Extending possibilistic logic over Godel logic

In this paper we present several fuzzy logics trying to capture different notions of necessity (in the sense of possibility theory) for Godel logic formulas. Based on different characterizations of necessity measures on fuzzy sets, a group of logics with Kripke style semantics is built over a restricted language, namely, a two-level language composed of non-modal and modal formulas, the latter, moreover, not allowing for nested applications of the modal operator N. Completeness and some computational complexity results are shown. (C) 2010 Elsevier Inc. All rights reserved.