Формализация нестандартных отношений выводимости в паранепротиворечивой логике.

Abstract

Various classes of deducibility relations are considered. The classification of non-standard paraconsistent deducibility relations are presented. These relations are divided in seven disjoint classes on the base of three properties: "to be comlete with respect to deductions from consistent assumption' "to be transitive" and "to be closed under the rule of substitution". There is shown that paraconsistent relation of deducibility which has all these properties simultaneously does not exist. Two non-standard paraconsistent deducibility relations from different classes are formalized by means of sequent calculi. The first is sequent calculus of immediate entailment HB. The second is sequent calculus of blocked contradiction ЗП. A number of theorems about HB and ЗП are formulated showing their pecularities and interrelations with classical logic.