Paraconsistent orbits of logics (Q2239383)

The paper examines \textit{paraconsistentization by consistent sets} of logics viewed as consequence relations. In this sense, given a logic \( L=(X,\vdash _{L})\), the paraconsistentization of \(L\) by consistent sets is, \textit{grosso modo}, the result of restricting \(\vdash _{L}\) to pairs \( \left\langle \Gamma ,A\right\rangle \) where \(\Gamma \) is an \(L\)-consistent set (cf. \S 4). In the first ten pages of the paper, the authors review some results by them on the topic. A notable conclusion is that \textit{paradeduction} and \textit{paraconsequence} ``are syntactical and semantical notions mirroring paraconsistentization at the proof-theoretical and semantical dimensions'' (p. 286). In the rest of the paper, the authors consider the notions of \textit{ paraconsistentization by multideduction} and \textit{paraconsistent orbits of a given logic}. The former one consists, roughly, in ``splitting'' the consequence relation of a particular logic in different consequence relations, producing as a result different systems, each one of which has its proper consequence relation. On the other hand, the \textit{paraconsistent orbit of a logic }\(L\) can generally be described as the logic obtained by a particular method for paraconsistentizating it, whence the set of all paraconsistent orbits \(L\) equals the set of logics obtained by all methods of paraconsistentization applicable to \(L\).