Hybrid logic for possibilistic reasoning

Hybrid logic is an extension of modal logic with nominals for referring to the possible worlds. A nominal is an atomic formula which is true at exactly one point in any model. By using hybrid logic, the labelled deduction mechanism can be internalized to the object language, so the proof methods for the logic can be developed without resort to meta-linguistic devices. The article presents two hybrid logics for possibilistic reasoning. The first is based on the graded modal formulation of possibilistic logic, so its proof method is essentially a modification of the tableau system for hybrid multi-modal logic. The second is a kind of fuzzy modal logic and has a many-valued semantics. We present its proof method by using a tableau system for annotated formulas