An Overview of Hybrid Possibilistic Reasoning

The objective of this paper is to introduce the hybrid logic methodology into possibilistic reasoning. It has been well-known that possibilistic logic has some strong modal logic flavor. However, modal logic lacks the capability of referring to states or possible worlds though states are crucial to its semantics. Hybrid logic circumvents the problem by blending the classical logic mechanism into modal logic. It is a hybrid of classical logic and modal logic, however, unlike classical logic, it treats terms and formulas uniformly. We study some variants of hybrid possibilistic logic, including hybrid qualitative possibility logic, hybrid graded modal logic, and hybrid possibilistic description logic. The syntax and semantics of the logics are presented. Some possible applications of the proposed logics are also suggested.