Abstract
The present article shows that there are consistent and decidable many- valued systems of propositional logic which satisfy two or all the three criteria for non- trivial inconsistent theories by da Costa (1974). The weaker one of these paraconsistent system is also able to avoid a series of paradoxes which come up when classical logic is applied to empirical sciences. These paraconsistent systems are based on a 6- valued system of propositional logic for avoiding difficulties in several domains of empirical science (Weingartner (2009)).
Highlights
Newton da Costa is wellknown for his contributions to Paraconsistent Logics, more correctly it can be said he is the founder of this relatively new domain of Logic
The criteria Replacement Criterion (RC) and Reduction Criterion (RD) have been introduced in order to avoid paradoxes when logic is applied to empirical sciences
THE SYSTEM RMQ It was one of the purposes when constructing RMQ, to find a semantics with the help of finite matrices, which approximates the effects of the relevance restriction of the replacement (RC) and reduction (RD) criteria in such a way that what is classically valid but redundant or irrelevant or leading to disjuncts by those criteria, is materially valid but strictly invalid in RMQ
Summary
Newton da Costa is wellknown for his contributions to Paraconsistent Logics, more correctly it can be said he is the founder of this relatively new domain of Logic. The purpose of this paper is to construct two models in the sense of matrix calculi of propositional logic which satisfy either DC2 and DC3 or DC1, DC2 and DC3. These models are (weak/strong) paraconsistent alternatives of a basic logic (called RMQ) for the application in empirical sciences and especially in modern physics (Weingartner (2009)). This basic logic is a finite matrix system and it contains its own semantics. The modal logic included of RMQ will not be discussed in this paper.See Weingartner (2009)
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