TitleExploring Extensions of Possibilistic Logic over Gödel logic
Publication TypeConference Paper
Year of Publication2009
AuthorsDellunde P, Godo L, Marchioni E
EditorSossai C., .Chemello G
Conference Name10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2009)
Conference LocationVerona (Italy)
Date Published01/07/2009

In this paper we present completeness results of several fuzzy logics trying to capture di?erent notions of necessity (in the sense of Possibility theory) for G¨odel logic formulas. In a ?rst attempt, based on di?erent characterizations of necessity measures on fuzzy sets, a group of logics, with Kripke style semantics, are built over a restricted language, indeed a two level language composed of non-modal and modal formulas, the latter moreover not allowing for nested applications of the modal operator N . Besides, a full fuzzy modal logic for graded necessity over G¨odel logic is also introduced together with an algebraic semantics, the class of NG-algebras.