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Proving contradictions in formal theories. I. (English. Russian original) Zbl 0532.03007
Autom. Remote Control 44, No. 6, 781-790 (1983); translation from Avtom. Telemekh. 1983, No. 6, 113-124 (1983).
Summary: We consider the construction of logical calculi capable of proving contradictions in formal theories. The work is published in two parts. Part I considers the characteristic features of the logic of inconsistent systems (”paraconsistent logic”) in which contradictions are provable. A propositional calculus PCont (for ”contradiction”) and some extensions of this calculus are constructed. A criterion for derivability of formulas in PCont is established and some propositions concerning the relationship between PCont and classical logic are given.

MSC:
03B60 Other nonclassical logic
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