Handling Various Forms of Inconsistency in Possibilistic Logic

Possibilistic logic results from the application of possibility theory to classical logic, here propositional logic. Central in standard possibilistic logic (where propositional logic formulas are associated with lower bounds of their necessity measures), is the notion of inconsistency level of a possibilistic logic base. Formulas whose weight is strictly above this inconsistency level constitute a sub-base free of any inconsistency. However, several extensions, such as para consistent or multiple sources extensions of possibilistic logic, or extensions involving other possibility theory measures, provide other forms of inconsistency, while enlarging the representation power of possibilistic logic. The paper offers a structured overview of the various forms of inconsistency that can be accommodated in possibilistic logic.