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arXiv:0802.1738

Characterising through Erasing: A Theoretical Framework for Representing Documents Inspired by Quantum Theory

Álvaro Francisco Huertas-Rosero, Leif A. Azzopardi, C. J. van Rijsbergen

Published Feb 12, 2008• 13 citations
arXivHTMLPDF

Abstract

The problem of representing text documents within an Information Retrieval system is formulated as an analogy to the problem of representing the quantum states of a physical system. Lexical measurements of text are proposed as a way of representing documents which are akin to physical measurements on quantum states. Consequently, the representation of the text is only known after measurements have been made, and because the process of measuring may destroy parts of the text, the document is characterised through erasure. The mathematical foundations of such a quantum representation of text are provided in this position paper as a starting point for indexing and retrieval within a ``quantum like'' Information Retrieval system.

DOI
10.48550/arxiv.0802.1738

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The problem of representing text documents within an Information Retrieval system is formulated as an analogy to the problem of representing the quantum states of a physical system. Lexical measurements of text are proposed as a way of representing documents which are akin to physical measurements on quantum states. Consequently, the representation of the text is only known after measurements have been made, and because the process of measuring may destroy parts of the text, the document is characterised through erasure. The mathematical foundations of such a quantum representation of text are provided in this position paper as a starting point for indexing and retrieval within a ``quantum like'' Information Retrieval system.
The problem of representing text documents within an Information Retrieval system is formulated as an analogy to the problem of representing the quantum states of a physical system. Lexical measurements on text are proposed as a way of representing documents which is akin to physical measurements on quantum states. The representation of the text is only known after measurements have been made, and because the process of measuring may destroy parts of the text, the document is characterised through erasure. These so called “Selective Erasers” provide the basis for representation [1]. During my presentation, the mathematical foundations of such a quantum representation of text will be presented and discussed in the context of indexing and retrieval within a “quantum like” Information Retrieval system. The presentation will then outline the various directions for future work using Selective Erasers.
Purpose The paper aims to provide a semiotic interpretation of the role played by entanglement in quantum-based models aimed to information retrieval and suggests possible improvements. Actual models are capable of retrieving documents relevant to a query composed of a keyword and its acceptation expressed by a given context. The paper also considers some analogies between this technique and quantum-based approaches in other disciplines to discuss the consequence of this quantum turn, as epistemology and philosophy of language are concerned. Design/methodology/approach We use quantum geometry to design a formal model for textual semiotics. In particular, the authors refer to Greimas’s work on semantics and information theory, to Eco’s writings on semantic memory and to Lotman’s work on a cybernetic notion of culture. Findings Quantum approaches imply a particular point of view on meaning. Meaning is not a real, positive quality of a given word. It is a net of relations constructed in the text, whose value is progressively determined during the reading process. Furthermore, reading is not a neutral operation: to read is to determine meaning. If it is said that, from a general semiotic point of view, meaning is stored in quantum semantic memories and is read/written by semantic machines, then the operation of “reading/writing” is analogous to the operation of measuring in quantum theory: in other terms, meaning is a value, and this implies an instance (not necessarily human) according to which values are valuable. Research limitations/implications The authors are not proposing a complete quantum semantics. At the present, quantum information retrieval can detect the presence of semantic relations. The authors suggest a way to characterize them, leaving open the problem on how to formalize the document as a vector in four-state semantic space. Practical implications A quantum turn shows deep semiotic implications on the approach to language, which shows an immanent semantic organization not reducible to syntax and morphology. This organization is probabilistic and indeterministic and explains to what extent text fixes the meaning of its lexical units. Social implications In the authors’ perspective, signification is not the exclusivity of a human subject. Criticizing Turing test, the great semiotic and cybernetic scholar Jurij Lotman wrote that if we identify “intelligent” and “human”, we raise the failings of an actual form of intelligence to the rank of an essential characteristic. On this line, meaning is considered as a feature of social, artificial and biological systems. Originality/value The adoption of quantum formalism seems in line with cybernetic framework, involving a probabilistic, non-cartesian point of view on meaning aimed to critically discuss the human–machine relation. Furthermore, Quantum theory (QT) implies a phenomenological point of view on the conditions of possibility of meaning.
In this paper we introduce a formalization of Logical Imaging applied to IR in terms of Quantum Theory through the use of an analogy between states of a quantum system and terms in text documents. Our formalization relies upon the Schrodinger Picture, creating an analogy between the dynamics of a physical system and the kinematics of probabilities generated by Logical Imaging. By using Quantum Theory, it is possible to model more precisely contextual information in a seamless and principled fashion within the Logical Imaging process. While further work is needed to empirically validate this, the foundations for doing so are provided.
The mathematical formalism of quantum theory has been successfully used in human cognition to model decision processes and to deliver representations of human knowledge. As such, quantum cognition inspired tools have improved technologies for Natural Language Processing and Information Retrieval. In this paper, we overview the quantum cognition approach developed in our Brussels team during the last two decades, specifically our identification of quantum structures in human concepts and language, and the modeling of data from psychological and corpus-text-based experiments. We discuss our quantum-theoretic framework for concepts and their conjunctions/disjunctions in a Fock-Hilbert space structure, adequately modeling a large amount of data collected on concept combinations. Inspired by this modeling, we put forward elements for a quantum contextual and meaning-based approach to information technologies in which 'entities of meaning' are inversely reconstructed from texts, which are considered as traces of these entities' states.
The article considers the epistemology of quantum phenomena and the quantum eraser experiments as reflecting certain essential features of these phenomena, and uses these experiments to introduce a new concept, that of ‘erasure’. This concept is defined by the fact that a given quantum measurement destroys, ‘erases’, the usefulness of actual or even possible information associated with a given quantum system prior to this measurement, for the purposes of predictions concerning the experiments performed on this system after this measurement. The concept of ‘erasure’ allows one to capture certain fundamental aspects of quantum phenomena more sharply than previously, and to differentiate classical and quantum phenomena, and theories in a new way.