, Volume 20, Issue 4, pp 419-443
Date: 01 Apr 2011

Semantic Vector Models and Functional Models for Pregroup Grammars

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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.