Towards a Possibilistic Logic

In this paper, we investigate how linguistic information can be incorporated into classical propositional logic. First, we show that Zadeh’s extension principle can be justified and at the same time generalized by considerations about transformation of possibility measures. Using these results, we show how linguistic uncertainty about the truth value of a proposition leads to the introduction of the notion of a possibilistic truth value. Since propositions can be combined into new ones using logical operators, linguistic uncertainty about the truth values of the original propositions leads to linguistic uncertainty about the truth value of the resulting proposition. Furthermore, we show that in a number of special cases there is truth-functionality, i.e., the possibilistic truth value of the resulting proposition is a function of the possibilistic truth values of the original propositions. We are thus led to the introduction of possibilistic-logical functions, combining possibilistic truth values. Important classes of such functions, the possibilistic extension logics, directly result from the abovementioned investigation, and are studied extensively. Finally, the relation between these logics, and Kleene’s strong multi-valued systems is established.