Inferential paraconsistency

Grzegorz Malinowski
2004 Logic and Logical Philosophy  
Paraconsistent logics settle the basis for inconsistent but not trivial theories. Usually they are constructed as systems of theorems and rules, defining non explosive consequence relations : a consequence is explosive whenever from any set {α, ¬α} of contradictory formulas any other formula β follows, {α, ¬α} β, cf. [6] . Most aften paraconsistency is involved by the set of theorems or tautologies of a logic constructed or "rediscovered" for that purpose. Thus, it reflexes only in internal
more » ... nly in internal quality of the logic. The paper aims to show that paraconsistency can be generated outside of a system as a property of the inference. The gist of the proposal is the application of the so-called q-consequence, a special generalisation of Tarski consequence, cf. [3] . The actual q-extension of the three-valued Łukasiewicz logic results in a paraconsistent version of Ł 3 . Moreover, it leads to a natural dualisation of the q-consequence and thus the concept of paraconsistency. The discussion on the last question will perhaps also subscribe to the dispute whether the term parainconsistency is not more appropriate than paraconsistency in reference to the property so widely considered in the literature.
doi:10.12775/llp.2000.005 fatcat:acua4jpypvacddn3je2iu3y56q