Reason-maintenance Belief Logic with Uncertain Information

Abstract

In this article, we propose a logic for reasoning about belief based on fusion of uncertain information. The resultant reason-maintenance possibilistic belief logic can represent both implicit and explicit uncertain beliefs of an agent. While implicit beliefs stipulate what are believable, explicit beliefs can trace the process of belief formation by information fusion. To set up the formal framework, we start with developing a basic reason-maintenance belief logic, present its syntax and semantics, and investigate its axiomatization and properties. Then, we extend the basic logic to accommodate the possibilistic uncertainty of information and beliefs, provide a complete axiomatization of the extended logic, and show that it can address the reason-maintenance issue of partially inconsistent beliefs. We also demonstrate the applicability of our formalisms by using several examples in realistic scenarios.