The nonmonotonic Gentzen deduction systems for the propositional logic

Cungen Cao, Yuefei Sui, Yuhui Wang
2016 Artificial intelligence research  
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 G 1 , G 2 , G 3 , G 4 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
more » ... s traditional and others are variations of the traditional one. Moreover, G 1 , G 3 are monotonic in both Γ and ∆; and G 2 , G 4 are monotonic in Γ and nonmonotonic in ∆. Dually, G1, G3 are nonmonotonic in both Γ and ∆; and G2, G4 are nonmonotonic in Γ and monotonic in ∆.
doi:10.5430/air.v5n2p111 fatcat:lmnxxlposreapakgxiwaqkqbnq