Preller, A. & Sadrzadeh, M. J of Log Lang and Inf (2011) 20: 419. doi:10.1007/s10849-011-9132-2
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.
Compositional semanticsQuantum logicPregroup grammarsSemantic vector modelsSymmetric compact closed categoriesTwo-sorted functional first order logic