Exploring Extensions of Possibilistic Logic over Gödel logic
Publication Type:Conference Paper
Source:10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2009), Springer-Verlag, Volume 5590, Verona (Italy), p.923–934 (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.