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Discourse Semantics Discourse Semantics Nicholas Asher, Department of Philosophy, University of Texas at Austin March 13, 2004 1 Outline of Course • Why go dynamic? • Why have discourse structure? • Logical Forms with Discourse Structure • Building Logical Forms with Discourse Struc- ture, including an introduction to logical tools for defeasible inference. • Applications: the spatio temporal structure of texts, Presupposition, implicatures, agreement and disagreements in dialogue. 2 Texts and Requirements • a course packet with basic articles on dynamic semantics (sections of Kamp and Reyle, From Discourse to Logic, Kluwer 1993, van Eijk’s and Kamp’s article in the Handbook of Lan- guage and Logic, eds. J. van Bentham and A. ter Meulen) • N. Asher and A. Lascarides, Logics of Con- versation, Cambridge, 2003. • Course Requirements: Do most of the exercises in the notes. Slides will also be mailed in pdf format to those wishing them. 3 Setting the Stage • Semantics: traditionally ”what is said” – lexical semantics: the contribution of indi- vidual words to (discourse) content – compositional semantics: the way meanings of individual words compose together to yield sentence contents. • Pragmatics: traditionally, ”what is conveyed” over and above what is said. A Theory of the interactions between the linguistic message and other information sources. Implicatures – language users’ cognitive state (Carnap, Mor- ris, Grosz and Sidner), – the discourse context (Levinson, Vallduvi). 4 My Two Cents’ Worth Pragmatics supplements semantic content (often underspecified) by exploiting context and informa- tion in the cognitive states of discourse partici- pants. But careful, there are many different no- tions of context: Kaplan style contexts used to fix the referents of demonstratives and indexicals, con- texts for dynamic semantics, contexts that include limited information about the cognitive states of the participants, contexts that include all the knowl- edge that participants bring to interpretation. at the lexical and comopositional level. 5 Formal Methods in Semantics and Pragmatics • building from Tarski’s Theory of Truth for For- mal Languages (FOL), semantics establishes a hopefully compositional way of building a log- ical form in a formal language from a natural language discourse and then interprets it recur- sively relative to a model. • Compositionality (the meaning of the whole is a function of the meaning of the parts–Frege) • Different sorts of interpretations: static truth conditions, dynamic update conditions. • Pragmatics at the level of logical form: fill- ing in elements underspecified by semantics. Pragmatics also allows us to infer often defeasi- bly other information from logical forms—viz. about elements of the speaker’s or hearer’s cog- nitive state (intentions, beliefs). 6 Static Semantics-e.g., Montague Grammar • The sentence is the unit of meaning; its seman- tic value is a set of indices (those in which the sentence or its logical form is true). The mean- ing of a discourse is the intersection of the se- mantic values of its constituent sentences. • strict compositionality–the syntax of a natural language sentence completely determines how the meaning of a sentence is built up from the meaning of its constituents. • Every (disambiguated) word has a unique syn- tactic category and by strict compositionality a unique semantic type. Sentence Syntax ----> Logical Form -->Model • logical methods: higher order logic together with a typed lambda calculus. 7 A Simplified Extensional Example Every farmer owns a donkey • Every: λP λQ∀x(P x → Qx) • a: λP λQ∃y(P y ∧ Qy) • farmer: λxfarmer(x) • owns: λΦλxΦ[λyowns(x, y)] • donkey: λzdonkey(z) Construction from Bottom Up: • A donkey: λP λQ∃y(P y∧Qy){λzdonkey(z)} −→ • λQ∃y(λzdonkey(z){y}∧Qy) −→ λQ∃y(donkey(y)∧ Qy) (lambda conversion, twice) • owns a donkey: λΦλxΦ[λyowns(x, y)]{λQ∃y(donkey(y)∧ Qy)} −→ λxλQ∃y(donkey(y)∧Qy)[λyowns(x, y)] • −→ λx∃y(donkey(y) ∧ owns(x, y)) • every farmer owns a donkey: ∀x(farmer(x) → ∃y(donkey(y)∧owns(x, y))) 8 Exercise • Add to the basic vocabulary above a transla- tion for an intransitive verb like sleeps. How does it differ from the entry for owns? Specifi- cally do we need a lambda abstracted variable over DP denotations? Why do we need it for owns? • Use your entry to give a derivation of the ”proper” logical form for a farmer sleeps. • Try to construct the ”proper” logical form for if a farmer owns a donkey, he sleeps. What goes wrong? How could you fix this? 9 Anaphora and Static Semantics Pronominal Anaphora: (1) a. Sally likes her car. b. A farmer owns a donkey. He beats it. What are the semantic values of pronouns? Pronouns as bound variables (2a’) ∃x1(car(x1) ∧ owns(s, x2) ∧ like(s, x2)) But the translation of (2b) is problematic: First sentence: ∃x(farmer(x) ∧ ∃y(donkey(y) ∧ owns(x, y))) Second sentence: beats(x, y) How to bind the variables in the second formula? 10 One solution: Pronouns aren’t bound variables They’re disguised definite descriptions that con- text will tell us how to specify. Second attempt at translating 2nd sentence of (2b): beats(ιx(farmer(x)∧∃y(owns(x, y)∧donkey(y), ??) Still not ideal, because what do we put in for ?? —the most reasonable choice is y, but that’s still treating that variable as a bound variable. There are problems of dependency between the variables, and also problems with uniqueness. There could be several farmers that own donkeys and beat them. Exercise: what do you think about the unique- ness requirements? What if we just drop them? 11 Temporal Anaphora (2) Un homme entra. Il fuma une cigarette. Il partit. (A man entered. He smoked a cigarette. He left.) Traditional tense logic tells us simply that the three events introduced in the text occurred in the past. But there is an anaphoric dependency of one event on the other that static approaches miss. 12 Presupposition (3) a. A child is petting his cat. b. If a child own a cat, then he will want to pet his cat. Traditional semantics treats presuppositions sep- arately but there appears to be an important inter- action between presupposed and asserted content— e.g., the quantifier in the assertion must bind the variable introduced in the presupposition in (3b). Further, a presupposition’s ”projection” depends on the logical structure of the assertion. 13 Dynamic Semantics Dynamic Semantics (DRT, Dynamic Predicate Logic, Dynamic Montague Grammar) • The content of a sentence is not a static ele- ment but something dynamic that alters the context—more precisely, a relation from dis- course contexts to discourse contexts. • a discourse context is either a representational structure (as in DRT) or a set of assignment functions (for a fixed model) or a set of model assignment pairs, or a set of world assignment pairs (for a fixed model) (the latter is used to handle intensional constructions). 14 DRT— A version of Dynamic Semantics Sentence Syntax ----> DRS -->Model constr. alg. • In DRT a DRS is a semantic representation; it is a pair of sets < U, C > where U is a set of discourse referents, and C a set of conditions. • In DRT a context is modelled as a DRS. • Input Context + DRS −→ Output Context 0 • K + K = h(UK ∪ UK0), (CK ∪ CK0)i 15 DRT on Anaphora (4) John bought a book on semantics. He is reading it now. (5) Every book John buys is about semantics. He is reading it* now. first sentence of (4): j, x (4’) bought(j, x) book-on-semantics(x) Sentence 2: z, u read(z, u) (4”) z =? u =? 16 The DRS for the whole discourse: j, x, z, u bought(j, x) (4”’) book-on-semantics(x) read(z, u z =? u =? With the preferred values for the pronouns: j, x, z, u bought(j, x) book-on-semantics(x) (4+) read(z, u) z = j u = x 17 Remarks on Underspecification • Underspecified conditions for pronouns: e.g., z =? and u =? generated by the semantics of pronouns. are incomplete semantically. • Pragmatics completes underspecified conditions (replacing ? with the appropriate discourse ref- erents) but subject to semantic constraints • Alternatively, let the semantics freely generate all possible anaphoric bindings–some ruled out by semantic constraints (accessibility), some discarded on pragmatic grounds. 18 Accessibility A constraint stated on DRSs: Only discourse referents in a DRS universe to the left or above are accessible to conditions of the form z =? DRS for (5): j, x buys(j, x) ⇒ on semantics(x) (5’) book(x) read(z, u) z =? u =? 19 Dynamic Semantics and Temporal Structure (6) Un homme entra. Il fuma une cigarette. Il partit. (A man entered. He smoked a cigarette. He left.) x, e, n man(x) enter(e, x) e < n Rpt := T P pt = Ept := e 20 After the second sentence: x, e, e1, y, n man(x) enter(e, x) e < n cigarette(y) smoke(e1, x, y) e < e1 e1 < n Rpt := T P pt = Ept := e1 21 After the third sentence x, e, e1, e2, y, n man(x) enter(e, x) e < n cigarette(y) smoke(e1, x, y) e < e1 e1 < n leave(e2, x) e1 < e2 e2 < n Rpt := T P pt = Ept := e2 22 Summing up the Simple Past in DRT : Introducing notation that will come in handy the DRT predictions for tense sequences in French for simple sentences are as follows: (< α, β, λ > ∧PS(α) ∧ PS(β)) → eα < eβ Exercise: give a formal rule for the past tense in the sense that you can say what the past tense does to a DRS. 23 Formalizing Dynamic Semantics via Dynamic Pred- icate Logic: The syntax resembles that of first order logic. • logical symbols: ¬, ∃, ∧, = • grouping indicators: (, ) • nonlogical constants: predicate symbols (P, Q, R, . .), individual constants (a, b, c, .
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