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Logic and Logical Philosophy

Logic of classical refutability and class of extensions of minimal logic
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Logic of classical refutability and class of extensions of minimal logic

Authors

  • Sergei P. Odintsov Sobolev Institute of Mathematics, Novosibirsk

DOI:

https://doi.org/10.12775/LLP.2001.006

Abstract

This article continues the investigation of paraconsistent extensions of minimal logic Lj started in [6, 7]. The name “logic of classical refutability” is taken from the H.Curry monograph [1], where it denotes the logic Le obtained from Lj by adding the Peirce law.

References

Curry, H.B., Foundations of Mathematical Logic, McGrow-Hill Book Company, New York, 1963.

Grzegorczyk, A., “A philosophically plausible formal interpretation of intuitionistic logic”, Indagationes Mathematicæ 26, No. 5, 596–601 (1964).

Kanger, S., “A note on partial postulate sets for propositional logic”, Theoria 21, 99–104 (1955).

Karpenko, A.S., “Two three-valued isomorphs of classical propositional logic and their combinations”, First World Congress on Paraconsistency, Abstracts, Ghent, 92–94 (1997).

Kripke, S., “The system LE”, unpublished.

Odintsov, S.P., “Maximal paraconsistent extension of Johansson logic”, First World Congress on Paraconsistency, Abstracts, Ghent, 111–113 (1997).

Odintsov, S.P., “Isomorphs of the logic of classical refutability and their generalizations”, Proceedings of the seminar of logical center, Inst. of Philosophy of RAS, Moscow, 1998.

Odintsov, S.P., “Maximal paraconsistent extension of Johansson logic”, to appear in Proceedings of First World Congress on Paraconsistency.

Rasiowa, H., An Algebraic Approach to Non-Classical Logics, Amsterdam, North-Holland, 1974.

Rautenberg, W., Klassische und nichtclassische Aussagenlogik, Braunschweig, Vieweg, 1979.

Segerberg, K., “Propositional logics related to Heyting’s and Johansson’s”, Theoria 34, 26–61 (1968).

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Published

2004-01-19

How to Cite

1.
ODINTSOV, Sergei P. Logic of classical refutability and class of extensions of minimal logic. Logic and Logical Philosophy [online]. 19 January 2004, T. 9, nr 9, s. 91–107. [accessed 28.3.2023]. DOI 10.12775/LLP.2001.006.
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No. 9 (2001)

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