Referential Transparency and Inquisitiveness (2023)

Abstract: The paper extends a referentially transparent approach which has been successfully applied to the analysis of declarative quantified NPs to wh-phrases. This uses data from dialogical phenomena such as clarification interaction, anaphora, and incrementality as a guide to the design of wh-phrase meanings.

## introduction an alternative to generalized quantifier theory (gqt) has recently been developed in terms of referential transparency theory (rtt; @xcite . rtt draws its main motivation from data of natural language use as observed in dialogical interactions, where higher-order denotations postulated by gqt do not seem to be confirmed. hence, rtt pursues a witness-based approach to quantification, which arguably simplifies the representation of quantification phenomena. in this paper, we extend this to questions. this is prima facie tricky because in contrast to qnps wh-phrases (whps) are never referential. 1 indeed a crucial difference between declarative and interrogative quantified meaning is that the former involves predication-giving rise to descriptive potential, whereas the latter involves abstraction-giving rise to predicational potential. phenomena we discuss includes the following: clarificational potential: data from clarification allows for a considerable strengthening of compositionality, the classical syntaxsemantics interface desideratum. this via the reprise content hypothesis (rch) due to @xcite they distinguish different kinds of reprise fragments, including intended meaning requests, that is, reprise fragments that follow the template "a: . . . u 1 . . . b: u 1 ?" exemplified in (2). @xcite show further that reprise fragments of the intended meaning type, at least when they address a non-sentential constituent, do not query pragmatically inferred material but are restricted to direct semantic content. on the basis of this they posit the reprise content hypothesis whose strong version is given in (1): whereas non-interrogative qnps allow for clarification questions relating to their witnesses (but not to properties of properties, as would be expected in gq accounts), whphrases allow only for clarification of their restriction property (not to any propositional entities, as might be expected by gq accounts of interrogatives common in type-driven categorial grammar @xcite ). 2 (2) a. a: most students came to the party. b: most students? a: yes, all but tristan and isolde. a similar point can be made for intensional argument roles of verbs, which allow for clarification without expectation of witnesses @xcite ): the same holds for intensional argument roles of verbs: ideally it should be light blue. incremental potential: input is processed word by word (and indeed at a higher, sub-lexical latency). utterances with qnps are understood incrementally (urbach et al., 2015), as exemplified also in (6a,b). although we are not aware of similar empirical studies for whphrases, (6c,d) suggests that this is the case as well: foot_2 (6) a. a: everyone . . . b: who? b. a: [enters class] no students . . . oh, they're hiding. c. a: who. . . b: what are you going to ask me now? d. a: which student. . . b: in what class? approaches which treat wh-phrases as mediated via an operation like quantifier raising, where a quantifier is moved out of its syntactic surface position into another position in logical form or more generally involve longdistance binding @xcite , seems to be a serious obstacle to this empirical fact. answerhood: the substantive semantic contribution of wh-phrases is the answerhood conditions they give rise to, the details of which are discussed in section 2. response space: any dialogical theory of meaning needs to account for the class of responses a given utterance type gives rise to. in the case of questions there exists detailed empirical and formal work we build on @xcite , briefly summarized in section 2. an example that combines these aspects of wh-phrase meaning is in figure 1 , where the exophoric context triggers the bare whclarification question, which give rise to the short answer. in section 2, we sketch a theory of questions, answerhood, and responses. in section 3, we develop our account of wh-phrase meaning, which is applied to the initial data in section 4. ## a kos-ttr theory of questions our explication is formulated using the frameworks of type theory with records (ttr; @xcite (for the semantic ontology) and kos @xcite (for the theory of dialogue context). ## an rtt theory of whp meaning as we have suggested, building on much past work, qnps have more duties than merely contributing to truth conditions: qnps act as antecedents for anaphoric expressions, they supply verbal affiliates of co-speech gestures, and they are objects of discourse dynamics which becomes apparent in terms of acceptance or clarification requests (we restrict attention here to nominals, but the conditions generalize cross-categorially): referential transparency: a semantic representation for an np is referentially transparent if a. it provides antecedents for pronominal anaphora; b. it provides the semantic type required by a clarification request; c. it provides an attachment site for co-verbal gestures; recall from section 1 that the reprise content hypothesis provides a stronger claim than fregean compositionality: more complex contents are not just systematically combined from their parts, but the contributions from the parts have to be traceable within the complex content. this we achieve in virture of the feature constits mentioned above, whereas potential clarifiability arises from the update rule parameter identification, formulated above as (20) the "qnp anatomy" (a phrase due to cooper, 2013a), which will be an important basis for satisfying these desiderata, is based on a set triplet: the arrow indicates a plural predicate type (ptype), that is, a predicate that expects a setvalued argument. condition c2 simply states that refset and compset add up to the maxset. the value of condition c1 is donated by the head noun and distributed over all maxset members (and thereby over refset and compset). the quantificational workhorse is the quantifier condition "q-cond": it captures what can be called the descriptive meaning of a qnp. for instance, the q-cond of most states that the refset is larger than the compset (|refset| > |compset|). hence, q-cond not only expresses np-internal quantification (i.e., quantification without a scope set from the vp), it also implements quantifiers as "sieves", a metaphor due to @xcite . singular is seen as a special case of plural which just adds the following constraint: rtt involves a twist in predication: the compset gives rise to "two-headed" propositions. for example, the propositional structure for the simple sentence most squirrels sleep is given in (26), where sit-type is of type rectype: hence, there are several ways to form a propositional abstract from rtt propositions-namely over refset, compset, or refind. two remarks are in order: the basic contribution of a wh-phrase to an interrogative meaning is the domain from which a propositional function will be constructed. it is this domain clarification for which can be sought. hence, we add additional structure in abstr with a label wh-dom, which also gets projected as the dgb-params.x value of that sub-utterance. 7 hence, the basic "anatomy" of whp meaning in rtt is: the situation types of propositions on the rtt account factor out referential parameters in terms of q-params-see ( 24 ) and (26). hence, questions and answers are constructed in terms of these parameter sets. a question's abstr now works as follow: we think that a similar account can be developed for intensional argument roles used with qnps. such cases are analyzed in rtt, following @xcite , as the verb composing with a qnp's type value. hence all that is required is to ensure also that this value is projected as the dgb-params.x value. b. who does not sleep? note that refset abstraction accommodates both singular and plural answers. note further that the compset provides a straightforward link for maintaining situational identity between questions and answers in case of negative answers. for instance, answering "who sleeps?" with "not the squirrel" can be straightforwardly understood in an austinian manner as being about the same situation since the np negation indicates compset membership (cf. @xcite . simpleans(p?) is answer to polar question ("whether bill is running?" "no, he's not"/"bill is not running"), simpleans(λx.p (x)) involves not np ("who is running?" "not bill"). ## summary and conclusions in this paper we have sketched an extension of a recent theory of quantification to wh-phrases and questions. we have applied this account to several dialogical phenomena which we believe have not been addressed in previous work.