We show that most of the paraconsistent logics which have been investigated in the literature have no ﬁnite characteristic matrices, and in the most important cases not even ﬁnite characteristic non-deterministic matrices (Nmatrices). 1 Introduction over its elements. Var(ϕ) denotes the set of variables which occur in ϕ. There are many paraconsistent logics that have been devel- Deﬁnition 2.1 A (propositional) logic is a pair L =L, , oped over the years. The simplest of them, like Asenjo– such that L is a propositional language, and is a structural Priest’s logic LP (Asenjo 1966;Priest 1979), D’Ottaviano’s and non-trivial Tarskian consequence relation for L. logic J (D’Ottaviano 1985; Epstein 2012), and Sette’s logic P (Sette 1973), were based from the start on ﬁnite matrices Now we deﬁne the notion of “paraconsistent logic”. A (actually: three-valued matrices). However, it is known that very useful general deﬁnition can, e.g., be found in Arieli most of the paraconsistent logics that were designed on the and Avron (2015). However, for the purposes of this paper basis of other ideas, like relevance or formal inconsistency, the following much weaker notion used in Avron and Béziau do not have ﬁnite characteristic matrices. Our goal
Soft Computing – Springer Journals
Published: Jun 6, 2018
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