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Prime forms and minimal change in propositional belief bases

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Abstract

This paper proposes to use prime implicants and prime implicates normal forms to represent belief sets. This representation is used, on the one hand, to define syntactical versions of belief change operators that also satisfy the rationality postulates but present better complexity properties than those proposed in the literature and, on the other hand, to propose a new minimal distance that adopts as a minimal belief unit a “fact”, defined as a prime implicate of the belief set, instead of the usually adopted Hamming distance, i.e., the number of propositional symbols on which the models differ. Some experiments are also presented that show that this new minimal distance allows to define belief change operators that usually preserve more information of the original belief set.

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Authors and Affiliations

  1. Departamento de Ciência da Computação, Universidade Federal de Lavras, 37200-000, Lavras, MG, Brazil

    Jerusa Marchi

  2. Departamento de Automação e Sistemas, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, SC, Brazil

    Guilherme Bittencourt

  3. IRIT—Institut de Recherche en Informatique de Toulouse, Université de Toulouse, Université Toulouse 1 Capitole, 2 rue du Doyen Gabriel Marty, 31042, Toulouse Cedex 9, France

    Laurent Perrussel

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  1. Jerusa Marchi
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  2. Guilherme Bittencourt
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  3. Laurent Perrussel
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Correspondence to Jerusa Marchi.

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In memory of G. Bittencourt.

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Marchi, J., Bittencourt, G. & Perrussel, L. Prime forms and minimal change in propositional belief bases. Ann Math Artif Intell 59, 1–45 (2010). https://doi.org/10.1007/s10472-010-9206-x

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