LACL '97 Selected papers from the Second International Conference on Logical Aspects of Computational Linguistics
The Geometry of Information Retrieval
The Geometry of Information Retrieval
A Categorical Semantics of Quantum Protocols
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Toward discourse representation via pregroup grammars
Journal of Logic, Language and Information
Category theoretical semantics for pregroup grammars
LACL'05 Proceedings of the 5th international conference on Logical Aspects of Computational Linguistics
Clitic movement in pregroup grammar: a cross-linguistic approach
TbiLLC'09 Proceedings of the 8th international tbilisi conference on Logic, language, and computation
Experimental support for a categorical compositional distributional model of meaning
EMNLP '11 Proceedings of the Conference on Empirical Methods in Natural Language Processing
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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.