Matrix- based logic for avoiding paradoxes and its paraconsistent alternative

Abstract

The present article shows that there are consistent and decidable manyvalued 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)).