13 Facts About Paraconsistent logic

Paraconsistent logic is an attempt at a logical system to deal with contradictions in a discriminating way.

Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing "inconsistency-tolerant" systems of logic which reject the principle of explosion.

In some sense, then, paraconsistent logic is more conservative or cautious than classical logic.

Primary motivation for paraconsistent logic is the conviction that it ought to be possible to reason with inconsistent information in a controlled and discriminating way.

Paraconsistent logic makes it possible to distinguish between inconsistent theories and to reason with them.

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Research into paraconsistent logic has led to the establishment of the philosophical school of dialetheism, which asserts that true contradictions exist in reality, for example groups of people holding opposing views on various moral issues.

One well-known system of paraconsistent logic is the system known as LP, first proposed by the Argentinian logician Florencio Gonzalez Asenjo in 1966 and later popularized by Priest and others.

Intuitionistic logic allows A ? ¬A not to be equivalent to true, while paraconsistent logic allows A ? ¬A not to be equivalent to false.

However, intuitionistic logic is a specific logical system whereas paraconsistent logic encompasses a large class of systems.

Accordingly, the dual notion to paraconsistency is called paracompleteness, and the "dual" of intuitionistic logic is a specific paraconsistent system called anti-intuitionistic or dual-intuitionistic logic.

Every tautology of paraconsistent logic is a tautology of classical logic.

Any tautology of classical logic which contains no negations is a tautology of paraconsistent logic.

Paraconsistent logic has been applied as a means of managing inconsistency in numerous domains, including:.