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Weak Noun Phrases: Semantics and Syntax

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Weak Noun Phrases: Semantics and Syntax WEAK NOUN PHRASES: SEMANTICS AND SYNTAX Barbara H. Partee UMASS, Amherst mailto:[email protected] В работе рассматриваются современные Typical case: S семантические анализы слабых ИГ (a unicorn, more / \ than one unicorn, no unicorn). Главным свойством NP VP этого типа ИГ является возможность обозначать / \ walks свойства, т.е. интенсиализированные множества DET CN индивидов. every student 1. NPs as Generalized Quantifiers. CN: type e → t Classic formal semantics adopted Montague’s VP: type e → t proposal (Montague 1973) for the semantics of Noun DET: interpreted as a function which applies to Phrases (NPs). Every NP was interpreted as denoting a set of sets (strictly, a set of properties; we return to the CN meaning to give a generalized quantifier, a function distinction later.) In Montague’s type theory, the which applies to VP meaning to give truth value), type: (e → t) → ((e → t) → t) semantic type corresponding to NPs is (e → t) → t: characteristic functions for sets of sets of entities. NP: type (e → t) → t Sometimes it is simpler to think about DET Some NP interpretations: meanings in relational terms: John λP[P(j)] (the set of all of John’s properties) Every: as a relation between sets A and B (“Every A B”): A ⊆ B John walks λP[P(j)] (walk) ≡ walk (j) So ‘Every man walks’ means: || man || ⊆ || walk || (function-argument application) Some, a: A ∩ B ≠ ∅ . every student λP∀x[student(x) → P(x)] (the set of all of properties that every student has) No: A B = . ∩ ∅ every student walks Most (not first-order expressible): λP∀x[student(x) → P(x)] (walk) ≡ | A ∩ B | > |A - B|. ≡ ∀x[student(x) → walk(x)] (function-argument application) From the relational view, it is a small step to a student λP∃x[student(x) & P(x)] determiners as functions. For example, applying the (the set of all of properties function interpreting every to argument set A gives as that at least one student has) result {B| A ⊆ B}: the set of all sets that contain A as a subset. Equivalently: ║Every║(A) = {B| ∀x ( x ∈ A the king → x ∈ B)}. Equivalently: ║Every║ = λQ[λP[∀x ( Q(x) λP [∃x[king(x) & ∀y ( king(y) → y = x) & P(x))] → P(x) )]]. (the set of properties which the one and only king has) Some, a: takes as argument a set A and gives as result {B| A ∩ B ≠ ∅ }. The meaning of a Determiner like the, a, every is ║a║ = λQ[λP[∃x ( Q(x) & P(x) )]] then a relation between sets, or a function which applies to one set (the interpretation of the common noun CN) to give a function from sets to truth values, or Given this background, we consider the equivalently, a set of sets (the interpretation of the NP). interpretation of NPs as “weak” or “strong”. 2. “Weak” determiners and existential sentences. Neither correct answer is an even number ≠ Neither even number is a correct answer. Data: OK, normal: There is a new problem. (1) Many factors make it difficult to apply to Russian the test we used for English. A better, but provably There are three semantics textbooks. (2) equivalent, semantic test comes from symmetry: There are many unstable governments. (3) (a) Na kuxne tri černye koški ≡ Anomalous, not OK, or not OK without In kitchen 3 black cats special interpretations: ≡ Tri koški na kuxne černye. #There is every linguistics student. (4) 3 cats in kitchen black #There are most democratic governments. (5) #There are both computers. (6) (b) Na kuxne vse černye koški ≠ #There is the solution. (# With “existential” there ; OK with locative there.) (7) In kitchen all black cats Semantic explanation, with roots in (Milsark ≠ Vse koški na kuxne černye. 1977), formal development by (Barwise and Cooper 1981) and by Keenan. all cats in kitchen black (8) Definition (Keenan 1987): A determiner D is a It is also harder to find constructions in Russian basic existential determiner if for all models M and all which allow only weak determiners, for a variety of A,B ⊆ E, D(A)(B) = D(A∩B)(E). Natural language reasons. There do seem to be at least two: test: “Det CN VP” is true iff “Det CN which VP (i) The context in (9) is modeled on the English exist(s)” is true. A determiner D is existential if it is a weak-NP context involving have with relational nouns, basic existential determiner or it is built up from basic which I've discussed in print (Partee 1999). It’s existential determiners by Boolean combinations (and, important that the noun is relational. or, not). U nego est' ____ Examples: at him.GEN is ____ (i) Three is a basic existential determiner because it is true that: Three cats are in the tree iff three cats sestra / sestry / sester which are in the tree exist. sister.NOM.SG / sister.GEN.SG / sister.GEN.PL (ii) Every is not a basic existential determiner. If there are 5 cats, of which 3 are in the tree, “Every cat is ‘He has ____ sister(s).’ (9) in the tree” is false but “Every cat which is in the tree The context in (9) clearly accepts weak Dets exists” is true. including cardinal numbers, nikakoj sestry ‘no sister’, ni odnoj sestry ‘not a single sister’, nikakix sester ‘no sisters’ (the negative ones require replacement of est' Basic existential determiners = symmetric ‘be’ by net ‘not-be’, of course), neskol'ko ‘several’, determiners. mnogo ‘many’, nemnogo ‘few’. And it clearly rejects We can prove, given that all determiners are strong Dets vse ‘all’, mnogie ‘most’, eti ‘those’. conservative (Barwise and Cooper 1981), that Keenan’s (ii) Another context which allows only weak basic existential determiners are exactly the symmetric determiners, in at least English, Polish, and Russian is determiners. the following (Joanna Blaszczak, p.c.): dom s ______ oknom/oknami Symmetry: A determiner D is symmetric iff for all A, B, D(A)(B) ≡ D(B)(A). a house with _____ window/windows (10) Caution: as noted by Milsark (1974, 1977), many English determiners seem to have both weak and strong Testing: readings, and the same is undoubtedly true of Russian. Weak (symmetric): Three cats are in the kitchen ≡ Three things in the kitchen are cats. 3. Property-type NP interpretations More than 5 students are women ≡ More than 5 women are students. While some differences in the possible occurrence Strong (non-symmetric): Every Zhiguli is a of ‘weak’ and ‘strong’ NPs can be accounted for by Russian car ≠ Every Russian car is a Zhiguli. drawing semantic distinctions within the theory of generalized quantifiers, as in the account above, it has Montague (1973) argued that the same semantic been argued that in some cases, weak NPs are really of effect can be achieved with a simpler syntax, if NPs as a “property type” (an intensional variant of type e → t), unicorn express Generalized Quantifiers. In argument rather than generalized quantifiers. Property-type position, every category gets an intensional operator “^” analyses of various “weak NPs” are becoming applied to it (i.e. functions apply to the intensions of increasingly common in Western formal semantics, and their arguments). may have application to some problems in Russian For Montague, the relation between seek and try semantics, including the Russian Genitive of Negation to find is captured not by decomposition but by a (section 4.) meaning postulate. Meaning postulate: 3.1. Zimmermann 1993 on intensional verbs. seek’ (x, ^Q) Æ try’ (x, ^[Q(λy find’ (x,y))]). (13) Zimmermann (1993) argues that Montague’s So Montague treats a verb like seek as denoting a analysis of verbs like seek (“intensional transitive relation between an individual and an intensional verbs”, or “opaque verbs”) as taking arguments of type generalized quantifier. The transparent reading results “intension of Generalized Quantifier”, or from “quantifying in”. <s,<s,<e,t>>,t> is incorrect. He argues that the NP But there are problems with Quine’s and objects of opaque verbs should be semantically Montague’s classical analyses. Among other problems, interpreted as properties (or type <s,<e,t>>.) (Zimmermann 1993) points out an overgeneration problem with Montague’s (and Quine’s) account, in that true quantifier phrases are normally unambiguously 3.1.1. The fundamental properties of intensional “transparent” after intensional transitive verbs like contexts. compare, seek, although they are ambiguous in constructions like try to find. Simple indefinites with a, Caroline found a unicorn. on the other hand, are indeed ambiguous with (extensional, unambiguous) (11) intensional verbs. Compare: Caroline sought a unicorn. (a) Arnim compares himself to a pig. (intensional, ambiguous) (12) (ambiguous) Sentences with seek are ambiguous between a (b) Arnim compares himself to each pig. specific and a non-specific reading (or transparent vs. (unambiguously transparent) (14) opaque reading). (1) is unambiguous, (2) is ambiguous. On the opaque reading of (2), the existence of a unicorn is not entailed. (a) Alain is seeking a comic book. Substitution of extensionally equivalent expressions in an intensional context (on the opaque (ambiguous) reading) does not always preserve truth-value. E.g., the (b) Alain is seeking each comic book. extension of unicorn is the same as the extension of 13- leaf clover (both are the empty set in the actual world). (unambiguous; lacks ambiguity of (c)) Substituting a thirteen-leaf clover for a unicorn in (11) (c) Alain is trying to find each comic book. preserves truth-value. The same substitution in (12) might not. (ambiguous) (15) Examples of verbs taking intentional direct objects: seek, owe, need, lack, prevent, resemble, want, look for, request, demand. 3.1.3. Zimmermann’s alternative account. Zimmermann argues that we can capture the relevant generalizations once we note that definites and 3.1.2.
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