Distributional Sentence Entailment Using Density Matrices

Abstract : 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.
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Mohammed Taghi Hajiaghayi; Mohammad Reza Mousavi. 1st International Conference on Theoretical Computer Science (TTCS), Aug 2015, Tehran, Iran. Lecture Notes in Computer Science, LNCS-9541, pp.1-22, 2016, Topics in Theoretical Computer Science. 〈10.1007/978-3-319-28678-5_1〉
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Esma Balkir, Mehrnoosh Sadrzadeh, Bob Coecke. Distributional Sentence Entailment Using Density Matrices. Mohammed Taghi Hajiaghayi; Mohammad Reza Mousavi. 1st International Conference on Theoretical Computer Science (TTCS), Aug 2015, Tehran, Iran. Lecture Notes in Computer Science, LNCS-9541, pp.1-22, 2016, Topics in Theoretical Computer Science. 〈10.1007/978-3-319-28678-5_1〉. 〈hal-01446260〉

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