Exploring extensions of possibilistic logic over gödel logic

Abstract

In this paper we present completeness results of several fuzzy logics trying to capture different notions of necessity (in the sense of Possibility theory) for Gödel logic formulas. In a first attempt, based on different 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 Gödel logic is also introduced together with an algebraic semantics, the class of NG-algebras. © 2009 Springer Berlin Heidelberg.