An Approach to Inconsistency-Tolerant Reasoning About Probability Based on Łukasiewicz Logic.

In this paper we consider the probability logic over Łukasiewicz logic with rational truth-constants, denoted FP(RPL), and we explore a possible approach to reason from inconsistent FP(RPL) theories in a non-trivial way. It basically consists of suitably weakening the formulas in an inconsistent theory T , depending on the degree of inconsistency of T . We show that such a logical approach is in accordance with other proposals in the literature based on distance-based and violation-based inconsistency measures.