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 are 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.