LING 147. emantics of Questions Week 3 Yimei Xiang eptember 15, 2016 Last week I. Generalized quantifiers Hamblin emantics & Focus quantificational DPs are generalized quantifiers, which denote sets of sets (of type xet, ty); quantificational determiners denote relation between sets (of type xet, etty). (1) a. every cat λp xe,ty.@xrcat 1 pxq Ñ P pxqs b. some cat λp xe,ty.dxrcat 1 pxq ^ P pxqs (2) a. every = λq xe,ty λp xe,ty.@xrqpxq Ñ P pxqs b. some = λq xe,ty λp xe,ty.dxrqpxq ^ P pxqs ome shifting operations: (i) individuals (of type e) can also be shifted into generalized quantifiers via type-lifting; (ii) the quantification domain of an D-quantifier can be extracted via the BE-shifter. (3) a. LIFT λα τ λp xτ,ty.p pαq b. LIFTp John q λp xe,ty.p pjq (4) a. BE λpλzrppλy.y zqs b. BEp some cat cat 1 Quantifier raising and other phrasal LF movement: A. B. C. everyone VP Mary will VP α τ /α xτt,ty Mary saw x x come... x τ... II. Categorial approaches of question semantics Core assumptions: (i) short answers are bare nominal; (ii) questions denote lambda abstracts; (iii) wh-items denote lambda operators. (5) a. who came rpeople 1 pxq.came 1 pxqs b. who λp rpeople 1 pxq.p pxqs Advantages: (i) the relation between questions and short answers is very directly modeled; (ii) similarity of wh-questions and free relatives is captured nicely. Problems: (i) composing multi-wh questions suffers type mismatch; (ii) it assigns different semantic types to different questions, which makes it difficult account for question coordinations; (iii) it doesn t account for the existential semantics of wh-words in non-interrogative sentences. [But we also saw that those problems can be overcome.] 1
III. Intensionality The extension of an expression is world-dependent. The intension of an expression X is a function which applies to a possible world and returns the extension of X in that world. (6) a. X w ( the extension of X in w ) b. λw. X w ( the intension of X ) The intension of a sentence is a proposition: a function from worlds to truth values. The intension of a predicate of type xe, ty is a property: a function from worlds to xe, ty functions. The intension of a definite NP is an individual concept: a function from worlds to entities. Propositions can also be viewed as the set of possible worlds where this proposition is true. Hence, we can use set-theoretical operations to represent the following relations and operations: Relations and operations p entails q p contradicts q p and q p or q p is possible p is necessary et-theoretical notations p Ď q p X q p X q p Y q p p W Plan for today Intensionality (cont.) Hamblin emantics of questions 2
1 Intensionality (cont.) The extension of a proper name or a logical expression is not world-dependent. (7) a. For every w, John w j (controversial) b. For every w, it is not the case that w λp xs,ty λw. p w c. For every w, every w λq xe,ty λp xe,ty.@xrqpxq Ñ P pxqs Intensional-izing the theory of types (8) Types 1 a. Basic types: e (individuals/entities) and t (truth values). b. Functional types: If σ and τ are types, then xσ, τy is a type. c. Intensional types: If σ is a type, then xs, σy is an intensional type. (9) Domains a. D s W b. D xσ,τy tf f : D σ Ñ D τ u (functions from things of type σ to things of type τ) c. D xs,τy tf f : W Ñ D τ u (functions from possible worlds to things of type τ) Intensional-izing the theory of semantic composition (10) Intensional Functional Application If {β, γ} is the set of α s daughters, β P D xxs,σy,τy, and γ P D σ, then α β pλw. γ w q Example: (11) John believes that Mary left. 2 John 1 believes xst,ety that 1 Mary a. 1 left 1 pmq b. believe λp xs,ty e.believe 1 px, pq c. 1 believe pλw. 1 w q By IFA e.believe 1 px, λw.left 1 wpmqq d. 2 1 p John q by FA p e.believe 1 px, λw.left 1 wpmqqqpjq believe 1 pj, λw.left 1 wpmqq left Alternatively, we can assume that the predicate left carries an world variable w, which is then abstracted over by a λ-operator. (ee Percus 2000 Constraints on some other variables in syntax.) (11 1 ) John 1 believes xst,ety λw.left 1 wpmq λw left 1 wpmq Mary left w 1 Note that we are not actually adding s for possible worlds to our type theory. This is because (as far as we ve seen) there are no expressions of natural language that have specific possible worlds as their values 3
Discussion: (i) in (11 1 ), what composition rule is used for node 1? (ii) Compare the following LFs. Given the lexical entry of every in (7c), consider, which LF is well-formed? (12) Mary saw everyone. everyone λw everyone λw λw everyone Mary saw w x Mary saw w x Mary saw w x 2 Hamblin emantics of questions (Hamblin 1973) 2.1 Core assumptions A possible answer denotes a proposition. A short answer is an elliptical form of the corresponding full answer. (13) Who came? a. Mary came. (full answer) b. Mary came. (short answer) A wh-item denotes a set of individuals. (14) a. who tx : human 1 @pxq 1u b. what tx : thing 1 @ pxq 1u c. which cat @ tx : cat 1 @ pxq 1u A question denotes the set of propositions that are possible (direct) answers of this question, called a Hamblin (alternative) set. (15) a. who came? ta came, b came, a and b came,...u b. which person likes which person? ta likes b, b likes a,...u c. Did John come? tjohn came, John didn t comeu d. Does Mary like coffee or tea? ALT-Q tmary likes coffee, Mary likes teau e. Does Mary like coffee or tea? Y/N-Q tmary likes coffee or tea, Mary doesn t like coffee or teau f. How many cats does John have? tjohn has one cat, John has two cats,...u Hamblin sets are composed via Point-wise Functional Application. (16) Point-wise Functional Application If α is of type xσ, τy and β is of type σ, then a. α Ď D xσ,τy b. β Ď D σ c. αpβq is of type τ, and αpβq tapbq a P α ^ b P β u 4
2.2 Composing questions using Hamblin emantics Composing declaratives and wh-questions: A proper name Mary denotes a singleton set; thus a declarative denotes a singleton set. A wh-item denotes a set with many individuals, thus a wh-question denotes a set with many propositions. (17) a. Mary came. b. Who came? tλw.came 1 wpmqu tλw.came 1 wpxq : human 1 @pxq 1u Mary tmu came t.came 1 wpxqu who tx : human 1 @pxq 1u came t.came 1 wpxqu A note on wh-movement: In categorial approaches (and Karttunen emantics), (non-subject) whitems must undertake movement, so as to salvage type-mismatch. For wh-insitu languages (e.g., Chinese), categorial approaches and Karttunen semantics predicts covert movement of the wh-item. Hamblin emantics has no such prediction. Composing polar questions: Is it the case that denotes the set with the identity function on the question nucleus and its negation. (18) Is it the case that John left? tλw.left 1 wpjq, λw. left 1 wpjqu is it the case that tλp.p, λpλw. p w u tλw.left 1 wpjqu John left Exercise: Assume the type-shifted lexical entry of or in (19), derive the Hamblin sets of the alternative question in (20) using PFA. (19) or λα xst,ty λβ xst,ty.α Y β ( or applies to two sets of propositions, and returns the union of these two sets.) (20) Did JOHN come or MARY come? ALT-Q Exercise: Compose the following polar-q. [Consider: can we use the lexical entry of or in (19)?] (21) Is it the case that [[John came] or [Mary came]]? 5
2.3 Compare Hamblin emantics and traditional categorial approaches Discussion: Are the denotations of (22a-b) equivalent under Hamblin emantics? What about under categorial approaches? [Recall that categorial approaches assume that questions denote lambda abstracts.] (22) a. Did JOHN come or MARY come? ALT-Q b. [Among John and Mary,] which person came? Discussion: Can we derive a Hamblin set based on a lambda abstract? What about retrieving a lambda abstract out of the corresponding Hamblin set? An inclusive comparison between categorial approaches and Hamblin emantics Categorial approaches Hamblin emantics Retrieving the question nucleus Yes No Getting short answers Yes No Getting full answers Yes Yes Uniform semantic type No Yes: xst, ty Question coordinations No No Type-driven wh-movement Yes No Although Hamblin emantics treat questions uniformly as of type xst, ty, it still has imperfections in analyzing question coordinations. Conjunction is traditionally treated as set-intersection. (23) John left and Mary stayed John left X Mary stayed But, the conjunction of two questions cannot be the intersection of the Hamblin sets of the two questions: (24) who left and who stayed who left X who stayed H NO WAY! Hence, Hamblin emantics has to define conjunction as pointwise intersection. 2 (25) Q 1 and Q 2 tp X q : p P Q 1 ^ q P Q 2 u 2 Inquisitive emantics maintains the basic intersection semantics of conjunction by treating questions as sets of proposition sets. (ee Ciardelli et al. 2016, Composing Alternatives ) 6
3 Alternatives emantics of focus (Rooth 1992) Focus affects the suitability of a sentence as answer of the given question. Observe the prosodic dependence between questions and answers: (26) Who invited Bill? Core definitions a. JOHN invited Bill. b. # John invited BILL. c. # JOHN invited BILL. (27) Every expression α has an ordinary value α 0 and a focus value α f. a. α 0 is simply the truth value of α (i.e., the one that we already know). b. α f is the set of all ordinary semantic values obtained by substituting alternatives for any F-marked subparts of α. Compute the focus value compositionally: (28) Terminal " nodes (TN) t α 0 u if α is focused α F if α is not focused D typep α 0 q Pointwise Functional Application (PFA) αpβq f tapbq a P α f, b P β f u Exercise: Compute the focus value of the following sentences compositionally: (29) JOHN F invited Bill. JOHN F invited Bill Use the Rooth-style terms to define Hamblin sets: 3 (30) a. who 0 is undefined b. who f tx : human 1 @pxq 1u c. [ TP who came] 0 is undefined d. [ TP who came] f tλw.came 1 wpxq : human 1 @pxq 1u e. C r`whs [TP] 0 TP f (Beck & Kim 2006, see also himoyama 2001) (interrogative C 0 returns the focus-semantic value of TP as the ordinary semantic value of CP.) 3 Principle of Interpretability: An LF must have an ordinary semantic value (Beck 2006: p. 16) 7
Exercise: Use the following toy LF to derive the Hamblin set for Who does John like?. (31) CP C TP John invited who Explain the prosodic dependence between questions and answers: (32) Question-Answer Congruence (Rooth 1992: 86) A sentence is a possible answer of a question Q iff Q 0 Ď f Examples: (33) a. who invited Bill? 0 Ď JOHN F invited Bill f b. Did JOHN or MARY invited Bill? 0 Ď JOHN F invited Bill f 8