The RM paraconsistent refutation system

Tomasz Skura

DOI: http://dx.doi.org/10.12775/LLP.2009.005

Abstract


The aim of this paper is to study the refutation system consisting of the refutation axiom p ∧ ¬p → q and the refutation rules: reverse substitution and reverse modus ponens (B/A, if A → B ∈ RM). It is shown that the refutation system is characteristic for the logic of the 3-element RM algebra.

Keywords


refutation systems; paraconsistent logic; relevance logic

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References


Dunn, J.M., “Algebraic completeness results for R-Mingle and its extensions”, Journal of Symbolic Logic 35 (1970): 1–13.

Łukasiewicz, J., Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic, Oxford, 1951.

Skura, T., “Maximality and refutability”, Notre Dame Journal of Formal Logic 45 (2004): 65–72.








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