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Word vectors and quantum logic: Experiments with negation and disjunction
 In Proceedings of the 8th Mathematics of Language Conference
, 2003
"... A calculus which combined the flexible geometric structure of vector models with the crisp efficiency of Boolean logic would be extremely beneficial for modelling natural language. With this goal in mind, we present a formulation for logical connectives in vector spaces based on standard linear alge ..."
Abstract

Cited by 25 (3 self)
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A calculus which combined the flexible geometric structure of vector models with the crisp efficiency of Boolean logic would be extremely beneficial for modelling natural language. With this goal in mind, we present a formulation for logical connectives in vector spaces based on standard linear algebra, giving examples of the use of vector negation to discriminate between different senses of ambiguous words. It turns out that the operators developed in this way are precisely the connectives of quantum logic (Birkhoff and von Neumann, 1936), which to our knowledge have not been exploited before in natural language processing. In quantum logic, arbitrary sets are replaced by linear subspaces of a vector space, and set unions, intersections and complements are replaced by vector sum, intersection and orthogonal complements of subspaces. We demonstrate that these logical connectives (particularly the orthogonal complement for negation) are powerful tools for exploring and analysing word meanings and show distinct advantages over Boolean operators in document retrieval experiments. This paper is organised as follows. In Section 0.1 we describe some of the ways vectors have been used to represent the meanings of terms and documents in natural language processing, and describe the way the WORDSPACE used in our later experiments is built automatically from text corpora. In Section 0.2 we define the logical connectives on vector spaces, focussing particularly on negation and disjunction. This introduces the basic material needed to understand the worked
Structured information retrieval and quantum theory
 In QI ’09
, 2009
"... Abstract. Information Retrieval (IR) systems try to identify documents relevant to user queries, which are representations of user information needs. Interaction, context, and document structure are three important and active themes in IR research. We present how we propose to model the task of Stru ..."
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Cited by 4 (2 self)
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Abstract. Information Retrieval (IR) systems try to identify documents relevant to user queries, which are representations of user information needs. Interaction, context, and document structure are three important and active themes in IR research. We present how we propose to model the task of Structured IR (SIR) based on a QT inspired framework, with a focus on how to exploit user contextual information and user interaction in the search process. 1
Word Vectors and Quantum Logic: Experiments with negation and disjunction
, 2003
"... A calculus which combined the flexible geometric structure of vector models with the crisp efficiency of Boolean logic would be extremely beneficial for modelling natural language. With this goal in mind, we present a formulation for logical connectives in vector spaces based on standard linear alge ..."
Abstract
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A calculus which combined the flexible geometric structure of vector models with the crisp efficiency of Boolean logic would be extremely beneficial for modelling natural language. With this goal in mind, we present a formulation for logical connectives in vector spaces based on standard linear algebra, giving examples of the use of vector negation to discriminate between different senses of ambiguous words. It turns out that the operators developed in this way are precisely the connectives of quantum logic \citep{birkhofflogic}, which to our knowledge have not been exploited before in natural language processing.
Quantum Logic of Word Meanings: Concept Lattices in Vector Space Models
, 2003
"... This paper systematically develops the logical and algebraic possibilities inherent in vector space models for language, considerably beyond those which are customarily used in semantic applications such as information retrieval and word sense disambiguation. The cornerstone of the approach lies in ..."
Abstract
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This paper systematically develops the logical and algebraic possibilities inherent in vector space models for language, considerably beyond those which are customarily used in semantic applications such as information retrieval and word sense disambiguation. The cornerstone of the approach lies in a simple implementation of the connectives of quantum logic as introduced by Birkho# and von Neumann (1936), which defines the negation of a concept as the projection onto its orthogonal subspace, and the disjunction and conjunction of two concepts as the vector sum and intersection of their subspaces. This enables us to use the full lattice structure of a vector space, bringing these models much closer to traditional semantic lattice representations such as taxonomic concept hierarchies.