An extension of the possibility theory in view of the formalization of approximate reasoning

Abstract

Our aim is here to give some indications about the basis of a logic system in order to generalize the possibility theory in the following way:

We want that each sentence receive a couple of confidence values. We call them degrees of obligation and eventuality, in order to translate the notion of truth by the half-sum of these values, and a notion that we can see as the imprecision given to this truth value: the diference eventuality — obligation which we shall call the unknown rather than uncertainty.

In relation to the possibility theory, we whish to leave the general property max(ps(P), ps(−P))=1 and then leave:

$$nc(P) > \Rightarrow ps(P) = 1{\mathbf{ }}and{\mathbf{ }}ps(P) < 1 \Rightarrow nc(P) = 0$$

The aim of this extension is sitted in the tentation of modelising the degrees of truth and unknown, and their propagation when inferences, in the computing system about approximate reasoning.

We would like that linguistics appreciations with vagueness such “perhaps true”, “probably false”, “true always three times on four”, “often true but very uncertain” etc..., could receive those two degrees in order to determinate an interval whose the widness would be the measure of the imprecision given to the truth degree, and it is this that we call unknown.