Paraconsistent logic

Under paraconsistent logics and logics Parainkonsistenten refers calculi in which the logical principle contradictione ex quodlibet sequitur (Latin for " from a contradiction follows Any " ) does not apply where it is therefore not possible from two contradictory statements A, ¬ A or from a contradiction a ∧ ¬ A infer any statement.

Different systems para consistent logics

There are four directions:

• The Australian (Graham Priest, Richard Sylvan, etc.)
• The / Brazilian, for the work of Newton da Costa are central South America,
• The Belgian ( among others Diderik Batens ) and
• Polish ( influenced by Stanisław Jaskowski ).

In the Australian school ( cf. Priest, Tanaka ) the Dialeth ( e) ism takes a central position. As Dialeth ( e) ism, the view is referred to, that there are true contradictions. The other representatives para consistent logics do not share this view.

Be differences

• Non- adjunctive systems,
• Non-truth- functional systems,
• Multi-valued paraconsistent logics and
• Relevance logics.

Non- adjunctive systems of Stanisław Jaskowski ( Lvov -Warsaw School ) as part of the calculus of natural deduction systems developed calculi in which the following rule for the introduction of the conjunction is missing:

In particular, it follows from the two mutually contradictory statements and not the contradiction in a statement. This discursive ( discus immersive ) logic states in an interpretation Jaśkowskis that parties can be quiet contradictory opinion, because that does not means that an interlocutor contradicts himself.