Os paradoxos de Prior e o calculo proposicional deôntico relevante E¹

Abstract

Normative fragmento natural language makeup sentences that expressacts and describe norms. In this fragmentthere are criteriao flogic thuth and relation of consequence between sentences which constitute a natural d.eontic logic. This paper adopta translation function fromt hese tof sentence sof the normative fragmento natural language intot hese tof formulae intheformal 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, whichareknown as Prior's paradoxes. Cruz's paraconsistent d.eontic propositional calculus, D1 (1993) avoids some paradoxes, except that generated by the formula OB ~ O(A ~ B). One buildsa relevant deontic propositional calculusthat aims toavoidtheseparadoxesand keepsintact all other fundamental features of d.eontic operators, since the formulaB ~ (A ~ B) is improable'in somere lavant calculi.