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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DOI 10.1007/s10849-011-9132-2
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The Mathematics of Sentence Structure.Joachim Lambek - 1968 - Journal of Symbolic Logic 33 (4):627-628.
Toward Discourse Representation Via Pregroup Grammars.Anne Preller - 2007 - Journal of Logic, Language and Information 16 (2):173-194.
The Emergence of Syntactic Structure.Marcus Kracht - 2007 - Linguistics and Philosophy 30 (1):47 - 95.

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