THE DISJUNCTION PROPERTY IN THE CLASS OF PARACONSISTENT EXTENSIONS OF MINIMAL LOGIC

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Abstract

We consider the disjunction property, DP, in the class of extensions of minimal logic Lj. Conditions are described under which DP is translated from the class PAR of properly paraconsistent extensions of the logics of class Lj into the class INT of intermediate extensions and the class NEG of negative extensions, and conditions for its being translated back into PAR. The logic LF in PAR, which specifies conditions for DP to be translated from PAR into NEG, is defined and is characterized in terms of j-algebras and Kripke frames. Moreover, we show that LF is decidable and possesses the disjunction property.

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