Short answers as tests: A post-suppositional view on wh-questions and answers (2023)

Abstract: This paper explores a post-suppositional view on wh-questions and their answers with dynamic semantics. Inspired by Brasoveanu (2013); Charlow (2017); Bumford (2017), I propose a unified treatment of items like modified numerals, focus items, and wh-items: they (i) introduce a discourse referent (dref) in a non-deterministic way and (ii) impose definiteness tests (and additional tests) in a delayed, post-suppositional manner at the sentential / discourse level. Thus, with a question like “who smiled”, the (maximally informative) dref “the one(s) who smiled” is derived. A short answer like “Mary and Max” is considered another post-supposition-like, delayed test, checking whether the dref “the one(s) who smiled” is identical to (or includes) the sum “Mary⊕Max”. I analyze various question-related phenomena to see how far this proposal can go.

## introduction this paper explores a post-suppositional perspective on the semantics of wh-questions and (short) answers within a dynamic semantics framework. in this introduction, i present the conceptual and technical motivations behind this project. for a wh-question like (1), it is easy to see that the short answer in (1a) is guaranteed to be a complete true answer, and the corresponding propositional answer is actually tautological. however, despite its being true and complete, interlocutors usually don't accept such an answer, because it is derivable from the question and provides no new information. in contrast, (1b) illustrates what a typical acceptable short answer should look like. who smiled? a. the one(s) who smiled. short ans. short ans. ; mary and max smiled. the above observation suggests that a good short answer to a wh-question provides new information about something definite that has already been established and restricted by the wh-question. this observation is reminiscent of existing literature on post-suppositional phenomena, i.e., delayed tests that (i) check definiteness or (ii) provide additional information about something definite. @xcite provides a post-suppositionbased account for modified numerals in cumulativereading sentences. 1 (2) exactly 3 u boys saw exactly 5 ν movies. cumulative reading of (2): σxσy[boy(x) ∧ movie(y) ∧ see(x, y)] the mereologically maximal x and y satisfying these restrictions ∧ |y| = 5 ∧ |x| = 3 cardinality tests (σ: maximality operator; for notation simplicity, cumulative closure is assumed.) as sketched out in (2), the semantic contribution of modified numerals (i.e., the underlined parts) includes several layers: first, modified numerals introduce, in a nondeterministic way, (potentially plural) discourse referents (drefs), x and y (assigned to u and ν respectively). second, after various relevant restrictions are added onto these drefs (here @xcite , movie(y), and see(x, y)), modified numerals further contribute maximality tests and cardinality tests. specifically, (i) the maximality operators σ pick out the mereologically maximal x and y, i.e., x that is equal to the sum of all boys who saw any movies, and y that is equal to the sum of all movies seen by any boys; (ii) these mereologically maximal drefs are finally checked for their cardinality. therefore, eventually, (2) addresses the cardinality of all the boys who saw any movies (which is 3) and the cardinality of all the movies seen by any boys (which is 5). conceptually, cumulative-reading sentences and wh-questions are parallel in at least two aspects, which motivate a similar underlying analysis: the good short answer in (1b) also provides additional information with regard to all those who smiled. the lack of this kind of additional information would often result in triviality and thus degradedness (see ( 1a ) and ( 3 )). under the analysis of (2) by @xcite , relativized definiteness is realized via a global application of maximality operators. essentially, the derivation starts with non-deterministic alternatives. then, crucially, definiteness tests are not applied immediately at the local dp level, but as postsuppositions, delayed to a higher, sentential level, resulting in relativized definiteness. thus a pseudowide-scope effect in interpreting modified numerals is achieved, via splitting their semantic contribution into an indefinite part and a definite part. technically, the spirit of this post-suppositional (or split) analysis of @xcite can be realized in different ways: e.g., higher-order dynamic generalized quantifiers, update semantics, post-suppositions (see charlow 2017 for a detailed discussion and comparison). to facilitate presentation, here i adopt the dynamic semantics formalism of @xcite , which is based on the nondeterministic state monad developed by @xcite . a re-engineering of (2) is shown in (4). mereology-based maximality test: within this framework, as illustrated in (2), meaning derivation is a series of updates from one information state to another, and an information state m (of type @xmath0. an update is true if the output set of assignment functions is not an empty set; an update is false if the output set of assignment functions is an empty set. in (4), drefs are first introduced and various restrictions are added onto them (see 1 ). maximality operators (see ( 5 )) pick out the mereologically maximal drefs satisfying the restrictions (see 2 ). finally, cardinality tests (see ( 6 )) check the cardinalities of the maximal drefs (see 3 ). the cumulative-reading of (2) is true if the derivation does not return an empty set. the rest of the paper is organized as follows. section 2 presents the main proposal with this dynamic semantics formalism à la @xcite . section 3 explores further extensions of the proposal, analyzing various empirical phenomena hotly discussed in the existing literature on question semantics. section 4 briefly compares the current work with recent related works. section 5 concludes. maximality test (informativeness-based): good short answer as another test: in ( 7 ), who u first works like an indefinite and introduces a dref in a non-deterministic way. given that the domain of this wh-item, who, is typically a set of human individuals, i also include the restriction human(x) here (see 1 in ( 7 )). after other relevant restrictions are added (here smile(x), see 2 in ( 7 )), an operator ans u is applied to 2 (see ( 9 ) and 3 in ( 7 )), picking out the definite dref that eventually leads to the maximally informative true answer to the wh-question. obviously, in this specific example (7), where the domain of the wh-item is a set of individuals and the predicate smile is inherently distributive, ans u amounts to picking out the mereologically maximal dref, as shown in (9a). essentially, 2 means 'someone that smiled (smiled)', and 3 means 'the one(s) who smiled (smiled)'. in some sense, the question meaning (i.e., here 3 in ( 7 )) is equivalent to the meaning of its analytical answer -3 . basically, the above analysis shows (i) a compositional derivation of the meaning of a wh-question, (ii) the derivation of its (analytically) maximally informative true answer, and (iii) how a good short answer contributes information in addressing the wh-question. this analysis inherits many existing insights on question meanings. ## further extensions now i sketch out how the proposal can be extended to account for more question-related phenomena. ## summary this paper explores a post-suppositional view on wh-questions and answers. i analyze wh-items along with items like modified numerals: their semantic contribution all involves dref introduction and definiteness tests. based on this, for answers to wh-questions, we can separate the invariant, analytical part, and the new information part. the new information part further serves as tests on the invariant part. this papers also sketches out how a series of related phenomena are analyzed. further development and refinement is left for future work.