Os Paradoxos de Prior e o Cálculo Proposicional Deôntico Relevante Eo

Abstract

Normative fragment of natural language make up sentences that express acts and describe norms. In this fragment there are criteria of logic thuth and relation of consequence between sentences which constitute a natural deontic logic. This paper adopts at ranslation function from the set of sentences of the normative fragment of natural language in to the set of formulae in the formal language and claims that such function translates logically true sentences of the natural language into provable formulae of the formal calculus. With Von Wright's deontic calculus (1951), it does not fit and generates paradoxes, which are known as Prior's paradoxes. Cruz's paraconsistent deontic propositional calculus, D1 (1993) avoids some paradoxes, except that generated by the formula OB-O (A-B). One builds a relevant deontic propositional calculus that aims to avoid these paradoxes and keeps intact all other fundamental features of deontic operators, since the formula B -  (A - B) is improable in some relavant calculi.