Analytical tableaux for da Costa's hierarchy of paraconsistent logics Cn, 1≤ n< ω


Authors
Itala Maria Loffredo D'Ottaviano
Universidade Estadual de Campinas
Abstract
In this paper we present a new hierarchy of analytical tableaux systems TNDC n, 1≤n<ω, for da Costa's hierarchy of propositional paraconsistent logics Cn, 1≤n<ω. In our tableaux formulation, we introduce da Costa's “ball” operator “o”, the generalized operators “k” and “”, for 1≤k, and the negations “~k”, for k≥1, as primitive operators, differently to what has been done in the literature, where these operators are usually defined operators. We prove a version of Cut Rule for the TNDC n, 1≤n<ω, and also prove that these systems are logically equivalent to the corresponding systems Cn, 1≤n<ω. The systems TNDC n constitute completely automated theorem proving systems for the systems of da Costa's hierarchy Cn, 1≤n<ω.
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DOI 10.3166/jancl.15.69-103
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References found in this work BETA

First-Order Logic.Raymond M. Smullyan - 1968 - New York [Etc.]Springer-Verlag.
Introduction to Metamathematics.Stephen Cole Kleene - 1968 - Journal of Symbolic Logic 33 (2):290-291.
First-Order Logic.Raymond M. Smullyan - 1975 - Journal of Symbolic Logic 40 (2):237-238.

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