Semantic Vector Models and Functional Models for Pregroup Grammars.

Journal article

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. © 2011 Springer Science+Business Media B.V.

Authors: Preller, A; Sadrzadeh, M

• Journal: Journal of Logic, Language and Information
• Volume: 20
• Issue: 4
• Pages: 419-443
• Publication date: 2011-01-01
• DOI: 10.1007/s10849-011-9132-2
• EISSN: 1572-9583
• ISSN: 0925-8531
• Language: English
• Keywords: Two-sorted functional first order logic; Quantum logic; Symmetric compact closed categories; Semantic vector models; Compositional semantics; Pregroup grammars