An axiomatization of Wansing's expansion of Nelson's logic

Hitoshi Omori

Abstrakt

The present note o ers an axiomatization for an expansion of Nelson's logic motivated by Heinrich Wansing which serves as a base logic for the framework of nonmonotonic reasoning considered by Dov Gabbay and Raymond Turner. We also show that the expansion of Wansing is not conservative  intuitionistic logic, but at least as strong as Jankov's logic.

Słowa kluczowe: Nelson’s logic, intuitionistic logic, Jankov’s logic, nonmonotonic reasoning, axiomatization
References

D. M. Gabbay, Intuitionistic basis for non-monotonic logic, Proceedings of the 6th Conference on Automated Deduction, LNCS 138, Springer 1982, pp. 260{273.

N. Kamide and H. Wansing, Proof theory of Nelson's paraconsistent logic: A uniform perspective, Theoretical Computer Science 415 (2012), 1{38.

S. P. Odintsov, The Class of Extensions of Nelson Paraconsistent Logic, Studia Logica 80 (2005), 291{320.

R. Turner, Logics for arti cial intelligence, Ellis Horwood Ltd., 1985.

H. Wansing, Semantics-based Nonmonotonic Inference, Notre Dame Journal of For- mal Logic 36 (1995), 44{54.

H. Wansing, Negation, in: The Blackwell Guide to Philosophical Logic, L. Goble, Ed., Basil Blackwell Publishers, Cambridge/MA 2001, pp. 415{436.

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