Semantic Vector Models and Functional Models for Pregroup Grammars

Abstract
We show that vector space semantics and functional semantics in two-sorted first order logic are equivalent for pregroup grammars. We present an algorithm that translates functional expressions to vector expressions and vice-versa. The semantics is compositional, variable free and invariant under change of order or multiplicity. It includes the semantic vector models of Information Retrieval Systems and has an interior logic admitting a comprehension schema. A sentence is true in the interior logic if and only if the ‘usual’ first order formula translating the sentence holds. The examples include negation, universal quantifiers and relative pronouns.
Keywords Compositional semantics  Quantum logic  Pregroup grammars  Semantic vector models  Symmetric compact closed categories  Two-sorted functional first order logic
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    References found in this work BETA
    Marcus Kracht (2007). The Emergence of Syntactic Structure. Linguistics and Philosophy 30 (1):47 - 95.
    Anne Preller (2007). Toward Discourse Representation Via Pregroup Grammars. Journal of Logic, Language and Information 16 (2):173-194.
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    Similar books and articles
    Anne Preller (2007). Toward Discourse Representation Via Pregroup Grammars. Journal of Logic, Language and Information 16 (2):173-194.
    J. Lambek (2008). Pregroup Grammars and Chomsky's Earliest Examples. Journal of Logic, Language and Information 17 (2):141-160.
    Johan van Benthem (2005). Guards, Bounds, and Generalized Semantics. Journal of Logic, Language and Information 14 (3):263-279.
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