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Connectives, Indeterminates, and Quantificational Variability

Kook-Hee Gill, Steve Harlow and George Tsoulas

This paper examines the distribution and interpretation of quantificational elements formed by the composition of indeterminate pronouns (wh words) and conjunction/disjunction denoting morphemes in Japanese, Korean and Malayalam.
The main focus is on the compositional derivation of the existential and universal semantics. We argue for a representation of indeterminate pronouns in terms of logical metavariables (variables ranging of variables - not variable types) which are subsequently "unpacked" by the conjunction/disjunction operator to infinite disjunctions or conjunctions. We use this conception to explain some surprising Korean facts, i.e. the fact that, unlike what is found crosslinguistically, the indeterminate, when combining with a disjunction morpheme yields a universal rather than an existential quantifier. We show that syntactically these Korean quantifiers include a head-internal relative clause which provides the necessary operator to bind the free variables resulting from the aforementioned "unpacking" operation. The operator in question (the iota operator) is an antiadditive function which by virtue of the second de Morgan Law, when it has a disjunction in its scope entails the corresponding conjunction. furthermore, we used the notion of unbound variables resulting from the unpacking operation to explain the polarity sensitivity of the conjunctive quantifiers.

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