Hierarquias de sistemas de dedução natural e de sistemas de tableaux analiticos para os sistemas Cn de da Costa

AUTOR(ES)
DATA DE PUBLICAÇÃO

2004

RESUMO

In this work, we introduce the hierarchy of propositional natural deduction systems DNCn, 1≤n≤ω, and the hierarchy of quantificational natural deduction systems DNCn*, 1≤n≤ω. We prove that each one of the systems of the hierarchies is equivalent to the corresponding system of the hierarchy of da Costa´s propositional paraconsistent calculi Cn, 1≤n≤ω, and the hierarchy of da Costa´s quan-tificational paraconsistent calculi Cn*, 1≤n≤ω. We prove a Normalization Theorem, à la Fitch, and a Subformula Property for the systems DNCn and DNCn*, 1≤n≤ω. We introduce the hierarchy of analytical tableaux systems TNDCn, 1≤n<ω, in which da Costa´s “ball” operator “o”, the generalized operators “k”, “(k)”, 1≤k, and the negations “∼k”, k≥1, are primitive operators, differently to what has been done in the literature. We prove a version of Cut Rule for these systems, and prove that each one of these systems is equivalent to the corresponding system Cn, 1≤n<ω. The systems TNDCn constitute automated theorem proving systems for the sys-tems of da Costa s hierarchy Cn, 1≤n<ω.

ASSUNTO(S)

logica simbolica e matematica logica de primeira ordem logica logica matematica não-classica

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