On the question of the criteria for the paraconsistency of logics


Natalya E. Tomova


The paper discusses various aspects related to the definition of paraconsistent logics. The criteria of the paraconsistency of logical systems, which were proposed by S.Jaskowski and N. da Costa, are given. Various formulations of the principle <<from contradiction, anything follows>> ($\textit{ex falso quodlibet}$) and the corresponding definitions of paraconsistent logic are given. It is indicated in which cases these definitions may be equivalent. The problem of explosiveness of the consequence relation with respect to some operators and bundles is also described, and the solutions that have been proposed by various researchers are given. The paper deals with issues related to the paraconsistent negation, the properties of classical negation that are incompatible with the rejection of the principle of <<from contradiction, anything follows>> are indicated.
Different views on the necessity for non-verifiability the principle of non-contradiction in paraconsistent logics are regarded.




Non-classical logics


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