Conditional Questions

Transcription

1 James Isaacs Kyle Rawlins University of California Santa Cruz Language Under Uncertainty, Kyoto University January 22, Introduction Claim: conditional questions (CQs) like (1) can be analyzed by straightforwardly combining a semantics of conditionals with a semantics of questions. (1) If Alfonso comes to the party, will Joanna leave? Concern: responses like (2B), which are not available for parallel simple questions, call for the redefinition of the semantics of questions (Hulstijn 1997; Velissaratou 2000, among others). (2) A: If Alfonso comes to the party, will Joanna leave? B: Alfonso isn t coming. A three-way split: Responses like (2B) are not answers in the technical sense; i.e., they do not resolve the issue raised by the question. They indicate a species of presupposition failure, revealing a three-way split w.r.t. the presuppositions of conditionals. (Stalnaker 1968, 1975; Karttunen and Peters 1979; Fintel 1999; Ippolito 2003, and much other work) Indicative conditionals: antecedent is presupposed to be possible. Subjunctive conditionals: compatible with possibility or impossibility of antecedent. Counterfactual conditionals: antecedent presupposed to be false. Conditional questions are interpreted in two steps: 1. The antecedent calls for the creation of a derived context based on the context of utterance in which: 2. the question in the consequent is interpreted, partitioning the derived context. Thanks to Donka Farkas, Michela Ippolito, and Bill Ladusaw for discussion, and audiences at UCSC for comments.

2 2 Conditional questions in various forms The three main types of questions can be conditionalized. (3) Polar question If Alfonso comes to the party, will Joanna leave? (4) Constituent question If Alfonso comes to the party, who will leave? (5) Alternative question If Alfonso comes to the party, will Joanna leave or will she attack him? The three main types of conditionals can be questioned. (6) Indicative conditional If Alfonso comes to the party, will Joanna leave? (7) Subjunctive conditional If Alfonso were to come to the party, would Joanna leave? (8) Counterfactual conditional If Alfonso had come to the party, would Joanna have left? In this talk, we focus primarily on indicative polar conditional questions. 3 Denial of the Antecedent Answers are linguistic responses that resolve the issue raised by the question. Main question: Does denying the antecedent (2B) answer a conditional question? Some reasons to think so: They remove the issue raised by the question from consideration. They are pertinent to the discourse. Several reasons to think not (given in 3.2). 3.1 Denial of the antecedent as an answer Previous analyses: denying the antecedent answers the CQ (Hulstijn 1997; Velissaratou 2000). These analyses adopt a partition semantics of questions (Higginbotham and May 1981; Groenendijk and Stokhof 1997; Groenendijk 1999). Main question w.r.t. partition semantics of questions: How do worlds where the antecedent of a CQ is false fit into the partition? 2

3 Answers to this question are a main point of comparison among the theories. Hulstijn 1997: antecedent-denying worlds go in their own block of the partition. φ ψ worlds φ ψ worlds φ worlds Figure 1. The partition induced by if φ,?ψ Denying the antecedent is a (complete) answer, of the same status as yes and no. (This possibility was also suggested by Groenendijk and Stokhof 1997, fn 29.) Velissaratou 2000: weaken the standard requirement that questions divide contexts into exhaustive and mutually exclusive alternatives. Questions divide context sets into maximal covers (called alternatives) of those sets. Alternatives can overlap - and they do in the case of conditional questions. If there is no overlap among alternatives, the context set is partitioned. Worlds where the antecedent is false are in both alternatives introduced by the CQ. φ ψ φ φ ψ.. Figure 2. Velissaratou 2000: Alternatives introduced by If φ,?ψ. Denying the antecedent doesn t choose between maximal covers; it removes the worlds where the covers don t overlap. This behavior is assumed for all conditionals. 3.2 Arguments against answerhood Intuitive status of antecedent-denial An answer should be about an issue raised by a question. (2) A: If Alfonso comes to the party, will Joanna leave? B: Alfonso isn t coming. - The question in (2A) is about whether Joanna will leave. Denying the antecedent addresses the ground on which the question stands, not the question itself Does not generalize to all conditionals If responses like (2B) are answers, they should nullify conditional questions regardless of their type. Following subjunctive conditional questions like (9A), responses such as (9B) do not have the effect of nullifying the issue raised by the question. 3

4 (9) A: If Alfonso were to come to the party, would Joanna leave? B: Alfonso isn t coming. The same holds of counterfactual conditionals. (10) A: If Alfonso had come to the party, would Joanna have left? B: Alfonso didn t come to the party Partial answerhood If denying the antecedent (2B) is an answer, there are three possible complete answers (as in Figure 1). One (denying the antecedent) says that Alfonso isn t coming to the party, and effectively that whether Joanna leaves is irrelevant to the discourse. The other two say that if Alfonso does come, Joanna would either leave ( yes answer) or stay ( no answer). Antecedent-affirming responses should also be possible they should be partial answers. The response in (11B) is a partial answer it reduces the number of possible answers and brings us closer to answering the question. (11) A: What professor is teaching Syntax B this quarter? B: Not Jim. The response in (12B) should be parallel to the one in (11B), but it is not. (12) A: If Alfonso comes to the party, will Joanna leave? B: Alfonso is coming Yes and no Generalization: only polar questions allow yes and no answers. If denying the antecedent counts as an answer to a CQ, CQs cannot be polar questions (they would induce a partition with three blocks), yet yes and no are licensed Explanatory value Questioning the truth/falsity of the antecedent of a conditional is an issue related to conditionals, not to questions. Denying the antecedent has a similar effect regardless of the form of the consequent. The response in (13B), like the one in (2B), implies that the conditional is irrelevant. (13) A: If Alfonso comes to the party, Joanna will leave. B: Alfonso isn t coming. 4

5 Stipulating that antecedent-denial is an answer to CQs does not help explain what denying the antecedent actually does. 4 Our analysis 4.1 Avoid redefining the semantics of questions Denial of the antecedent should: Not involve answering the question Involve making the question moot for some kinds of conditionals (indicative), but not for all (subjunctive/counterfactual) 4.2 Background Dynamic possible world semantics, with a Stalnaker 1978-style context. Utterances denote context-change potentials (functions from contexts to contexts) Assumptions about questions We assume a partition semantics for questions (Higginbotham and May 1981; Groenendijk and Stokhof 1997; Groenendijk 1999) - in particular Groenendijk Questions partition the context into (mutually exclusive) blocks. Each block corresponds to a complete and exhaustive answer. Formally: a context is an equivalence relation on worlds (symmetric and transitive, represented as sets of pairs of worlds). A context updated with a question results in a partitioned context consisting of blocks in which the issue raised by the question is resolved in the same way. (14) Inquisitive update on contexts ( ) c φ = { w 1, w 2 φ w 1,c = φ w 2,c } A context updated with an assertion reduces the context to pairs of worlds where the assertion is true. (15) Assertive update on contexts ( ) c φ = { w 1, w 2 φ w 1,c = φ w 2,c = 1} 5

6 An example: (16) Initial context consisting of five worlds (w 1...w 5 ). w 1, w 1 w 2, w 1 w 3, w 1 w 4, w 1 w 5, w 1 w 1, w 2 w 2, w 2 w 3, w 2 w 4, w 2 w 5, w 2 w 1, w 3 w 2, w 3 w 3, w 3 w 4, w 3 w 5, w 3 w 1, w 4 w 2, w 4 w 3, w 4 w 4, w 4 w 5, w 4 w 1, w 5 w 2, w 5 w 3, w 5 w 4, w 5 w 5, w 5 A polar question partitions the context into two blocks the worlds in which it is raining constitute a block, as do the ones in which it is not. (17) Is it raining? (assume it s raining in worlds w 1, w 2 and w 3 ) = w 1, w 1 w 2, w 1 w 3, w 1 w 1, w 2 w 2, w 2 w 3, w 2 w 1, w 3 w 2, w 3 w 3, w 3 w 4, w 4 w 5, w 4 w 4, w 5 w 5, w 5 A complete answer reduces the partition to a single block. (18) Yes, it s raining. = w 1, w 1 w 2, w 1 w 3, w 1 w 1, w 2 w 2, w 2 w 3, w 2 w 1, w 3 w 2, w 3 w 3, w Assumptions about conditionals A decompositional approach to conditionals: the antecedent and the consequent are separate units that affect the context independently. (Stalnaker 1968; Heim 1982; Veltman 2005) This allows us to combine a standard partition semantics for questions, and a standard dynamic semantics of conditionals. Heim 1992, following Stalnaker 1968; Lewis 1973; Kratzer 1977 and others: (19) c + [[if φ] ψ] = {w c : Sim w (c + φ) + ψ = Sim w (c + φ)} (20) Sim w (φ) = {w W : w φ w resembles w no less than any other w φ} The similarity function arises compositionally from a (possibly covert) modal in the consequent of the conditional, following Kratzer 1977, 1981 and others. We will typically abstract away here from the modal, and from the reasons for using a premise or ordering semantics. 6

7 We capture the compositionality by assuming that the consequent of a conditional has some complex structure. Here we decompose the consequent into just a modal and the propositional content of the consequent. If φ, ψ would be structured as in (21). See e.g. Ippolito 2003 for an approach with greater decomposition of the antecedent. (21) S S if φ Modal ψ 4.3 Contexts and derived contexts We abstract away from contextual parameters such as speaker, hearer, world of utterance, time of utterance, location of utterance, etc. and consider the part of the context referred to in Stalnaker 1978 as the context set - the worlds the participants in the discourse take to be candidates for the actual world. Following Groenendijk 1999, a context is a set of pairs of worlds. Dynamic view (Stalnaker 1968; Karttunen 1974; Heim 1982, among others): conditionals involve a two step update procedure: 1. A derived context is created by updating the speech context with the antecedent of the conditional. 2. The derived context is updated with the consequent. In the standard view, derived contexts are discarded after the interpretation of declarative conditionals. No future interpretation makes reference to them. There is no formal mechanism for retaining derived contexts. We propose that derived contexts are not generally discarded after the interpretation of conditional questions. The consequent question partitions the derived context, rendering it inquisitive. Because it is inquisitive, it can t be discarded. We treat derived contexts for conditionals on par with the derived contexts involved in some analyses of modal subordination (Frank 1996; Kaufmann 2000) and other phenomena (Farkas 2003). Kaufmann 2000 takes a similar position regarding declarative conditionals. There is independent support for non-temporary derived contexts in conditionals: (22) If a thief breaks into the house, he will take the silver. If in addition he finds the safe, he will open it. (Frank 1996, ch. 3, ex. 79) 4.4 The stack model Our formalization uses the stack-based model proposed in Kaufmann 2000 (to account for modal subordination) to maintain derived contexts. (see references therein for previous uses of stack structures to maintain discourse information, and in particular Zeevat 1992) 7

8 Modal subordination pushes (inserts at the top) a derived context onto the stack. Subsequent utterances can continue to use the top context. If a subsequent utterance has no cues for modal subordination, the subordinate context is popped (removed from the top) off the stack. We propose that the interpretation of a conditional in the stack model involves the following: 1. A derived contexts is created by making a copy of the current top of the stack. a) The derived context is updated with the antecedent. b) The updated derived context is pushed onto the top of the stack. 2. Update the (new) top of the stack with the consequent of the conditional If the conditional is a conditional question, the second step involves partitioning the derived context. 4.5 Formal implementation A macro-context is a stack: an ordered sequence of contexts. (23) a. is a macro-context. b. If c is a context and s is a macro-context, then c, s is a macro-context. c. Nothing else is a macro-context. d. If s is a macro-context, then s n is the nth member (counting from 0 at the top) and s is its size (excluding its final empty element). (24) push operator push(s, φ) = φ, s (25) pop operator pop( c, s ) = c, s if s =, s otherwise (26) s is the number of times plus one you can recursively apply pop to s without getting back s. s n is the element of s you would get if you applied pop n times. (27) Definition of { c c φ = w 1, w 2 c or w W s.t. w 1, w c or w, w 2 c w 1, w 2 c φ c c φ should be read as learning in a context c that another context c supports φ A pair of worlds is in c c φ iff either (i) neither world in the pair appears in c (but the worlds are in c), or (ii) the worlds would remain if c were updated with φ. is used to update only the worlds in some context set that are also present in another. (28) Assertive update on macro-contexts (given a simple declarative sentence φ): c, s + φ = c φ, τ where s = τ = n and s i c φ = τ i for all 0 i < n An assertion of φ amounts learning in every context in the stack that the top context supports φ. (similar to Kaufmann s Conclude operation). 8 }

9 (29) Inquisitive update on macro-contexts (given a simple interrogative sentence φ): c, s + φ = c φ, s Heim 1992 s similarity function must be updated to deal with pairs of worlds in the context. The new version in (30) is defined using Heim s similarity function (20). (30) Sim w,v (φ) = { a, b : a Sim w ({u : u : u, u φ}) and b Sim v ({u : u : u, u φ})} This provides everything needed to interpret declarative and interrogative conditionals. (31) Macro-CCP of an indicative conditional: s + [if φ, ψ] = push(s, s 0 + [if φ]) + ψ Admittance conditions: [If φ, ψ] is admissible in a macro-context s iff s 0 φ Recall that the consequent will always contain a modal of some sort (see (21)). When this is covert it can be described as: (32) Modal φ w,c = { w, v : (Sim w,v (c) φ w,c ) = Sim w,v (c)} This is the source of the similarity function in conditionals An example (on next two pages) 9

10 Example computation of a conditional question Computation State of macro-context (33) Assume an input macro-context s = c, for some arbitrary context c. s = s0 : c = s0 : w1, w1 w2, w1 w3, w1 w 4, w1 w1, w2 w2, w2 w3, w2 w 4, w2 w1, w3 w2, w3 w3, w3 w 4, w3 w1, w 4 w2, w 4 w3, w 4 w 4, w 4 Alfonso comes to the party in w1, w2 and doesn t come in w3, w 4. Joanna leaves the party in w1, w3 and doesn t leave in w2, w 4 (34) s+ [If [Alfonso comes to the party]], [will Joanna leave?] (35) = push(s, s0 [Alfonso comes to the party]) + [Will Joanna leave?] (semantics of conditionals) (36) = c [Alfonso comes to the party], c, + [Will Joanna leave?] (definition of push) s0 : c [Alfonso...] s1 : c (37) = (c [Alfonso comes...]) [Joanna leaves], c, (definition of +) s0 : (c [Alfonso...]) [Will Joanna...?] s1 : c (38) = (39) = w 1, w2 c (definition of ) { w1, w2 c (definition of ) [Alfonso comes...] w1,c = [Alfonso comes...] w 2,c = 1 [Joanna leaves], c, [Alfonso comes...] w 1,c = [Alfonso comes...] w 2,c = 1 and Joanna leaves w 1,c [Alfonso...] = Joanna leaves w 2,c [Alfonso...] } s0 : w 1, w1 w2, w1 w1, w2 w2, w2 s1 : c, c, s0 : } { w 1, w1 s1 : c [Will Joanna...?] w2, w2 } A following answer is interpreted w.r.t. the derived context: (40) The macro context (39) + [yes.] (41) = ((c [Alfonso comes...]) [Joanna leaves]) [Joanna leaves], c (c [Alfonso...]) [Joanna...] [Joanna leaves], { } w 1, w1 [Joanna leaves] w2, w2 s1 : c (c [Alfonso...]) [Joanna...] [Joanna leaves] s0 : 10

11 { w 1, w1 } s0 : (42) = s1 : c s0 [Joanna leaves] Expanding the, still in step (42): { w 1, w1 } w1, w1 w3, w1 w 4, w1,... [Alfonso comes...] w1,c = [Alfonso comes...] w2,c = 1 and J. leaves w 1,c [Alfonso...] = J. leaves w 2,c [Alfonso...] and J. leaves w 1,(c [Alfonso...]) [J. leaves] = J. leaves w 2,(c [Alfonso...]) [J. leaves] = 1 w 1, w2 c s0 :... c (c [Alfonso...]) [Joanna...] [Joanna leaves], w1, w3 w3, w3 w 4, w3 w1, w 4 w3, w 4 w 4, w 4 s1 : (definition of + for declaratives) Because the derived context is no longer inquisitive, it can be popped (assuming no further subordination cues), leaving: (43) c (c [Alfonso...]]) [Joanna...] [Joanna leaves], s0 : c (c [Alfonso...]) [Joanna...] [Joanna leaves] 11 ), The effect of the answer lives on, due to the above: ( w, w2 (c [Alfonso...]) [Joanna...] (44) = w either w 1, w2 c or w1, w (c [Alfonso...]) [Joanna...] or w1, w2 c [Joanna leaves] (definition of ) ( ) [Alfonso comes...] w,c = [Alfonso comes...] w 2,c = 1 and Joanna leaves w,c [Alfonso...] = Joanna leaves w 2,c [Alfonso...] ( ) [Alfonso comes...] or w 1,c = [Alfonso comes...] w,c = 1, and Joanna leaves w 1,c [Alfonso...] = Joanna leaves w,c [Alfonso...] Joanna leaves w 1,c = Joanna leaves w 2,c = 1 ) w1, w1 w3, w1 w 4, w1 (45) = ( or either w w1, w2 cs w1, w3 w3, w3 w 4, w3 w1, w 4 w3, w 4 w 4, w 4 s0 : This is the same state that would be reached by a declarative conditional If Alfonso comes to the party, Joanna will leave.

12 4.6 Accounting for denial of the antecedent Denial of the antecedent has a split behavior: Indicative CQs: denial of the antecedent felicitously makes the question go away. (The hearer is no longer obligated to provide an answer.) Subjunctive/counterfactual CQs: denial of the antecedent has no effect on the question (the hearer is still obligated to provide an answer), and denial of the antecedent is somewhat infelicitous/inappropriate. This split behavior patterns with the presuppositions of conditionals. (Stalnaker 1968, 1975; Karttunen and Peters 1979; Fintel 1999; Ippolito 2003, among others) Indicative conditionals presuppose that their antecedent is a live possibility at the time of utterance. (46) If Alfonso goes to the store, he will buy some milk. (presupposes: it is possible that Alfonso will go to the store) Subjunctive conditionals are neutral w.r.t. possibility of the antecedent. (47) If Alfonso were to go to the store, he would buy some milk. (compatible with it being possible or not possible for Alfonso to go) Counterfactuals presuppose/implicate that their antecedent is false. (Stalnaker 1975; Karttunen and Peters 1979; Fintel 1999; Ippolito 2003, among others) (48) If Alfonso had gone to the store, he would have bought some milk. (presupposes: Alfonso didn t go to the store.) Satisfying this presupposition (which is a presupposition of the conditional) is a precondition to creating the derived context, and interpreting the antecedent. Indicative CQs: Denial of the antecedent of an indicative CQ indicates that the denier failed to interpret the conditional, due to presupposition failure. No derived context created, no partition induced (for the denier). Other speakers, who may have had neutral beliefs w.r.t. the presupposition, now perform belief revision to add to their private beliefs the impossibility of the antecedent - in the process reverting to a context prior to the failed CQ. The branch of discourse where the question is asked is abandoned (the conditional would create an empty derived context anyway). Subjunctive/counterfactual CQs: Conditionals are compatible with the falsity/impossibility of the antecedent - i.e. they are not restricted to worlds that represent live alternatives. Derived context are built normally, partitions are induced. Denying the antecedent doesn t indicate presupposition failure. 12

13 Denial of the antecedent is either: * Interpreted w.r.t. the derived context, in which case it reduces that context to null (a very odd thing to do), without answering the question. * Interpreted w.r.t. main context (due to lack of a subordination cue), in which case it doesn t answer the question. Either way, the (perfectly legitimate) question doesn t get answered, and the hearer hasn t behaved appropriately w.r.t. the question game. This follows straightforwardly from our analysis. The denial of the antecedent effects are due to independent properties of conditionals. 5 Concluding remarks We give an analysis of conditional questions that straightforwardly combines a standard analysis of questions with one of conditionals. By treating our derived contexts on par with those used in analyses of modal subordination, our analysis can be used for questioning in cases of modal subordination. We predict that any utterance type can appear in the consequent of the conditional. In the terms of Krifka 2001, the if -clause is scoped over a speech-act operator in the consequent of the conditional. This prediction is borne out, as illustrated by the conditional command in (49) and the conditional exclamation in (50). (49) If Alfonso calls, tell him I ve been trying to get in touch with him. (50) If it s sunny, what a nice picnic we ll have. We also predict that conditionals can be conditionalized (51). (51) If it s raining, will we go to the concert if it happens? A final repercussion of our analysis is that conditionals with declarative consequents consist of an if -clause taking scope over an assertion. 13

14 BIBLIOGRAPHY Bibliography Farkas, Donka Assertion, belief and mood choice. Presented at ESSLLI, Conditional and Unconditional Modality Workshop, Vienna. Fintel, Kai von The presupposition of subjunctive conditionals. In Uli Sauerland and Orin Percus, eds., The Interpretive Tract, MIT Working Papers in Linuistics 25, MITWPL. Frank, Anne Context Dependence in Modal Constructions. PhD thesis, Institut für maschinelle Sprachverarbeitung, Stuttgart. Groenendijk, Jeroen The logic of interrogation. In T. Matthews and D. L. Strolovitch, eds., Proceedings of SALT IX. CLC Publications. Groenendijk, Jeroen and Martin Stokhof Questions. In J. van Benthem and A. ter Meulen, eds., Handbook of Logic and Language, Elsevier/MIT Press. Heim, Irene The Semantics of Definite and Indefinite Noun Phrases. PhD dissertation, University of Massachusetts, Amherst. Distributed by the Graduate Linguistic Students Association, UMass Amherst. Heim, Irene Presupposition projection and the semantics of attitude verbs. Journal of Semantics 9: Higginbotham, James and Robert May Questions, quantifiers, and crossing. Linguistic Review 1: Hulstijn, Joris Structure information states. raising and resolving issues. In A. Benz and G. Jäger, eds., Proceedings of MunDial97. University of Munich. Ippolito, Michela Presuppositons and implicatures in counterfactuals. Natural Language Semantics 11: Karttunen, Lauri Presuppositions and linguistic context. Theoretical Linguistics 1: Karttunen, Lauri and Stanley Peters Conventional implicature. In Coon-Kyu Oh and David Dinneen, eds., Syntax and Semantics, Vol. 11: Presupposition, Academic Press. Kaufmann, Stefan Dynamic context management. In Martina Faller, Stefan Kaufmann, and Marc Pauly, eds., Formalizing the Dynamics of Information. CSLI Publications. Kratzer, Angelika What must and can must and can mean. Linguistics and Philosophy 1: Kratzer, Angelika The notional category of modality. In Hans-Jürgen Eikmeyer and Hannes Rieser, eds., Words, Worlds, and Contexts: New Approaches in World Semantics, Berlin: Walter de Gruyter. Krifka, Manfred Quantifying into question acts. Natural Language Semantics 9:1 40. Lewis, David Counterfactuals. Blackwell. Revised printing Stalnaker, Robert A theory of conditionals. In N. Resher, ed., Studies in Logical Theory. Blackwell. Stalnaker, Robert Indicative conditionals. Philosophia 5: Stalnaker, Robert Assertion. In Peter Cole, ed., Pragmatics, Academic Press. 14

15 BIBLIOGRAPHY Velissaratou, Sophia Conditional questions and which-interrogatives. Master of Logic Thesis, University of Amsterdam. ILLC Publications. Veltman, Frank Making counterfactual assumptions. To appear in Journal of Semantics. Zeevat, Henk Presupposition and accommodation in update semantics. Journal of Semantics 9(4):