Type-shifting and beyond Henriëtte de Swart Barcelona, May 2005

Advantages of GQ Unified type for all NPs:,t> Unified interpretation for all NPs: PQ(P). Unified type for all Determiners:,,t>>>. Unified interpretation for all Dets: P Q Det(P)(Q).

Disadvantages of GQ theory Not fine-grained enough to account for traditional classifications in terms of quantificational, predicative, referential. Type-shifting (Partee 1987) has been proposed as a possible way to merge insights from GQ theory with other views.

Reference to individuals Partee ‘triangle’: quantificational NPs (‘strong’) denote in type,t> only; other NPs denote in type e or as well. Type-shifting analyses: availability of a type reading for indefinites after application of Partee’s BE operation. BE provides property denotation for weak NPs and definites, not for strong NPs.

Applications Empirical phenomena in which type denotations are relevant: Intensional verbs (seek) ‘Light verbs’ (have) and scrambling Existential contexts (there is/are) Discourse anaphora Incorporation Predicative constructions (to be (a) linguist) Generic reference

Evaluation Intensional verbs, ‘light’ verbs, existential contexts: restricted distribution of NPs (only weak NPs). Lexical treatment in terms of an argument of type justified. Question: how do we extend the property approach to weak readings of NPs in general?

Combinatorics Assume: all weak NPs have a type denotation. Do weak readings of NPs in ‘normal’ contexts have a type denotation? If so, how do they combine with a verb that also takes GQs? Susan ate an apple/two apples/no apples/ every apple/neither apples/most apples

Lexical ambiguity Transitive verbs have a denotation (i) as a relation between two individuals and (ii) as a relation between an individual and a property (van Geenhoven 1998, van Geenhoven & McNally 2005). Eat 1 : y x Eat(x,y) Eat 2 : P x  y  Eat(x,y  P(y)) Derives narrow scope for weak NPs.

Evaluation I Advantage: we can maintain function application as only combinatory rule. Disadvantage (i): systematic ambiguity throughout the lexicon. But maybe: lexical rule deriving two interpretations (VG&McN 2005).

Evaluation II Disadvantage (ii): how to extend to monotone decreasing quantifiers (no existential closure!). But: lexical decomposition (McNally 1998, Van Geenhoven & McNally 2005). However: is lexical decomposition always correct and desirable? E.g. few interpreted as not many.

Closure operations I Alternative: maintain uniform interpretation of transitive verb as relation between two individuals. Enrich combinatorics: allows other modes of composition besides function application. Heim (1982): existential closure. De Swart (2001): existential, universal and exact existential closure.

Closure operations II De Swart (2001): Existential closure applies to properties that are derived from mon  quantifiers (a, some, three, at least five, many, …). Universal closure applies to properties that are derived from mon  quantifiers (no, at no more than three, most five, few,.).

Existential closure  C for predicative NPs derived from mon  quantifiers: For Q a predicate of type, and P min a predicative NP of type, which denotes a minimal property derived from a mon  quantifier:  C:  x Q(x)(P min )   C  x(Q(x)  P(x))

Universal closure  C for predicative NPs derived of mon  quantifiers: For Q a predicate of type and P max a predicative NP denoting a maximal property, derived from a mon  quantifier, the combination of Q and P max introduces universal quantification:  C: x Q(x)(P max )   C  x(Q(x)  P(x))

Evaluation I Advantages: no lexical ambiguity of verbs, no lexical decomposition of NPs, no asymmetric treatment of mon  and mon  NPs (rule based). Disadvantage (i): how are monotonicity properties of the underlying NP recoverable, lexical rule?

Evaluation II Disadvantage (ii): complication in combinatorics (function application + three closure rules). But: recent accounts of e.g. incorporation also allow combinatory rules other than function application.

Discussion I What is the class of expressions that has a type denotation? Largest class: all weak NPs (= all NPs that have a non-empty denotation after application of Partee’s type-shift BE, cf. Zimmermann 1993, McNally 1998, van der Does & de Hoop 1998); definites. Relevant for: intensional verbs, ‘light’ verbs, existential contexts, weak readings of NPs in ‘normal contexts.’

Discussion II Class of indefinites that licenses discourse anaphora, and escapes from scope islands: a N, two N, some N; not no N, at least/at most two N, etc. Discourse anaphora: A student i came in. She i had a question. Every student i came in. #She i had a question about the exam.

Discourse Representation theory A student came in. Indefinites introduce discourse referents. Embedding into model: existential closure. She asked a question. New information added to already introduced dr. u Student(u) Came_in(u) u,v,w Student(u) Came_in(u) Ask(w,v) u = w

Quantifiers in DRT Every student came. #She asked a question. dr u not available as antecedent for she. u Student(u) Came_in(u) v = ?? Ask(v) v 

Plurals and anaphora Two students i came to see me. They i had a question about the exam. Exactly two students i came to see me. #They i had a question about the exam. Most students i came to see me. #They i had a question about the exam. Quantificational NPs can take A  B as their antecedent (‘refset’), but not simply A.

Plural indefinites Two students i came to see me. They i had a question about the exam. U, v, W Student(U) Two(U) Came_in(U). Question(v) U=W Ask(W,v)

Scope islands I If a cousin of mine dies, I’ll inherit a fortune. ‘I have a cousin such that, if he dies, I’ll inherit a fortune.’ If every/no cousin of mine dies, I’ll inherit a fortune.  For every/no cousin of mine, if he dies, I’ll inherit a fortune.

Scope islands II If three cousins of mine die, I’ll inherit a fortune. ‘I have three cousins, such that, if they (all die), I’ll inherit a fortune.’  ‘I have three cousins, and for each of them, if he dies, I’ll inherit a fortune’ No escape from scope islands for true quantifiers, only for indefinites.

Choice function approach Choice function approach: Reinhart (1997), Winter (1997), Kratzer (1998). Indefinites like a cousin of mine, three cousins of mine, etc. denote choice functions: expressions of type,e> The choice function picks an individual from a set. The choice function gets existential closure outside of the scope island.

Choice functions denoting expressions Denote choice functions: singular indifinites like a cousin of mine; plural indefinites like three cousins of mine. Do not denote choice functions: other weak quantifiers such as at least/at most three/no students of mine; strong quantifiers.

Relations between choice functions and DRT Roughly: equivalence between choice function approach and DRT (Farkas 2002). Same set of expressions. Same interpretation: introduce set of individuals, select one that satisfies descriptive content.

Note on bare plurals Bare plurals introduce discourse anaphora: I bought books i on semantics. They i are very good. Bare plurals do not denote choice functions (they never take wide scope!): If cousins of mine die, I will inherit a house.

Bare plurals in DRT Mary bought apples i. They i were nice. Bare plural introduces plural dr m, U, V Apples(U) Bought(m,U) Nice(V) U=V

Narrow scope Bare plurals have narrow scope: (i) because they directly refer to kinds (Carlson 1977) (ii) because they always denote properties (Van Geenhoven 1996). (iii) because their discourse referent is accomodated, and accomodation is ‘local’ (Farkas & de Swart 2003).

Lexical ambiguity Transitive verbs have a denotation (i) as a relation between two individuals and (ii) as a relation between an individual and a property (van Geenhoven 1998, van Geenhoven & McNally 2005). Eat 1 : y x Eat(x,y) Eat 2 : P x  y  Eat(x,y  P(y)) Derives narrow scope for weak NPs.

Thematic arguments in DRT Farkas and de Swart (2003): enrich DRT. Distinction between thematic arguments and discourse referents. Common nouns, verbs: lexical expressions that involve thematic arguments. Determiners: introduce discourse referents by instantiating thematic arguments.

Instantiation I A student left. Input syntactic structure: [ S [ DP [ D a [ NP student(z)]][ VP leave(x)]] u [ S [ DP [ D u [ NP student(z)]][ VP leave(x)]] Introduction of dr by determiner

Instantiation II u [ S [ DP [ D u [ NP student(u)]][ VP leave(x)]] D-instantiation u [ S [ DP [ D u [ NP student(u)]][ VP leave(u)]] A-instantiation Final output: same as in ‘standard’ DRT.

Plurals in FdS I Plural morphology on noun introduces presupposition that a plural dr exists. Two cats are asleep. K K’ u x [ S [ DP [ D two [ NPpl cats(x)]][ VP are asleep(z)]] plural(u x ) K assertion; K’presupposition (vdSandt 91)

Plurals in FdS II Determiner two introduces dr + condition of cardinality K K’ v x u x Two(v x ) [ S [ DP [ D two [ NPpl cats(x)]][ VP are asleep(z)]] plural(u x )

Plurals in FdS III Plural determiner: binding of presupposition upon D-instantiation; K’ resolved against K. v x Two(v x ) Plural(v x ) Cat(v x ) Asleep(v x )

Bare plurals in FdS I Cats were playing in the garden. Assume: full argument position requires introduction of discourse referents. Prediction: bare singulars are blocked (thematic argument only). Bare plurals OK, for presupposition on existence of plural dr accomodated.

Bare plurals in FdS II Cats were playing in the garden. K K’ u x [ S [ NPpl cats(x)][ VP play(z)]] plural(u x ) K assertion; K’ presupposition

Bare plurals in FS III Presupposition resolution by accomodation Result: bare plurals OK in full argument position. u x Plural(u x ) [S [NPpl cats(x)][VP play(z)]]

Scope effects Resolution by binding: dr can be instantiated anywhere in the DRS (‘free’ scope of indefinites). Resolution by accomodation: accomodated is always ‘local’; occurs in the (sub) DRS in which we find presupposition on plural dr. Result: accomodation leads to narrow scope of bare plurals.

Cross-linguistic variation Bare plurals OK in full argument position in languages that allow accomodation. English: accomodation freely allowed. French: no accomodation; no bare plurals; plural indefinite article des required. Spanish: both accomodation (bare plurals) and plural indefinite article unos.

Consequence French plural indefinite article des: just like un, i.e. required for the introduction of a discourse referent (de Swart 2005) Resolution of plural presupposition by binding predicts free scope. Si des cousins à moi meurent, je serai riche. If indef_pl cousins of mine die, I will be rich.

Questions about Spanish Do bare plurals and NPs with unos both license discourse anaphora? Is there a contrast between bare plurals and unos in the possibility of the plural getting free scope (e.g. scope out of scope islands)? More in general: relation between unos NPs and bare plurals, distribution of labor?