Refutations in Wansing’s Logic

Tomasz Skura

Abstrakt

A refutation system for Wansing's logicW(which is an expansion of Nelson's logic) is given. The refutation system provides an efficient decision procedure for W. The procedure consists in constructing for any normal form a finite syntactic tree with the property that the origin is non-valid if some end node is non-valid. The finite model property is also established.

Słowa kluczowe: Nelson’s logic, nonmonotonic inference, decision procedures, refutation systems
References

[1] Y. Gurevich, Intuitionistic logic with strong negation, Studia Logica 36 (1977), 49-59.

[2] S. P. Odintsov, Constructive Negations and Paraconsistency, Springer, Dordrecht, 2008.

[3] H. Omori, An axiomatization of Wansing's expansion of Nelson's logic, Reports on Mathematical Logic 50 (2015), 41-51.

[4] H. Omori, A note on Wansing's expansion of Nelson's logic - a correction to "An axiomatization of Wansing's expansion of Nelson's logic", Reports on Mathematical Logic 51 (2016), 133-144.

[5] T. Skura, Refutation systems in propositional logic, Handbook of Philosophical Logic 16 (2011), 115-157.

[6] T. Skura, Refutation Methods in Modal Propositional Logic, Semper, Warszawa, 2013.

[7] H. Wansing, Semantics-based nonmonotonic inference, Notre Dame Journal of Formal Logic 36 (1995), 44-54.

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