A Context-theoretic Framework for Compositionality in Distributional Semantics

Techniques in which words are represented as vectors have proved useful in many applications in computational linguistics, however there is currently no general semantic formalism for representing meaning in terms of vectors. We present a framework for natural language semantics in which words, phrases and sentences are all represented as vectors, based on a theoretical analysis which assumes that meaning is determined by context. In the theoretical analysis, we define a corpus model as a mathematical abstraction of a text corpus. The meaning of a string of words is assumed to be a vector representing the contexts in which it occurs in the corpus model. Based on this assumption, we can show that the vector representations of words can be considered as elements of an algebra over a field. We note that in applications of vector spaces to representing meanings of words there is an underlying lattice structure; we interpret the partial ordering of the lattice as describing entailment between meanings. We also define the context-theoretic probability of a string, and, based on this and the lattice structure, a degree of entailment between strings. We relate the framework to existing methods of composing vector-based representations of meaning, and show that our approach generalises many of these, including vector addition, component-wise multiplication, and the tensor product.Comment: Submitted to Computational Linguistics on 20th January 2010 for revie

Corpus Analysis and Lexical Pragmatics: An Overview

Lexical pragmatics studies the processes by which lexically encoded meanings are modified in use; well-studied examples include lexical narrowing, approximation and metaphorical extension. Relevance theorists have been trying to develop a unitary account on which narrowing, approximation and metaphorical extension are all explained in the same way. While there have been several corpus-based studies of metaphor and a few of hyperbole or approximation, there has been no attempt so far to test the unitary account using corpus data. This paper reports the results of a corpus-based investigation of lexical-pragmatic processes, and discusses the theoretical issues and challenges it raises

A Proof-Theoretic Approach to Scope Ambiguity in Compositional Vector Space Models

We investigate the extent to which compositional vector space models can be used to account for scope ambiguity in quantified sentences (of the form "Every man loves some woman"). Such sentences containing two quantifiers introduce two readings, a direct scope reading and an inverse scope reading. This ambiguity has been treated in a vector space model using bialgebras by (Hedges and Sadrzadeh, 2016) and (Sadrzadeh, 2016), though without an explanation of the mechanism by which the ambiguity arises. We combine a polarised focussed sequent calculus for the non-associative Lambek calculus NL, as described in (Moortgat and Moot, 2011), with the vector based approach to quantifier scope ambiguity. In particular, we establish a procedure for obtaining a vector space model for quantifier scope ambiguity in a derivational way.Comment: This is a preprint of a paper to appear in: Journal of Language Modelling, 201

On embedded implicatures

The Gricean approach explains implicatures by assumptions about the pragmatics of entire utterances. The phenomenon of embedded implicatures remains a challenge for this approach since in such cases apparently implicatures contribute to the truth-conditional content of constituents smaller than utterances. In this paper, I investigate three areas where embedded implicatures seem to differ from implicatures at the utterance level: optionality, epistemic status, and implicated presuppositions. I conclude that the differences between the two kinds of implicatures justify an approach that maintains Gricean assumptions at the utterance level, and assumes a special operator for embedded implicatures

Language and scientific explanation: Where does semantics fit in?

This book discusses the two main construals of the explanatory goals of semantic theories. The first, externalist conception, understands semantic theories in terms of a hermeneutic and interpretive explanatory project. The second, internalist conception, understands semantic theories in terms of the psychological mechanisms in virtue of which meanings are generated. It is argued that a fruitful scientific explanation is one that aims to uncover the underlying mechanisms in virtue of which the observable phenomena are made possible, and that a scientific semantics should be doing just that. If this is the case, then a scientific semantics is unlikely to be externalist, for reasons having to do with the subject matter and form of externalist theories. It is argued that semantics construed hermeneutically is nevertheless a valuable explanatory project

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

Plurals: individuals and sets in a richly typed semantics

We developed a type-theoretical framework for natural lan- guage semantics that, in addition to the usual Montagovian treatment of compositional semantics, includes a treatment of some phenomena of lex- ical semantic: coercions, meaning, transfers, (in)felicitous co-predication. In this setting we see how the various readings of plurals (collective, dis- tributive, coverings,...) can be modelled