A Possibilistic Analysis of Inconsistency

International audienceCentral 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 level is strictly above this inconsistency level constitute a sub-base free of any inconsistency. Some extensions, based on the notions of paraconsistent completion of a possibilistic logic base, and of safely supported formulas, have been proposed for handling formulas below the level of inconsistency. In this paper we further explore these ideas, and show the interest of considering the minimal inconsistent subsets in this setting. Lines for further research are also outlined

Inconsistency Management from the Standpoint of Possibilistic Logic

International audienceUncertainty and inconsistency pervade human knowledge. Possibilistic logic, where propositional logic formulas are associated with lower bounds of a necessity measure, handles uncertainty in the setting of possibility theory. Moreover, central in standard possibilistic logic is the notion of inconsistency level of a possibilistic logic base, closely related to the notion of consistency degree of two fuzzy sets introduced by L. A. Zadeh. Formulas whose weight is strictly above this inconsistency level constitute a sub-base free of any inconsistency. However, several extensions, allowing for a paraconsistent form of reasoning, or associating possibilistic logic formulas with information sources or subsets of agents, or extensions involving other possibility theory measures, provide other forms of inconsistency, while enlarging the representation capabilities of possibilistic logic. The paper offers a structured overview of the various forms of inconsistency that can be accommodated in possibilistic logic. This overview echoes the rich representation power of the possibility theory framework