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Modelling Selectional Super-Flexibility⋆ Modelling Selectional Super-Flexibility? Kristina Liefke Department of Philosophy, Ruhr University Bochum, Germany [email protected] Abstract The selectional flexibility of some attitude verbs (e.g. know) between declarative and interrogative complements is a core topic in con- temporary formal semantics. Despite this focus, little attention has been paid to verbs (e.g. see, remember, observe) that embed an even wider vari- ety of complements (incl. subject-controlled gerundive clauses and con- crete object-denoting DPs). Since the familiar types of some of these com- plements resist an embedding in the type for questions [= sets of proposi- tions], these verbs challenge Theiler et al.'s (2018) uniform interpretation strategy for the complements of declarative/interrogative-neutral verbs. Our paper answers this challenge by interpreting the complements of selectionally super-flexible verbs like remember in a generalized type for questions, viz. as parametrized centered questions. The resulting seman- tics captures the intuitive entailment pattern of these verbs. Keywords: Responsive verbs · Experiential attitude verbs · Comple- mentation · Cross-categorial entailment · Inquisitive semantics. 1 Introduction Responsive verbs, i.e. verbs like know that are selectionally flexible between de- clarative (e.g. (1a)) and interrogative clauses (e.g. (1b); see [11, 17]), have been at the center of much recent work in formal semantics (see e.g. [8, 36, 37, 41, 42, 44]). (1) a. that Mary was wearing a crazy hat (declarative clause) John knows b. whether Mary was wearing a crazy hat (interrogative) Responsive verbs are particularly interesting since their flexibility cannot be attributed to an ambiguity between a declarative- and an interrogative-embedding use. Such attribution is excluded by the fact that declaratives can be coordinated with interrogatives in the complements of these verbs (see (2); ff. [12, p. 93]): (2) John knows [that Mary was wearing a crazy hat] and [whether she bought it at the party supply store] Interest in responsive verbs is further fuelled by the observation that their de- clarative and interrogative complements can stand in semantic inclusion relations (see (3) [for uni-directional inclusion] and (4) [for mutual inclusion]): ? I thank my anonymous reviewers for SALT 31 for valuable comments on the abstract of this paper. The paper has profited from discussions with Floris Roelofsen, Frank Sode, Markus Werning, and Ede Zimmermann. The research for this paper is suppor- ted by the German Research Foundation (via Ede Zimmermann's grant ZI 683/13-1). 2 K. Liefke (3) a. John knows [that Mary was wearing a crazy hat (when she arrived)] ) b. John knows [whether Mary was wearing a crazy hat :::] (4) a. #John knows [whether Mary was wearing a crazy hat] and [that she was wearing a rainbow squid hat] (redundant) ≡ b. John knows [that Mary was wearing a rainbow squid hat] The validity of entailments like (3) is typically ascribed to the observation that the information content of the interrogative clause in (3b) (i.e. `Mary was or was not wearing a crazy hat') is contained in the content of the declarative in (3a). The redundancy { and attendant markedness { of (4a) is due to the fact that the true answer to the question denoted by the first conjunct in the complement of (4a) (`Mary was wearing a crazy hat') is already informationally contained in the content of the second conjunct in (4a), where rainbow squid hats are crazy hats. The informational relations between embedded declaratives and interroga- tives pose an important empirical constraint on any adequate semantics for resp- onsive verbs. However, a suitable account of this constraint is challenged by the fact that declaratives and interrogatives are typically associated with objects of a different semantic type: while declaratives are commonly interpreted as proposi- tions (analyzed as [characteristic functions of] sets of possible worlds, type1 (s; t); see [16, 26]), interrogatives are interpreted as questions (analyzed as [characteris- tic functions of] sets of propositions, type ((s; t); t); see [7, 13, 16]). The different types of declaratives and interrogatives block an easy2 analysis of the relation be- tween the complements in (3a) and (3b) as set-theoretic inclusion and disable the familiar interpretation of natural language and in (2) and (4a) as set intersection. To answer the above challenge, Theiler et al. [36] propose that declaratives and interrogatives are uniformly interpreted in the type for questions, ((s; t); t). In this type, the common denotations of declaratives can be represented through the type-shifter λp(s;t)λq(s;t)(8ws)[q(w) ! p(w)] that sends sets of worlds p to their powersets P(p), i.e. to downward-closed sets of propositions (see [7, 8, 36]). The downward closure of these sets effects that, if these sets include p, they also include every informationally stronger proposition/set of worlds q, where q ⊂ p.3 The results of this type-shift meet the type-requirement (viz. type-identity) on entailment and coordination, and capture the intuitive relations between de- clarative and interrogative complements (see [8, 33]). Consequently, they readily account for the data in (3) and (4). My simplified account of this data (in (6), (7)) 1 To distinguish centered propositions from properties (see below), I here use multiary function types (see [30, 38]). The latter are types of the form (α1× :::×αn) ! αn+1 that are associated with functions from n-tuples of objects of the types α1, :::, αn to objects of type αn+1. Following Tich´y[38], I write (α1 × ::: × αn) ! αn+1 as (α1 : : : αn; αn+1) and identify the type (α) with α. 2 Arguably, one can enable this analysis by coding propositions as questions (see [40]). However, Theiler et al. argue (in [36, p. 413], [37]) that this move fails to explain the selectional restrictions on non-responsive verbs (e.g. the anti-rogativity of believe). 3 This differs from Alternative Semantics [13], Possibility Semantics [8], and Uegaki's [40] semantics, which identify questions with the maximal elements in these sets (cal- led alternatives). For reasons against this move, the reader is refereed to [7, 8, 33]. Modelling Selectional Super-Flexibility 3 uses the semantics for know in (5), where know := λT ((s;t);t): 9q 2 T [q(w)]: λws e 0 w 0 0 λz : 9p 2 T [p(w) ^ (8w : DOXz (w ) ! p(w ))] (see [40, p. 631]). For better read- ability, the semantic complement of know is highlighted in (6) and (7):4 ((s;t);t) s e (5) know = λT λw λz [knoww(T )(z)] J K 0 0 (6) a. knoww λp 8w : p(w ) ! (9x: crazy-hatw0 (x) ^ wearw0 (x)(m)) (j) 0 0 0 b.( 8T )(8w)(8z)[knoww(T )(z) ! (8T :T ⊆ T ! knoww(T )(z))] 0 0 ) c. knoww λp.(8w : p(w ) ! (9x: crazy-hatw0 (x) ^ wearw0 (x)(m))) _ 0 0 (8w : p(w ) !:(9x: crazy-hatw0 (x) ^ wearw0 (x)(m))) (j) 0 0 (7) a. knoww λp. ((8w : p(w ) ! (9x: crazy-hatw0 (x) ^ wearw0 (x)(m))) _ 0 0 (8w : p(w ) !:(9x: crazy-hatw0 (x) ^ wearw0 (x)(m)))) ^ 00 00 (8w : p(w ) ! (9x: squid-hatw00 (x) ^ wearw00 (x)(m))) (j) b.( 8x)(8w)[squid-hatw(x) ! crazy-hatw(x)] 0 0 , c. knoww λp 8w : p(w ) ! (9x: squid-hatw0 (x) ^ wearw0 (x)(m)) (j ) In particular, (6) models the entailment in (3) through the inclusion of Pfw0 j 9x: 0 crazy-hatw0 (x)^wearw0 (x)(m)g (see (6a)) in the union of P fw j 9x: crazy-hatw0 0 (x)^wearw0 (x)(m)g and P fw j :9x: crazy-hatw0 (x)^wearw0 (x)(m)g (see (6c)). 2 The Challenge from Experiential Attitude Verbs Its merits notwithstanding, Theiler et al.'s semantics fails to capture the selec- tional flexibility of a particular, but salient, subclass of responsive verbs: veridical experiential attitude verbs (see [14, 35]). The latter are verbs like see, remember, and observe that also combine with direct object DPs (e.g. (8e)) and with subject- controlled and non-controlled gerundive clauses (e.g. (8d, c); see [1, 14, 44]): (8) 8 a. that Mary was wearing a crazy hat( s; t); generally:((ss; t) > > b. whether Mary was wearing a crazy hat(( s; t); t) Ron <> remembers c. Mary wearing a crazy hat( s; t) or v (event) > d. PRO wearing a crazy hat( (se; t) > : e. a / Mary's crazy hat( (s; ((s;(e; t)); t)) Like the complements of know in (3) and (4), the complements of the different occurrences of remember from (8) stand in semantic/informational inclusion rela- tions to each other. These relations are exemplified in (9) to (11). They include { next to the familiar relations between declarative and interrogative complements (see (9)) { the entailment from gerundive small clauses to that-clauses (e.g. (10); as argued by [31, 43]) and to concrete object-denoting DPs (e.g. (11); see [2, 35]): (9) a. Ron remembers [that Mary was wearing a rainbow squid hat] ) b. Ron remembers [whether Mary was wearing a crazy hat] 4 For simplicity, we neglect tense and aspect of the matrix verb. 4 K. Liefke (10) a. Ron remembers [i. PRO / ii. Mary wearing a crazy hat] 6( ) b. Ron remembers [that there was a crazy hat (which i. he himself / ii. Mary was wearing)] (11) a. Ron remembers [i. PRO / ii. Mary wearing a crazy hat] 6( ) b. Ron remembers [a crazy hat] The modelling of the above relations is impeded by the observation that some of the above complements (viz. the red-marked ones in (8)) resist an interpre- tation as questions. This holds especially for concrete object-denoting DPs (see (8e)) and for subject-controlled complements (see (8d)).
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