Distributional Sentence Entailment Using Density Matrices

Categorical compositional distributional model of Coecke et al. (2010) 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.Comment: 11 page

A Generalised Quantifier Theory of Natural Language in Categorical Compositional Distributional Semantics with Bialgebras

Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier theory of natural language, due to Barwise and Cooper. The underlying setting is a compact closed category with bialgebras. We start from a generative grammar formalisation and develop an abstract categorical compositional semantics for it, then instantiate the abstract setting to sets and relations and to finite dimensional vector spaces and linear maps. We prove the equivalence of the relational instantiation to the truth theoretic semantics of generalised quantifiers. The vector space instantiation formalises the statistical usages of words and enables us to, for the first time, reason about quantified phrases and sentences compositionally in distributional semantics

Learning to distinguish hypernyms and co-hyponyms

This work is concerned with distinguishing different semantic relations which exist between distributionally similar words. We compare a novel approach based on training a linear Support Vector Machine on pairs of feature vectors with state-of-the-art methods based on distributional similarity. We show that the new supervised approach does better even when there is minimal information about the target words in the training data, giving a 15% reduction in error rate over unsupervised approaches

Distributional semantics beyond words: Supervised learning of analogy and paraphrase

There have been several efforts to extend distributional semantics beyond individual words, to measure the similarity of word pairs, phrases, and sentences (briefly, tuples; ordered sets of words, contiguous or noncontiguous). One way to extend beyond words is to compare two tuples using a function that combines pairwise similarities between the component words in the tuples. A strength of this approach is that it works with both relational similarity (analogy) and compositional similarity (paraphrase). However, past work required hand-coding the combination function for different tasks. The main contribution of this paper is that combination functions are generated by supervised learning. We achieve state-of-the-art results in measuring relational similarity between word pairs (SAT analogies and SemEval~2012 Task 2) and measuring compositional similarity between noun-modifier phrases and unigrams (multiple-choice paraphrase questions)