Explaining Crossover and Superiority As Left-To-Right Evaluation

EXPLAINING CROSSOVER AND SUPERIORITY AS LEFT-TO-RIGHT EVALUATION CHUNG-CHIEH SHAN AND CHRIS BARKER Abstract. We present a general theory of scope and binding in which both crossover and superiority violations are ruled out by one key assumption: that natural language expressions are uniformly evaluated (processed) from left to right. Our theory is an extension of Shan's (2002) account of multiple-wh questions, combining continuations (Barker 2002a) and dynamic type-shifting. Like other continuation-based analyses, but unlike most other treatments of crossover or superiority, our new analysis does not postulate a level of Logical Form or other representation distinct from surface syntax. One advantage of using continuations is that order-of-evaluation for programming languages is standardly modeled using continuations; that work provides us with a natural and independently-motivated character- ization of what it means to evaluate expressions from left to right. We give a combinatory categorial grammar that models the syntax and the semantics of quantifier scope and wh- question formation. It allows quantificational binding but not crossover, in-situ wh but not superiority violations. 1. Crossover as a Processing Constraint Typically, a quantifier must precede a pronoun in order to bind it. Thus (1a) can mean that each person loves their own mother, but (1b) cannot analogously mean that each person's mother loves them. (1) a. Everyonei loves hisi mother. b. *Hisi mother loves everyonei. At first glance, a processing explanation seems promising: if humans process sentences from left to right, then arriving at the ungrammatical crossover interpretation in (1b) would require postponing the interpretation of the pronoun until encountering the quantifier that binds it. In general, allowing for crossover interpretations would require the processing mechanism to postpone interpretation of pronouns indefinitely just in case a quantifier occurs later. Since doing so would place an extra load on memory, we expect the bound interpretation for (1b) to be at the very least dispreferred. One challenge for a processing approach is distinguishing the behavior of quantificational binding from quantifier scope. In at least some configurations, quantifier scope also seems to show a left-to-right processing bias: (2) a. A student called every professor. b. Every professor called a student. For instance, (2a) is more likely than (2b) to be interpreted to mean that the same student spoke with each professor. If quantifiers that are processed earlier take wider scope, then this preference is again expected. Date: May 25, 2003. Thanks to Daniel Buring,¨ Svetlana Godjevac, Chris Potts, and Stuart Shieber. The first author is supported by National Science Foundation Grant IRI-9712068. 1 2 CHUNG-CHIEH SHAN AND CHRIS BARKER The problem is that if quantifier scope preferences and crossover arise from the same mechanism, we would expect them to behave similarly. But the left-to-right pattern is at best a preference for quantifier scope, while it is a requirement (in most situations) for quantificational binding. In fact, it is possible for a quantifier to take scope over a pronoun that it cannot bind: (3) *A student of hisi colleague called every professori. The quantificational NP every professor can take scope over the subject, as long as the pronoun is taken to refer to some deictic individual (say, the Dean). So right-to-left scope, though awkward, is at least possible. But under most circumstances it is impossible to interpret the pronoun as bound by the quantifier, even when the quantifier takes scope over it.1 The puzzle for a processing story is that there is no obvious di®erence between quantificational binding and scope from a processing point of view: it seems as if any logic that makes a backwards binding relationship more di±cult presumably ought to make a backwards scope relationship di±cult too. The two theoretical questions, then, are: if quantifier scope and crossover are both connected to processing biases, why is the crossover constraint so much stronger? And: when a quantifier does take scope over a pronoun, what prevents the quantifier from binding the pronoun? 1.1. Solutions that depend on Quantifier Raising (QR). The traditional way out of this dilemma is to propose multiple stages for the derivation of a sentence, with binding and scoping taking place at di®erent stages. Reinhart's (1983) approach is an influential exam- ple, and Buring¨ (2001) provides a recent analysis that uses the same basic strategy. The idea is to postulate two distinct levels of representation: first a level of surface structure at which binding relationships are established by some syntactic relationship based on c- command, then a level of Logical Form at which quantifiers take their semantic scope. This way, even though a quantifier may raise at LF to take scope over a pronoun, it can still only bind the pronoun if it c-commands the pronoun from its surface position. The claim is that crossover is an essentially syntactic phenomenon: quantificational binding depends on syntactic relations at the surface. In contrast, quantifier scope depends on relations at the level of Logical Form. Analyses of this sort refer crucially to multiple levels of representation.2 Moreover, this standard treatment is framed in terms of hierarchical structure (c-command) rather than linear order.3 Since syntactic structure in English is predominantly right-branching, c- command mostly coincides with linear order, so that even on a c-command account, quantifiers will in e®ect only bind pronouns that follow them in surface structure. In this paper, we will suggest that linear order is the correct generalization after all, at least for English 1Postal (1993) (see also the discussion in Potts 2001) points out that crossover interpretations sometimes be- come better if own or only is added: ?A student of hisi own advisor contacted every professori. This amelioration e®ect is poorly understood, and we will not discuss it further here. 2Indeed, the very name `crossover' comes from Postal's (1971) proposal for a general constraint on movement, roughly: an NP may not move across a coindexed pronoun (p. 62). Even some accounts that attempt to state a crossover-like constraint in terms of single representation (e.g., Pesetsky's (1982) path containment condition for superiority) crucially depend on access to a post-QR structure, and therefore also rely on multiple levels of representation. 3Higginbotham (1980) is a notable exception: he relies both on quantifier raising and a re-indexing rule that is sensitive to linear order. Since our binding system does not use indices, we could not restate Higginbotham's re-indexing rule even if we wanted to; nevertheless, we a±rm his suggestion that linear order plays an irreducible role in determining quantificational binding relationships. EXPLAINING CROSSOVER AND SUPERIORITY AS LEFT-TO-RIGHT EVALUATION 3 and maybe also Japanese (Kuno and Kim 1994). We leave a discussion of languages in which c-command does not correlate strongly with linear order for another occasion.4 1.2. A new solution based on continuations. In contrast to QR-based accounts, we present in this paper a new account of quantifier scope and quantificational binding that does not postulate multiple stages of derivation or multiple levels of representation, and in fact does not even mention c-command. On our account, crossover is a consequence of the following stipulation: (4) Evaluate expressions from left to right. We formally characterize what it means to evaluate expressions from left to right, adopting a concept developed independently for describing the evaluation order of subexpressions in programming language semantics (see Section 7.2). As formally implemented below, (4) naturally follows from the commonplace assumption that people process (evaluate) expressions that they hear first before those they hear later. There is abundant evidence (e.g., Tanenhaus et al. 1990 and references there) that people begin to process language immediately, i.e., as soon as they hear the beginning of an utterance, and incrementally, building partial interpretations without waiting for the remainder of the utterance. Furthermore, incremental processing seems to integrate in- formation from all grammatical levels, including morphological, syntactic, semantic, and pragmatic. Of course, there are many ways that a grammatical framework could be consis- tent with incremental processing, but (4) embodies incrementalism in a natural and direct manner. But if people process utterances from left to right, how could the quantifier in, say, (2a) be evaluated last in the sentence yet take semantic scope over the subject? It seems paradoxical, yet this is exactly how our system works. 1.3. An informal sketch of the analysis of crossover. There are four main steps to un- derstanding our account of crossover. The first step presents our treatment of quantifier scope. Our system uses continuations (Barker 2001; 2002a; de Groote 2001) with an important innovation: Previous continuation-based accounts of quantification involve first- order continuations only and no dynamic type-shifting. In those analyses, scope ambiguity arises because expressions can be evaluated in a variety of orders—the earlier a quantifier gets evaluated, the wider its scope. In the present theory, which implements higher- order continuations (Danvy and Filinski 1990) using dynamic type-shifting, expressions are evaluated strictly left-to-right. Scope ambiguity

Load more