Credibilistic Satisfiability and Credibilistic Entailment

Credibilistic logic is a branch of multi-valued logic for dealing with fuzzy knowledge, which explains formula as fuzzy variable, and defines its truth value as credibility measure. In this paper, conditional formula is introduced to credibilistic logic by defining its credibility value as conditional credibility measure, and the conditional modus ponens is proved. In addition, a Sufficient and necessary condition for credibility function is proved, which provides an equivalent axiomatic definition for credibility value. The problem of credibilistic satisfiability is proposed to verify the consistency of a set of credibility values for formulas, and an algorithm is designed to solve this problem. Furthermore, for a set of consistent credibility values for formulas, the problem of credibilistic entailment is proposed to estimate the credibility value of an additional formula. In order to solve this problem, several nonlinear optimization models are designed by applying the maximum entropy principle, minimum cross-entropy principle and so on. Finally, as an application of credibilistic satisfiability and credibilistic entailment, a simplified example concerning the problem of position estimation of a mobile robot is shown.