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Conservative Retractions of Propositional Logic Theories by Means of Boolean Derivatives: Theoretical Foundations

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Intelligent Computer Mathematics (CICM 2009)

Abstract

We present a specialised (polynomial-based) rule for the propositional logic called the Independence Rule, which is useful to compute the conservative retractions of propositional logic theories. In this paper we show the soundness and completeness of the logical calculus based on this rule, as well as other applications. The rule is defined by means of a new kind of operator on propositional formulae. It is based on the boolean derivatives on the polynomial ring \({\mathbb F}_2[{\bf x}]\).

Partially supported by Minerva -Services in Mobility Platform- Project WeTeVe (2C/040) and Ayudas a grupos de investigación, Junta de Andalucí a (TIC 137).

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Aranda-Corral, G.A., Borrego-Díaz, J., Fernández-Lebrón, M.M. (2009). Conservative Retractions of Propositional Logic Theories by Means of Boolean Derivatives: Theoretical Foundations. In: Carette, J., Dixon, L., Coen, C.S., Watt, S.M. (eds) Intelligent Computer Mathematics. CICM 2009. Lecture Notes in Computer Science(), vol 5625. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02614-0_9

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  • DOI: https://doi.org/10.1007/978-3-642-02614-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

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