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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.

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Authors and Affiliations

  1. LIRMM-CNRS, Montpellier, France

    Anne Preller

  2. Computing Laboratory, Oxford, UK

    Mehrnoosh Sadrzadeh

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  1. Anne Preller
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  2. Mehrnoosh Sadrzadeh
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Correspondence to Anne Preller.

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Preller, A., Sadrzadeh, M. Semantic Vector Models and Functional Models for Pregroup Grammars. J of Log Lang and Inf 20, 419–443 (2011). https://doi.org/10.1007/s10849-011-9132-2

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