The nonmonotonic Gentzen deduction systems for the propositional logic

Cungen Cao, Yuefei Sui, Yuhui Wang


The traditional propositional logic is monotonic. With the same logical language as, the same valuation as and the validity of a sequent different from the traditional propositional logic, a propositional logic could be nonmonotonic. In this paper, the four Gentzen deduction systems G1,G2,G3,G4 and their dualities G1,G2,G3,G4 will be given which are proved to be sound and complete with respect to the four definitions and their dualities of the validity of sequents, among which one is traditional and others are variations of the traditional one. Moreover, G1, G3 are monotonic in both Г and Δ; and G2, G4 are monotonic in Г and nonmonotonic in Δ. Dually, G1, G3 are nonmonotonic in both Г and Δ; and G2, G4 are nonmonotonic in Г and monotonic in Δ.

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Artificial Intelligence Research

ISSN 1927-6974 (Print)   ISSN 1927-6982 (Online)

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