Matrix- based logic for avoiding paradoxes and its paraconsistent alternative

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)).