Table-analytical Axiomatizations of Expansions of Logic Par

Abstract

In this work we offer table-analytical axiomatizations of a row of logics. These logics are such expansions of known paraconsistent and paracomplete logic $Par$ from [1] which are paralogics, that is paraconsistent or/and paracomplete logics. According to [2] there are only four paralogics including logic $Par$ . For each of these the paralogic we describe simply arranged table-analytical axiomatization convenient for the organization of search of the proof. Rules of a reduction in all these axiomatizations same, as well as the principles of creation of analytical tables. Calculations differ from each other only in definition of the closed set of the marked formulas. Table-analytical constructions are carried out in style of Fitting (see [4]). Following [4], we consider two markers for formulas. These markers —$T$ and $F$. The main difference of a set of the rules of a reduction offered here from a set of the rules of a reduction used in [4] consists that we use along with usual rules of a reduction which delete separate logical connectives, rules of a reduction deleting the whole complexes of logical connectives. So, all logics are investigated here, language of each of which is the propositional language $L$ defined below, and each of which includes known paranormal logic of $Par$ and is paraconsistent or/and paracomplete logic. Our aim — for any such logic to describe an adequate table-analytical calculation convenient for search of a proof.