%0 Conference Proceedings
%T Distributional Sentence Entailment Using Density Matrices
%+ Queen Mary University of London (QMUL)
%+ University of Oxford
%A Balkir, Esma
%A Sadrzadeh, Mehrnoosh
%A Coecke, Bob
%< avec comité de lecture
%( Lecture Notes in Computer Science
%B 1st International Conference on Theoretical Computer Science (TTCS)
%C Tehran, Iran
%Y Mohammed Taghi Hajiaghayi
%Y Mohammad Reza Mousavi
%3 Topics in Theoretical Computer Science
%V LNCS-9541
%P 1-22
%8 2015-08-26
%D 2015
%R 10.1007/978-3-319-28678-5_1
%Z Computer Science [cs]Conference papers
%X Categorical compositional distributional model of Clark, Coecke, and Sadrzadeh suggests a way to combine grammatical composition of the formal, type logical models with the corpus based, empirical word representations of distributional semantics. This paper contributes to the project by expanding the model to also capture entailment relations. This is achieved by extending the representations of words from points in meaning space to density operators, which are probability distributions on the subspaces of the space. A symmetric measure of similarity and an asymmetric measure of entailment is defined, where lexical entailment is measured using von Neumann entropy, the quantum variant of Kullback-Leibler divergence. Lexical entailment, combined with the composition map on word representations, provides a method to obtain entailment relations on the level of sentences. Truth theoretic and corpus-based examples are provided.
%G English
%Z TC 1
%Z WG 1.8
%2 https://inria.hal.science/hal-01446260/document
%2 https://inria.hal.science/hal-01446260/file/385217_1_En_1_Chapter.pdf
%L hal-01446260
%U https://inria.hal.science/hal-01446260
%~ IFIP-LNCS
%~ IFIP
%~ IFIP-TC
%~ IFIP-TC1
%~ IFIP-LNCS-9541
%~ IFIP-WG1-8
%~ IFIP-TTCS