Semantic Vector Models and Functional Models for Pregroup Grammars
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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.
KeywordsCompositional semantics Quantum logic Pregroup grammars Semantic vector models Symmetric compact closed categories Two-sorted functional first order logic
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- Abramsky, S., & Coecke, B. (2004). A categorical semantics of quantum protocols. In Proceedings of the 19th annual IEEE symposium on logic in computer science, pp. 415–425.Google Scholar
- Benthem, J.v., & Doets, K. (1983). Higher-order logic. In Handbook of Philosophical Logic (pp. 275–329). Dordrecht: Reidel Publishing Company.Google Scholar
- Clarke, D. (2007). Context-theoretic Semantics for natural language, an algebraic framework, PhD thesis. U.K.: University of Sussex.Google Scholar
- Clark S.B.C., Sadrzadeh M. (2008) A compositional distributional model of meaning. In: Bruza W.L.P., van Rijsbergen J. (eds) Proceedings of conference on quantum interactions. University of Oxford, College PublicationsGoogle Scholar
- Clark, S., Coecke, B., Grefenstette, E., Pulman, S., & Sadrzadeh, M. (2010). Concrete compositional sentence spaces. In Compositionality and distributional semantic models, ESSLLI 2010.Google Scholar
- Lambek, J. (1993). From categorial grammar to bilinear logic. In Substructural logics (pp. 207–237). Oxford: Oxford University Press.Google Scholar
- Lambek J. (2008) From word to sentence. Polimetrica, MilanoGoogle Scholar
- Preller, A. (2005). Category theoretical semantics for pregroup grammars. In P. Blache, E. Stabler (Eds.), Logical aspects of computational linguistics (vol. 3492, pp. 254–270). of Lecture Notes in Artificial Intelligence.Google Scholar
- Preller, A., & Prince, V. (2010). Quantum logic unites compositional functional semantics and distributional semantic models. In Compositionality and distributional semantic models, ESSLLI 2010.Google Scholar
- Preller, A., & Sadrzadeh, M. (2009). Bell states and negated sentences in the distributed model of meaning. In 6th Workshop on quantum physics and logic.Google Scholar
- Sadrzadeh, M. (2007). High-level quantum structures in linguistics and multi-agent systems. In AAAI spring symposium on quantum interactions.Google Scholar