to choose one of these possibilities each time the SF is computed, and stick to it during the computation. Again, there is the situation where a free variable is a part of an SF expression translating a constituent, as it was with the [AUX] trace in Section 3. This view of type variables does not reflect the fact that, if a constituent contains a variable, then the interpretation of the constituent functionally depends on the interpretation of this variable. If this fact is to be a guiding principle, then the dependence must be locally expressible. Merely rendering the trace as a variable is not sufficient in itself. So I propose an extended solution: the variable rendering the trace must be abstracted at the first node dominating it. If this solution is adopted, the 'abbreviation' view of the type variables is slightly inadequate. The problem is that the order of ^-conversions is not fixed. Hence, if type 1 is chosen for the trace variable, instantiating x at once would yield on one conversion order (55) as the interpretation of the first node

(55) (i) Xv:[ACC].(v (Xx: [ACC] Xy:[DAT] Xz: [EXT].SHOWxyz)) (ii) Xv: [ACC] Xy: [DAT] Xz: [EXT] .SHOWvyz eliminating the information about the trace! Eliminating semantic information about the trace at this point is undesirable, since so far there is only syntactic evidence about it then; hence, the syntactic type with the missing constituent does not correspond to the unique semantic type any longer. Moreover, note that since there is no syntactic type match with the next highest DP, Assign cannot be invoked and we must resort to functional composition if the tree is not to remain uninterpreted, deviating from the general view of how semantics is tied to syntax, since introducing functional composition at this point allows for any complement order whatsoever. If the semantic type variable is taken at face value, however, the situation is different. First, we get a very similar 346 Topicalization, Scrambling, and Argument Scope in German

expression (s6)(i), but it behaves differently since it cannot be reduced. Second, we can treat the designated variable now as if it were a DP, hence make the syntactic types but not the semantic types match, so that Assign can apply two times, yielding (s6)(ii).

(56) (i) X.v:.v @ (hi:[ACC] \y: [DAT] Xz: [EXT].(SHOWxyz)) (ii) XV:(T, [ACC]> Xy:[DAT] Xz:[EXT].(v @ (Xx: [ACC].(SHOWxyz))) Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021

It is as yet impossible properly to assign the dative 0-role because the abstracted ambiguous variable is in the way. This is also a case for functional composition. But it is governed by the information contained in the ambiguity of SF typing: there must be an antecedent to the ambiguously typed variable. These considerations motivate the next two rules. The first one, (57), shows how the SFM of a trace [:DP] is combined with the SFM of a V-projection. It is the variable x^ (with k for some case) which is the translation of the trace which is a variable on which to be abstracted. It will turn out to be quite useful, that this rule operates on VPs irrespective of where they occur, since the entire VP can be in a displaced position. This rule is ^-abstraction by which the trace is locally bound formally. I emphasize that the difference between just leaving a variable in the position of the trace and abstracting it is the same as everywhere else where X-operator is used to bind a variable instead of leaving it free.

(57) ||VP[:DPK]|| - Xx^T.tDPjII @ ||V'||)

The second rule, (58), applies functional composition to two arguments if the index of the x-typed abstracted variable is k, and the DP has some other index in the configuration given by [viijupryi DPj V'[:DPk]]. The rule form of (58) shows the X-prefix of the VP constituent exported out of the functional sign ||.. .|| for the sake of illustrativeness. (58) IVfDPJI - Xk^TpPJ 0 K @ (X£|V[-DPJD)

By virtue of these two rules a VP with a DP gap is always an ambiguously typed i function, e.g. Xxn^xt @ (Xz.||V[:DPk]())). Note that the relative hierarchy of the DP and the x variable is not changed by this rule. The essential ingredient of this rule is again simple functional composition XPQXx:t.Q((P)x), with the requirement that the type expression of the first argument of P be a variable. This is a bit of polymorphism, but not spectacular. However, this local encoding of functional dependence conflicts with the global approach to interpreting topicalization suggested at the beginning of this section, i.e. that the trace variable be abstracted over at C. The simplest solution possible is to abandon the global proposal. There is actually no problem then, hence no specific solution, because the moment a finite verb |CJ is X-converted Anatoli Strigin 347 into its original position by rule (47), the abstracted ambiguously typed trace variable is available. The calculation of the SF of (36) yields (58') which reduces to (59) or to (60) resolving the scope ambiguity.

(58') ||fj_Gemaelde||bc:.||er||Xz:< 1 ,EXT>.||m_e_Besucher||Xy:< 1 ,DAT).x @

(focSHOWxyz) Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 (59) ||fj_Gemaelde|lXx:.||er)|Xz:.||m_e_Besucher)|Xy:. (SHOWxyz) (60) ||er||Xz:< 1 ,EXT).|m_e_Besucher||ty:< 1 ,DAT).||fj_Gemaelde||(Xx< 1ACC). SHOWxyz) Thus we have arrived at a satisfactory treatment of simple cases of topicalization. Moreover, there is automatically a treatment of cases of scrambling in (61) and (62). Assuming that scrambling implies that the external argument is set off by some means, it is the highest argument in the c-command hierarchy, and whenever another DP is placed higher than the external argument, this DP has a trace somewhere below the external argument. In other words, if the DP in the nominative is not the highest DP in the c-command hierarchy, the sentence exhibits scope ambiguity.

(61) erj HAT tj mindestens ein Gemdlde/ fast jedem Besucher t{ gezeigt he-nom has at-least one picture-dec (to) almost every viskot-dat shown (62) den meisterij HAT fast jedes Gemaldej mindestens ein Kenner t(tj gezeigt (to) the most-dat has almost every picture-acc at-least one expert-Horn shown

The predictions are that (61) and (62) are ambiguous, under the VERUM-focus. In (61) it is the accusative DP which has been scrambled over (i.e. has been placed higher than) the dative. In (61) the accusative DP has been scrambled over the nominative, and the dative DP has been topicalized. This is a case which theoretically should allow a six-way scope ambiguity. There is one more application of the theory, as it stands now, relating to another possibility of topicalization in German when a VP is topicalized. The theory has a number of things to say about such more complex cases of VP topicalization, e.g. (63) and (38), repeated here 348 Topicalization, Scrambling, and Argument Scope in German

(63) CP

HAT VP DP V[\FIN] I Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 fast jedes DP VP Gemalde gezeigt er VP [:V,FIN]

DP [:VP, \FIN]

mindestens einem Besucher

(38)

DP VP I mindestens VP einem Besucher [:DP /] V [\FIN] [:VP k] [:V, FIN] fast jedes Gemalde gezeigt

4 VP-TOPICALIZATION

4.1 Some basic elements of the treatment ofVP topicalization Using the rules for VP we obtain the representation (64) for the topicalized VP in (63). (64) X.yz.||fast jedes Gemaelde|(Xx.(SHOWxyz)) Anatoli Strigin 349

It has to be combined with C. As yet we have no rules interpreting C projections, except (47), where it is assumed that ||C|| is just equal to the |V|| of V it dominates, and the variable of the appropriate type in VP is abstracted. But there is still the question of how the topicalized VP should be related to the rest of the sentence. Clearly there must be a variable abstracted at C in the long run. One difficult point here is how the semantic type of the VP, which can vary,

is related to the type of the variable interpreting its trace, and to the type of the Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 variable abstracted at C. There are three possible answers to this. First, it is possible to ignore the semantic types altogether and to proceed on the basis of syntactic types only. Second, we can use another semantic type variable and fix its value only after the type of the antecedent is computed, i.e. determine the type of the abstraction and the trace dynamically, but since there is no type conflict like in the case of DP arguments, there will be no type ambiguity either, hence there will be no scope ambiguity due to the displaced VP. And third, we could also try to determine the correct types statically at C since it seems that the silent syntactic information about the displaced VP determines its semantic type completely. All three ways seem to work, so there is actually no problem as to how to determine the type of the abstracted variable, but we should consider the problem of where the abstraction should be done in the light of these possibilities. Another difficult point is whether to try to maintain the uniformity of the treatment of all topicalizations. This implies treating VP similarly to DP by assuming that VP projection is functionally dependent on the trace of the topicalized VP, too. Then C is made functionally dependent only indirectly, after the finite auxiliary has been X-converted into its original position. An alternative is to argue that the functional dependency is established not locally at VP, but at C, and I will discuss this possibility in Section 4.2. For the moment the rules for the C projections are simply application in (65) and (66).

(65)||CP||-||DP||@||C'[:DP]|| (66) |CP|| - ||VPj| @ |C'[:VP]||

We could perhaps allow for another type variable and at least postulate a rule propagating functional VP-dependence as in the case of DPs. But instead of formulating this variant in detail, I would rather have a look at what it buys us first Example (63) is unambiguous, its SF structure shown in (67) by associating computation steps with nodes via numbers. Again, @ has been left out to save space. 350 Topicalizarion, Scrambling, and Argument Scope in German

(67) 13)CP

3)VP

1 10)VP 1)0P ajW '™ Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 fast jedes 9)DP 8)VP Gemalde gezeigt I er 6)VP 7)[:V,RN]

4)DP 5)[:VR \FIN]

mindestens einem Besucher

1) ||fast jedes Gema lde|| 2) Xxyz.SHOWxyz 3) Assign (||fj_Gema' lde||, (Xxyz.SHOWxyz)) - tyz.||fj_q|(Xx.(SHOWxyz)) 4) ||m_e_B|| 5) xv, which will become (VP, (1, 1,0)) later 6) Xx:i/.(|m_e_B||x) 7) w:(o,o) 8) Xx.((||m_e_B|W(w)) 9) IN 10) Xx.||er||((||m_e_B||x)w) 11) I 12) I(Xwx.||erf((||m_e_B||x)w)) = bc.||erj|(||m_e_B|(x) 13) Xyz.||fj_q|(Xx.(SHOWxyz))(Xx.||eii|(||m_e_B|lx)) here, the right abstraction is the functor

H)||ei||(G|m_e_B||)XxZ.||fJ_q|(Xx.(SHOWxyz))) 15) ||er||Assign((||m_e_BD, Xyz.(||fj_q|(Xx.(SHOWxyz))))

16) ||er||XZ.((||m_e_B|^y.0|fJ_q|(Xx.(SHOWxyz)))) Here I introduced another type variable v to compute dynamically the correct type of x, and decided to propagate the functional dependence on |[VP|| via composition which may be syntactically governed. But topicalizing VP with the DP in (38) is claimed to show scope ambiguity for the verb zeigen. The reason is that die assumed structure of VP contains the Anatoli Strigin 351

trace of the accusative DP which has been scrambled out of it. The SF of (38) is (68)

(38) Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021

[:DP /] V [\FIN] [:VP k] [:V, FIN] fast jedes Gemalde

gezeigt (68) 1) ||m_e_B| 2) w:x 3) Xxyz.SHOWxyz 4) Xw.Assign(w,(Xxyz.SHOWxyz)) - Xw.(Xyz.w(Xx.(SHOWxyz))) 5) Xw.Assign(||m_e_B||,(>iyz.(w(Xx.SHOWxyz)))) = Xwz.(||m_eJB||(ty.(w(Xx.SHOWxyz)))) 6) v:(o,o> 7) x:g 8) Xx.xv 9)

11) I(Xvx.||er||O|fJ_q|(xv))) 12) (\wz.(||m_e_B||(^y.(w(Xx.SHOWxyz)))))(Xx.||er||(||fj_q|(Ix))) here, the right abstraction is the functor, so

13) ||eiflO|fj_q|(I(Xwz.(|m_e_B||(Xy.(w(^SHOWxy2))))))) H)||er||(||fj_q|(Xwz.(lm_e_B||(Xy.(w(Xx.SHOWxyz)))))) and we now have to choose the value of x, obtaining either (15) or (16) 15) ||er||Xz.(||m_e_B|Piy.0|fj_q|(Xx.(SHOWxyz)))) i.e. x — ((1, o), o), the functor is on the right 3 52 Topicalization, Scrambling, and Argument Scope in German

with T — i, and it transpires now, that the decision to interpret traces as inducing functional dependence by abstracting the trace variables at the node immediately dominating them spares us quite a problem noted by Engdahl (1983). Consider what the situation would have been were we simply to abstract at the node which is the sister of the scrambled constituent. Consider (38) again.

Suppose the abstraction of a variable x:x were done at node 8). Since the Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 variable itself is missing in the domain of abstraction at 8) VP, for it is at 2), the abstraction would be vacuous, giving wrong predictions if T is specified as ((1, o), o) and X.-conversion at node 8) were effected before the topicalized ||VP|| was converted into its original position. Not only that, the topicalized ||VP|| could not be converted into its position at all, since it had a free variable x:x which would have become bound by Xx:t at 8) after the conversion of ||VP|. This transition in the status of a variable is prohibited by the rules of X- calculus. Though the objection was raised by Engdahl against the treatment of pronouns in this way, topicalizing VPs with traces raises it, too. The proposal here is not subject to this objection. Now it is time to return to the problem of the domain of abstraction. Leaving things as they are would imply that for sentences like (52) the ambiguously typed variable must be transported all the way up.

(52) fastjedes Gemalde, sagte Hans (zu)jedem Mitarbeiter, hatte er mindestens einem Besucher gezeigt

Moreover, precautions must be taken somehow in order not to allow X.- abstraction to be used at some point between the two topic positions.

4.2 Storing topicalization in [TOP] and the C-rules The first solution which seems to take care of the unwanted use of the ambiguously typed abstraction in wrong places consists in naming exactly one of the features which contain silent information TOP(ic), and requiring that this feature be eliminated at the node which dominates the topicalized constituent, and only there, and moreover requiring that the highest node containing it is the place for ^.-abstraction. The method requires the rules in (69), the indices being any relevant syntactic information, and rule (iv) being just a plausibility.

(69) (i) [CP, \TOP]:- DP; C'[TOP:[:DPi]] (ii) [CP, YTOP]:- VP;[\EXT] C'[TOP:[:VPi]] (iii) C'tpCPj, [W[FIN]] := C[:V[FIN]] VP[[-XPJ, [:X[FIN]], EXT] (iv) C[:V[FIN]j := V[FIN] Anatoli Strigin 353

If there is now a topic extraction from the embedded clause, it leaves an ambiguously typed variable here. We may let the syntactic combination of C and the TOP feature license the choice of the type value, and only this combination. It is then rigidly ((1, o), o) outside the clause, and still can vary inside. From then the, by now, conventional machinery could take over, abstracting at CP and propagating this abstraction to the next highest topic position. The rigid typing outside the origin clause provides then only the Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 reconstruction option, limiting the scope of the extracted constituent to the origin clause. However, this solution does not seem to be really well motivated. Moreover, it is cumbersome, since the ^.-abstraction has to be transported all the way up in the embedding sentence, and even higher, depending on the depth of embedding. It would be much easier if this X-abstraction were licensed at the C node, and only there. But this contradicts the assumptions about displaying functional dependence immediately at the first relevant node. Abandoning this assumption would at once beg Engdahl's objection. There is a compromise, though. The topicalized VPs prompt the direction in which the solution might be sought. Clearly, Engdahl's problem does not arise as long as topicalized constituents have no free variables. Since German allows exactly one [MAXIMAL] constituent to be topicalized, this state of things obtains whenever the relevant projection, i.e. the one which contributes the [TOP] information, has its variables bound. Hence, the combination [TOP, MAXIMAL] must enforce the abstraction of the ambiguously typed variable. The remaining problem would be the fact that there will be two abstractions: the one at the MAXIMAL constituent which contains the trace of the topicalized constituent, and the other at C which is then vacuous. It is here that a compromise is possible. The compromise consists then in using intermediate traces, allowed by (33)(iii). This rule must be modified to allow for an exceptional use of the feature [MAXIMAL] in this context, i.e. as in (33 ')(iii):

(33') (iii) VP[MAXIMAL, TOP: [:DPJ] := [:TOP[:DPk,]] VP[:DPk, \TOP] It remains for the trace marked [:TOP] to be translated exclusively with the SF type of the topicalized constituent, and not with the type required by the lexical sister of its foot (although a type variable can be used if the typing is dynamic, but it will be treated differently from the ambiguously typed variable since there is no type conflict at this position, as in the case of the foot of DP arguments). Then it is possible to use only syntactic TOP feature to abstract the variable at the complement of the C node of any clause, and the topicalized constituent will always be converted to the [:TOP] trace position. I think the treatment is feasible, but since topicalization out of finite subordinate clauses in German is not always acceptable, I will leave it at that, without trying to speculate on the structure of C-projection in the subordinate clause. 354 Topicalizarion, Scrambling, and Argument Scope in German

The free [AUX] variable Let us return to the problem, or perhaps drawback of the treatment noted after (46), where it was stated that the free variable introduced by the [AUX] trace is disconcerting. It stands apart from the general principle of showing functional dependencies immediately at the mother node. This principle does not raise the

issue of giving an interpretation to free variables, so it seems worthwhile trying Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 to extend it to cover the case of [AUX], too. There are two subcases, as shown in (70), with a phonologically realized VP complement in (i), and with the VP trace in (ii). (70) (i) VP [:AUX] (ii) [:VP] [:AUX] The abstraction at the mother node should be combined with composition, however, because of the type mismatch at this node, cf. (71). (71) ||VP[\FIN,\EXT]||:, o> te:(i, [EXT]) Xv:«o, o>, [AUX]>.fl[:V°, AUX]||(Pz)) In this rule the correctness of the abstraction is ensured by the feature types of v, and composition is superimposed on the abstraction. Note that the expression in (72) has the variable v already abstracted, and must be applied to VP[EXT]. If the VP[\FIN, \EXT] complement is non-empty, we have (73) at the next step of the construction. (73) |pP|| @ ^[EXT^vjV0, AUX].vQ|VP[\FIN]||x) Where |DP|| is of type ([EXT], ((1, o), o). At this point there is a type mismatch again, but this time because the type of the expression translating the subject- sister VP here is (1, «o, o), o), and the type of the DP[EXT] is «i, o), o). Now the fact that the syntactic type of the variable v is [:V°] implies that there must be an antecedent, hence the use of type coercion is licensed. The Assign operation can be used. If the complement VP is a trace, the type of the P -variable in (72) enforces some more type coercions by composition, but requires no changes of principle. This treatment of the [AUX]-trace has two positive traits: it is uniform, and it takes the subject into the scope of the [AUX] abstraction. Anatoli Strigin 355

5 RELATING SF TO DISCOURSE REPRESENTATIONS

To complete the account of some properties of argument scope in German, there is a residue which needs to be taken care of. As indicated at the beginning, scope is a relation defined on discourse representation structures, which implies

that there must be an algorithm translating SF into discourse representations. Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 Updating the discourse context by a DR of a sentence can be done after van der Sandt (1992). But since I am not interested in pronouns here, discourse structures are kept simple, suppressing the anaphoric part. I will confine myself to a simple illustration, since constructing such an algorithm for the fragment described in this paper does not seem to be difficult, and in any case the use of structures like those of Asher (1993) seems to be possible. The output data of the preceding considerations are a binary SF structure of the form (A @ B) which is properly typed if the T-type ambiguities are resolved. Until now no assumptions about the SFM of DPs have been made, except for dieir type. Assume now that a DP like mindestens ein Besucher has the structure (73')- (73') [DP[D mindestens ein]^ Besucher]] Moreover, let VISITOR(x) be the SF of the noun Besucher, and Xx.VISITOR(x): (1,0) its complete lexical entry. There is no difference between the SFM of the NP Besucher and its lexical SFM. The SFM can be viewed as an abbreviation of DRs of a specific kind. Discourse structures are feature structures with two features U and Cond whose values are sets. Now treat VISITOR(x) as an abbreviation for the following feature structure (74).

(74)

Here, U is the set of discourse referent parameters (a unit set actually), and Cond the set of conditions on these parameters (also a unit set here), which is just a schema for discourse representation structures of the kind used in DRT. Analogously for Gemalde. Then the parameter is abstracted over. The abstraction produces the structures in (75) as the complete lexical entry. (75) Xx.(U:{x), Cond: {picture '(x)}> A word of caution is appropriate here. The abstraction is carried out over a variable, and not over a discourse referent This fact could be a source of mis- understanding. Another implementation of this idea is the lambda-list feature of lambda-DR in Bos etal. (1994). Discourse referents proper are introduced by determiners. Let the SF of determiners translate as a two-place function 356 Topicalization, Scrambling, and Argument Scope in German providing one and the same discourse referent for its two arguments, e.g. (76)(i) for atjeastone, and (ii) for almostevery

(76) (i) AL (dr) (ii) AE(dv)

Both functions are relativized to the discourse referent dr. The dr-part of the function will be instantiated anew at every occurrence in the SF structure, e.g. Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 by discourse referents ui, U2, etc. These stipulations define, for instance, the structure in (77), which is an execution of the SF structure (60).

(77)

J: 0,Con{SHOWxyz}>

Now the application nodes with determiners in (77) are interpreted by (78), which is just the instruction for how to compute the function associated with determiner Det. In the present case the instances o(Det are AL and AE.

(78) Det(dr){kx.(DRi(x)))(kx.(DR2(x)))- {Det{dr),({hc.(DRi(x)))dr,(hc.(DR2(x)))dr»

Here DRi and DR2 are lambda-abstracted DRs for NP. The right side of the equality in (78) is a so-called complex condition, where Det is the label introduced by the determiner. This label distinguishes discourse representations of different quantifiers. The pronoun er is not translated yet, as it is waiting for the Update operation to find its antecedent outside the sentence. A tripartite DR structure of van der Sandt (1992) is needed to take care of that, but is of no avail in this small illustration. Proper names can be treated as having type 1. They can be directly converted at SF and do not participate in scope ambiguities. They will be substituted for by discourse referents which are situated in the main universe of discourse during the update, as usual. So, for example, if instead of er we had Toby, the final result before updating would be (79). Anatoli Strigin 357

(79)

(80) u3 Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 u3 = Toby I AE(u1) I

u1 u2 visitor (u1) picture (u2) SHOW (u1, u2, u3)

This example provides, I hope, an illustration of how a translation of SF into discourse representations can be carried out.

6 SUMMARY

Here is a summary of the main points of the paper. I assumed, like a number of people, that the semantic structure of the verbal lexical entries defines a hierarchy of arguments. Moreover, it seems that this hierarchy defines a configuration of argument scope in German which does not allow scope ambiguities, provided such scope-influencing devices such as focusing are neutralized. It is thus in a sense a basic scope configuration. I proposed a Lexical Scope Hypo- thesis to account for this. Its major theses are: there is a mapping from the argument hierarchy to the hierarchy of grammatical relations, which I called Argument Structure; due to some properties of German (the most important one being the fact that quite a lot of intricate German data can be explained with very simple assumptions), Argument Structure is basically a monotone mapping from the lexical semantic hierarchy to the minimal c-command hierarchy of S-Structure (or some similar syntactic representation structure). Evidently, then, displacing constituents could be expected to lead to scope ambiguities, and I suggested an explanation of why this expectation is confirmed for German. If some information preserving principle like recover- abiliry of deletion or projection principle is assumed, traces of moved constituents should remember their semantic characteristics, e.g. their semantic types, like <(i, o), o) for DPs. This is a strong version of preservation, but it seems to be necessary in any kind of 'reconstruction' accounts of movement 358 Topicalization, Scrambling, and Argument Scope in German effects. Simultaneously, there is a strong influence of the verbal semantic form on the trace which requires it to have the type i of individuals. The tension between the two typing requirements on the trace is taken to lead to the two scopes of a quantified argument DP, the narrow one when typing the trace ((i, o), o), and the broad one when typing it i. The restriction to quantified argument DPs reflects the general philosophy of the author who

is sympathetic with the DR account of definites, indefinites, etc. Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 To substantiate the above picture the paper presents a small fragment of German which uses feature structures and ^.-calculus. The feature structures of Cardelli & Mitchell (1990) were preferred to those of Pollard & Sag (1987) for the following reason: the moment feature structures with unification are made to simulate ^.-abstraction, it is simple to use the latter, and this is possible in Cardelli & Mitchell (1990) version of feature structures which in general fit better the notions of object oriented paradigm in allowing methods (e.g. X- expressions) to be values of features. It is exactly this view of the semantic form of linguistic representations which has been adopted here: they are computing agents. On the other hand, I am quite sympathetic with the integrative point of view on different kinds of information on which HPSG of Pollard & Sag (1987) is based. It seems quite reasonable that, for example, phonological information can be made available to control computations at the level of semantic form, so that, in principle, integrating the treatment of focus effects in Krifka (1992) into the framework of the paper is possible. A side-effect of using ^.-calculus is that the assumptions about the nature of semantic operations can be made explicit. The paper uses application and two forms of functional composition. One form is used, for example, in the basic operation of Argument Structure, Assign. It is a polymorphic composition characterized by the typing rule (Ti), with vector arrows abbreviating sequences of types.

This operation is triggered by the semantic type mismatch, and controlled by syntactic information. The requirement is that the case types of both the first verb argument and the DP be the same. The other form of polymorphic composition is triggered by a syntactic type mismatch, whereas the semantic type is kept ambiguous, e.g. (T2).

(T2) «T, (O, O>», «I, O>, O> => (X, «O, O>, «I, O>, O>» The requirement here is that the case types oft and the DP should be different. This machinery covers three widespread constructions of German: DP topicalization and scrambling, and VP topicalization with or without a DP scrambled out of the topicalized VP. None of the theories discussed in the Anatoli Strigin 3 59

Introduction treats the latter case, as far as I know, except Frey (1993), which is a syntactic generalization without underlying semantic explanation. Most of the theories reviewed here there are too permissive in allowing scope ambiguities where they are not observed. This objection does not apply to the present proposal. But this proposal has some drawbacks, too. In particular, it suggests

indirectly that there could be many possible factors which influence argument Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 scope—which I think is a correct suggestion—but it leaves unaccounted for preferences in the availability of different scope relations which presumably arise due to the interaction of different factors, as discussed in Pafel (1991). Accounting for these preferences might require complicating the overall picture.

Acknowledgements I am grateful to Manfred Bierwisch, Reinhard Blutner, Hans Kamp, Manfred Krifka, Antje Rofideutscher, and Use Zimmermann for critical discussion and their willingness to help. I am also indebted to the two anonymous reviewers, whose suggestions considerably improved the paper.

ANATOLI STRIGIN Received: 00.00.00 Max-Planck Research Group Revised version received: 00.00.00 'Structural Grammar' Jaegerstrasse 1 oh 1 10117 Berlin Germany

APPENDIX

The rules are listed here in the order of their appearance in the text under the corresponding numbers. The short comments provide simple characterizations. (26) [Assign) \f:«i,o),o)Xg:[:DPk] 360 Topicalization, Scrambling, and Argument Scope in German

General conventions on silent information. (40) |C| - |Afl @ |B| (41) pC| - X.F3(LE).F4(LE) where X dominates LE Two basic assumptions about the interpretation of syntactic structures in constructing SF.

The scheme for type coercion using (26). (45') |[:+V. -N, AUX]| - x:«o, o), [AUX]>

(46) |VP[:AUX; FIN]1 - (\P:[\FIN]Q:[FIN]Xz:[EXT].Q(P(z)))|VP|| ||[:V, AUX]| Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 (47) |C'[\:V[AUX]]I - ||CJ @ (Xv: [AUX].|VP[:V[AUX]D

(58) [V[:DPk]|| - te^ipPJ @ (xk @ (*zJV[:DPk]D) Rules of SF construction. (69) (i) [CP, \TOP]:- DP, C'[TOP:[:DP,]] (ii) [CP.VTOP]:- VP,[\EXT] C'[TOP:[:VP,]] (iii) C'[[:XPi], [\:V[FIN]] :- C[:V[FIN]] VP[[:XPi], [:V[FIN]], EXT] (iv) C[:V[FIN]j:- V[FIN]

(33') (iii) VP[MAXIMAL, TOP: [:DPJ]:- [:TOP[:DPk,]] VP[:DPk, \TOP] Sentence-structure in German. (72) A.P:«i,[EXT]>, o> te

NOTES

1 This can be defined semantically, e.g. it can now be ordered according to their can be the smallest constituent of type t. depth of embedding with the help of the 2 A native speaker's judgement seems to be following convention: a variable v which that the sentences are acceptable only is the argument of an operator Op is more with a special kind of intonation pattern prominent than a variable v' embedded called hat pattern, a rise accompanied by a either in Op or in the argument to which fall (cf. Fery 1992, Cohen & Hart 1967), the result of the application Op(v) is e-g-(i): applied. This convention gives the following prominence hierarchy (ii), with (i) fast jedem Besucher gezeigt HAT z being the most prominent variable. Hans mindestens ein Gemalde (ii) z < e' < y < x 3 See the paper by Klein & Sag (1985). 4 Bierwisch has also interesting things to 5 I will discuss feature structures used in say on the origin of the hierarchy. this paper in detail in the section on Bierwisch (1989b) gives the following syntax. There were two reasons for decomposition of SHOW. splitting lambda-expressions in the lexical entries into the lambda-prefix, and the (i) DO z (Cause e' ((SEE x)y)) expression without ic to simplify the The formula intends to convey that z acts transition to Discourse Representation somehow, and in so acting calls some Structures at the end of the paper, and to event e' into existence which is the cause keep to the idea of feature structure. of y seeing x. The variables of the formula Starting with Section 3, I will use the Anatoli Strigin 361

lambda calculus format, which is more 10 It is difficult to keep up with the current appropriate in this paper, by allowing principles-and-parameters theories' ter- feature structures to contain functions as minology, let alone to assess the relevance feature values (similar to objects in of feature labels. And fully lexicalist posi- object-oriented programming languages tions are not very much in vogue at pre- or functional programming). Bos et al. sent, or so it seems, so I do not see any (1994) contains an implementation of harm in ignoring these more or less DRT which uses feature structures morphologically motivated projections. Downloaded from https://academic.oup.com/jos/article/11/4/311/1640111 by guest on 01 October 2021 throughout to stimulate lambda 11 Perhaps this EXT feature can be realized abstraction. as ACC or DAT in sentences like mich 6 Conjoinable types of Partee & Rooth frierl, but I will not treat them here. (1983)- 12 It is possible to define the ©-operation in 7 Node A minimally c-commands node B terms of composition, the way Krifka iff A c-commands B (i.e. the first branch- (1992) does it. I am more concerned with ing node dominating A also dominates B), finding simple components. and there is no other node C c-com- 13 Another possibility is to equip every manding B and c-commanded by A. feature structure with the feature con- 8 Klein & Sag (1985) have already used the taining its X-prefix, the way it is done in standard translation of a syntactic node by Bos etal. (1994). an application node, and type coercion, 14 As already mentioned, opinions differ as but the latter only in the lexicon. to whether it should be a maximal con- 9 The structures used here are records of Cradelli & Mitchell (1990).

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