Polymorphic Quantifier

The generalized quantifier theory does not apply to Japanese quantifiers since: i) the number of NP argument is unspecified; and, ii) quantities are often expressed by predicative adjectives. The word order changes the interpretation, e.g., non-split quantifiers correspond to definite NPs with uniqueness and maximality conditions while split NPs are wide scope indefinites. This paper shows that adjectival quantifiers are polymorphic, and that continuation-based combinatory categorial grammar (1) accounts for different meanings between (non)split quantifiers. 1 Limit to Generalized Quantifier Theory The generalized quantifier theory in (2) maps the syntactic constituency between a noun and a determiner into a quantifier. Such view and even relational view on generalized quantifier which considers the relation between two sets (3, 4) cannot handle Japanese quantificational words whose number of argument is not necessarily two. Moreover, being a determiner-less language, quantities are often expressed by predicates naturally. A quantificational phrase and a modified noun show long distance dependency as a split NP or a floating quantifier. 1.1 Predicative Adjectival Quantifiers In English, quantifiers are normally noun phrases as in Many people attended. However, as (5) observes, numbers and quantities are more naturally expressed as a predicate in Japanese. While English-type quantifiers are possible as in (1a), predicative adjectives (1b) are more natural. (1) a. Oku-no nihonjin-wa A-gata-da. many-gen Japanese-top A-type-be ‘Many Japanese are type A’ b. Nihonjin-wa A-gata-ga oi. Japanese-top A-type-nom many ‘Many Japanese are type A’ 2 S. Nishiguchi: Polymorphic Quantifier While weak determiners such as many, few, and five can appear as predicative adjectives, strong determiners like every and most cannot in English. In Japanese, both weak and strong quantifiers appear as predicative adjectives (2b). (2) a. The number of attendants was {many/few/forty/*most/*every}. b. Shussekisha-ga {okat/sukunakat/yonju-nin-dat/hotondo-dat/zen-in-dat}-ta. attendant-nom many/few/40-cl/most/every-be-past ‘The attendants were many/few/40/most/all’ Since adjectives denote a property or a set of entities, the denotations of many and three would be the sets of entities whose numbers are considered to be many, and three, respectively. (7) proposes the function BE which shifts generalized quantifiers such as an authority in type (et, t) into (et) in predicate position (Mary considers John competent in semantics and an authority on unicorns). As far as adjectival quantifiers predicate only one argument and cardinal numbers are concerned, the (et) analysis works. However, Japanese quantificational adjectives predicate more than one argument. 1.2 Unspecified Number of Argument Since quantifiers in Japanese, which is a language without overt determiners, do not correspond to noun phrases as in English, (5) points out that the NPquantifier universal in (2) should be rejected. (3) U1 NP-Quantifier universal: “Every language has syntactic constituents (called noun-phrases) whose semantic function is to express generalized quantifiers over the domain of discourse.” (2,177) Even though Japanese generalized quantifiers do not correspond to noun phrases, (5) claims that quantification in Japanese is still based on a relation between two predicates. (8) further proposes that Japanese generalized quantifiers are relational. (4) a. (Tokyo-wa) (gakusei-ga) oi(E) Tokyo-top dog-nom many ‘There are many students in Tokyo’ b. (hitobito-wa) hotondo(E) (kaetteshimatta). people-top most went home-past ‘Most people have left’ 1 Weak quantifiers are admitted in there-sentences while strong quantifiers are not (6, 2). 2 (7) says that every NP and most NP cannot appear in the complement of consider. (i) Mary considers that two islands/*every island/*most islands. Proceedings of Logic and Engineering of Natural Language Semantics 2007 3 This analysis works as far as quantificational words take exactly two arguments. However, in arguably non-configurational language Japanese, the number of argument is not specified. (9) proposes generating sentences by means of phrase structure rule in (5):