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Cut elimination, identity elimination, and interpolation in super-Belnap logics. (arXiv:1803.03822v1 [math.LO])

来源于:arXiv
We develop a Gentzen-style proof theory for super-Belnap logics (extensions of the four-valued Dunn-Belnap logic), expanding on an approach initiated by Pynko. We show that just like substructural logics may be understood proof-theoretically as logics which relax the structural rules of classical logic but keep its logical rules as well as the rules of Identity and Cut, super-Belnap logics may be seen as logics which relax Identity and Cut but keep the logical rules as well as the structural rules of classical logic. A generalization of the cut elimination theorem for classical propositional logic is then proved and used to establish interpolation for various super-Belnap logics. In particular, we obtain an alternative syntactic proof of a refinement of the Craig interpolation theorem for classical propositional logic discovered recently by Milne. 查看全文>>