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. 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. 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') 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.