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arXiv:quant-ph/0309022 · Journal of Physics A Mathematical and General

Quantum aspects of semantic analysis and symbolic artificial intelligence

Diederik Aerts, Marek Czachor

Published Mar 9, 2004• 137 citations
arXivHTMLPDF

Abstract

Modern approaches to semantic analysis if reformulated as Hilbert-space problems reveal formal structures known from quantum mechanics. A similar situation is found in distributed representations of cognitive structures developed for the purpose of neural networks. We take a closer look at similarities and differences between the above two fields and quantum information theory.

DOI
10.1088/0305-4470/37/12/l01

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Modern approaches to semantic analysis if reformulated as Hilbert-space problems reveal formal structures known from quantum mechanics. A similar situation is found in distributed representations of cognitive structures developed for the purpose of neural networks. We take a closer look at similarities and differences between the above two fields and quantum information theory.
The mathematical formalism of quantum mechanics has been successfully employed in the last years to model situations in which the use of classical structures gives rise to problematical situations, and where typically quantum effects, such as 'contextuality' and 'entanglement', have been recognized. This 'Quantum Interaction Approach' is briefly reviewed in this paper focusing, in particular, on the quantum models that have been elaborated to describe how concepts combine in cognitive science, and on the ensuing identification of a quantum structure in human thought. We point out that these results provide interesting insights toward the development of a unified theory for meaning and knowledge formalization and representation. Then, we analyze the technological aspects and implications of our approach, and a particular attention is devoted to the connections with symbolic artificial intelligence, quantum computation and robotics.
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This article is an exploratory account of the the non-monotonic behaviour of conceptual associations in the light of context. Computational approximations of conceptual space are furnished by semantic space models which are emerging from the fields of cognition and computational linguistics. Semantic space models not only provide a cognitively motivated basis to underpin human practical reasoning, but from a mathematical perspective, they are real-valued Hilbert spaces. This introduces the highly speculative prospect of formalizing aspects of human practical reasoning via quantum mechanics. This account focuses on how to formalize context effects in relation to concepts as well as keeping an eye on operational issues.
Nowadays quantum models became very applicable in artificial intelligence development. Mathematical basis of quantum mechanics allows its well use for tasks of cognitive informatics: conceptual analysis, learning and information retrieval. For farther development of concepts formation, learning, and information retrieval technologies utilization of quantum methods of contextuality and entanglement, interference, quantum range and semantic similarity are very important: they introduced the new step in information science and technology. In presented paper some methods and tools of quantum information technologies are observed. On the basis of quantum interactions concepts formation and their properties within information retrieval tasks were investigated.
The study of computational processes based on the laws of quantum mechanics has led to the discovery of new algorithms, cryptographic techniques, and communication primitives. This book explores quantum computation from the perspective of the branch of theoretical computer science known as semantics, as an alternative to the more well-known studies of algorithmics, complexity theory, and information theory. It collects chapters from leading researchers in the field, discussing the theory of quantum programming languages, logics and tools for reasoning about quantum systems, and novel approaches to the foundations of quantum mechanics. This book is suitable for graduate students and researchers in quantum information and computation, as well as those in semantics, who want to learn about a new field arising from the application of semantic techniques to quantum information and computation.