How Questions and Answers Cohere

When a syntactically complete sentence is uttered in answer to a wh-question, the asserted content may go beyond what is compositionally derivable from the sentence uttered. This paper provides an account of this observation, arguing that the Direct Answer relation is semantically significant. When a discourse segment is construed as a direct answer, special update rules apply. The content derivable from the surface form of the answer is merged with the content of the question using a procedure to be specified. For the Direct Answer relation to be licensed, the merge procedure must result in assignment of a value to the wh-variable in the question, which is treated here as a forward looking anaphor. This constraint gives content to the notion of Direct Answerhood. 1 The basic observation When a declarative sentence is uttered in response to a question, the asserted content may be richer than the compositionally derivable content for that sentence. Here are some illustrative examples: (1) Q:What did Clara draw with her new pencil? A: She drew a dragon. Asserted content: Clara drew a dragon with her new pencil. (2) Q: What’s Jane wearing for the wedding? A: She’s wearing jeans and a t-shirt. Asserted content: Jane is wearing jeans and a t-shirt for the wedding. (3) Q: What’s Harriet knitting for Henry? A: She’s knitting a scarf. Asserted content: Harriet is knitting a scarf for Henry. I make here the strong claim that in these cases, the richer content is asserted, and is not merely implied or implicated. The claim reflects the intuition that the A speaker is fully committed to the truth of the richer claim – as long as she is considered to be answering the question. The only way that the speaker of (1), for example, could evade commitment to the proposition that Clara drew a dragon with her new pencil (rather than the weaker claim that Clara drew a dragon, with no specification of the instrument) would be to make explicit that her assertion is not intended as an answer to the question (but perhaps instead as a potentially relevant non-answer). There is thus a clear connection between the observed enrichment and the existence of a questionanswer relation between Q and A. More specifically, the enrichment relies on A being taken as a direct answer to the question, a notion which will gain substance in the course of the paper. In this paper, I argue that the direct answer relation is semantically relevant. Specifically, I argue that there is a specialised update procedure for utterances construed as answers, and that it is this procedure which results in the enrichment seen in (1)(3). The central idea is that an utterance which serves as a direct answer is not interpreted independently. Rather, contents of question and answer are merged in the interpretation procedure. I spell out this account in DRT (Kamp 1981), enriched with notions from SDRT (Asher 1993, Lascarides & Asher 1993). While most of the discussion requires only the machinery of DRT, some of the additional resources of SDRT are required, specifically: (a) the mechanism for distinguishing distinct discourse segments (via the assignment of labels to segments) and (b) procedures for inferring and representing discourse relations between segments. For the sake of perspicuity I will present the proposal (almost) entirely within the language of DRT. It will be important at various points, however, to recall that the DRT machinery is assumed to be embedded in the richer SDRT framework; and I will point out those places where these assumptions are necessary. Articulation of the account requires that I provide an account of the representation of whquestions in DRT. My goal is not, however, to offer any new account of the semantics of questions. The goal is to provide an account of the semantics of answers. 2 Preliminary assumptions: the discourse relation DirAns Throughout this discussion, I will make the following assumption: When a question is asked and the next discourse move is an utterance of a declarative with assertoric intonation by the addressee of the question, then that utterance is assumed to be intended as a direct answer. The interpretation procedure therefore proceeds by specifying that the Direct Answer relation (DirAns) holds between the two segments. In SDRT, positing a particular discourse relation between two segments may introduce additional requirements on the interpretation of the segments. For example, if the relation Narration is established between two segments, S1 and S2, this imposes constraints on the temporal relations between events in the two segments. If these constraints cannot be met (perhaps because satisfying the constraints would introduce a contradiction), then the discourse relation posited between S1 and S2 must be revised. These additional requirements are 1 Asher and Lascarides 1998 propose a discourse relation Question Answer Pair (QAP) for similar purposes. They assign this relation a particular semantics, which I do not adopt for DirAns, hence I use a different term. expressed in coherence constraints associated with each discourse relation. In this paper, I will propose coherence constraints on the DirAns relation which must be satisfied in order to maintain the assumption that this relation indeed holds between two segments. 3 Representing the content of questions The first step is to specify a DRS representation for wh-questions (cf. Asher and Lascarides 1998). My treatment of questions is informed by the structured meaning approach (Krifka 2001), according to which questions are predicates. Part of the appeal of this approach is to highlight the tight semantic relation between questions and their answers, for on this view, answers provide the argument to which the question-predicate is applied to produce the asserted answer. The approach developed here can be seen as an attempt to articulate the questions-as-predicates view within a discourse-oriented framework, in a way which accommodates both short and long answers. In developing a DRS construction rule for whquestions, I assume that at some level of representation, a wh-question has the form shown in (4), where one or more wh-operators take scope over a sentence which contains whtraces co-indexed with and grammatically linked to the wh-expressions. (4) [wh1 ...[ whn [S ...x1 ... xn... ]] I further assume that semantic type information (e.g. person for who, non-person for what, location for where etc.) is “left behind” as a feature on the variable. The embedded S can then be treated using standard DRS construction rules. The only special rule that is required is for the wh-traces. These are treated by the rule in (5). (5) DRS construction rule for wh-traces Given the syntactic configuration: [XP xi: φ1...φn ], ( φ1...φn being the semantic type features derived from the wh-expression itself), where xi is bound by a wh-expression: i. introduce a new discourse referent xi into the universe of the DRS under construction, and conditions φ1(xi)...φn(xi) into the set of conditions of that DRS. ii. Then, add a condition of the form , ?xi to the set of conditions of the DRS. Having created a DRS for the content of the embedded S, we need to represent that this is the content of a question rather than asserted content. To do this, I use the notation shown in (6): (6) λx...y [...x, y...: ...?x, ?y] This structure is to be interpreted as a set of entities which have the properties characterized by the embedded DRS. This DRS is inert in the procedure for determining the truth of any larger DRS which contains it. It will makes its truth conditional contribution in the effect it has on the interpretation of utterances construed as direct answers. More must be said regarding the new condition ?xi introduced by part ii. of rule (5) above. This condition marks xi as a forward looking anaphor. While a standard anaphor requires an antecedent in the existing DRS or at least in a superordinate position, a forward looking anaphor is an indication that some new predication containing information about the discourse referent in question is anticipated in the subsequent discourse. Generally, this will be accomplished by identifying the forward looking anaphor with some new discourse referent introduced in a later utterance. I propose that a central requirement for a segment to count as a direct answer to a question is that it provide a value for the forward looking anaphor in the question. I formulate this requirement as the Answerhood Constraint, proposed as a coherence constraint on DirAns. Answerhood Constraint, version 1 Let πi, πj be discourse segments; let Ki be the DRS corresponding to πi, where ?x1∈Con(Ki); and let Kj be the DRS corresponding to πj. If DirAns(πi, πj) then the result of updating with Kj must provide a suitable value for xi. The remainder of the paper will involve specifying how this constraint is to be satisfied, and how a discourse referent in the answer is determined to be a suitable value for the forward looking anaphor. 4 First attempt: extracting short answers The cases that are of interest to us are those in which wh-questions are given a full-sentence, or long, answer. However, such questions naturally invite a constituent, or short, answer, as illustrated in (1)’ and (2)’: (1)’ Q: What did Clara draw with her new pencil? A: A dragon (2)’ Q: What is Jane wearing for the wedding? A: A scarlet dress. Cases like these provide a straightforward way to satisfy the Answerhood Constraint, as the response introduces a single discourse referent of the appropriate type to be identified with the forward looking anaphor of the question. Let’s assume for current purposes that once the forward looking anaphor has been assigned a value, the λ-operator is deleted (as assigning a value to this anaphor is equivalent to applying the question-predicate to an argument), and the DRS originally in the scope of this operator comes to be asserted content. 2 The entire procedure is illustrated below for the case in (1)’. (DRSs are simplified for perspicuity.) i. KQ: λx3 [e1, x1, x2, x3 : x1=Clara, her-newpencil(x2), draw(e1), Ag(e1, x1), Instr(e1, x2), Th(e1, x3), non-person(x3), ?x3 ] ii. KA: [y : dragon(y)] 2 We will be able to drop this assumption in the full version of the proposal laid out in section 5.