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A Polynomial Model for Logics with a Prime Power Number of Truth Values

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Abstract

This paper is concerned with a polynomial model (residue class ring) for a given q-valued propositional logic (where q is a power of a prime integer). This model allows to transfer logic problems into algebraic terms, resulting in an immediate computational approach to Knowledge Based Systems based on multi-valued logics. By means of this new approach, we have extended an already existent algebraic model to logics with a prime power number of truth values, while also getting more straightforward proofs and a more direct enunciation of the central theorem of this model.

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Authors and Affiliations

  1. Departamento de Sistemas Inteligentes Aplicados, Escuela Universitaria de Informática, Universidad Politécnica de Madrid, Madrid, Spain

    Antonio Hernando

  2. Departamento de Álgebra, Facultad de Educación, Universidad Complutense de Madrid, Madrid, Spain

    Eugenio Roanes-Lozano

  3. Departamento de Inteligencia Artificial, Facultad de Informática, Universidad Politécnica de Madrid, Madrid, Spain

    Luis M. Laita

Authors
  1. Antonio Hernando
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  2. Eugenio Roanes-Lozano
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  3. Luis M. Laita
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Correspondence to Antonio Hernando.

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Hernando, A., Roanes-Lozano, E. & Laita, L.M. A Polynomial Model for Logics with a Prime Power Number of Truth Values. J Autom Reasoning 46, 205–221 (2011). https://doi.org/10.1007/s10817-010-9191-0

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  • DOI: https://doi.org/10.1007/s10817-010-9191-0

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