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paraconsistent logic
A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing paraconsistent (or "inconsistency-tolerant") systems of logic.
Inconsistency-tolerant logics have been discussed since at least 1910 (and arguably much earlier, for example in the writings of Aristotle); however, the term ''paraconsistent'' ("beside the consistent") was not coined until 1976, by the Peruvian philosopher Francisco Miró Quesada.〔Priest (2002), p. 288 and §3.3.〕
==Definition==
In classical logic (as well as intuitionistic logic and most other logics), contradictions entail everything. This curious feature, known as the principle of explosion or ''ex contradictione sequitur quodlibet'' (Latin, "from a contradiction, anything follows")〔Carnielli, W. and Marcos, J. (2001) ("Ex contradictione non sequitur quodlibet" ) ''Proc. 2nd Conf. on Reasoning and Logic'' (Bucharest, July 2000)〕 can be expressed formally as
Which means: if ''P'' and its negation ¬''P'' are both assumed to be true, then ''P'' is assumed to be true, from which it follows that at least one of the claims ''P'' and some other (arbitrary) claim ''A'' is true. However, if we know that either ''P'' or ''A'' is true, and also that ''P'' is not true (that ¬''P'' is true) we can conclude that ''A'', which could be anything, is true. Thus if a theory contains a single inconsistency, it is trivial—that is, it has every sentence as a theorem. The characteristic or defining feature of a paraconsistent logic is that it rejects the principle of explosion. As a result, paraconsistent logics, unlike classical and other logics, can be used to formalize inconsistent but non-trivial theories.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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