Extending possibilistic logic over Gödel logic

In this paper we present several fuzzy logics trying to capture different notions of necessity (in the sense of possibility theory) for Gödel 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. © 2010 Elsevier Inc. All rights reserved.They also acknowledge partial support from the spanish projects CONSOLIDER (CSD2007-0022), MULOG2 (TIN2007-68005-C04-01) and ARINF (TIN2009-14704-C03-03), by the ESF Eurocores-LogICCC/MICINN project FFI2008-03126- E/FILO and by the Generalitat de Catalunya under the grants 2009-SGR 1433 and 1434. E. Marchioni also acknowledges partial support of the Juan de la Cierva Program of the Spanish MICINPeer Reviewe