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

One-variable fragments of intermediate logics over linear frames

A correspondence is established between one-variable fragments of (first-order) intermediate logics defined over a fixed countable linear frame and Gödel modal logics defined over many-valued equivalence relations with values in a closed subset of the real unit interval. It is also shown that each of these logics can be interpreted in the one-variable fragment of the corresponding constant domain intermediate logic, which is equivalent to a Gödel modal logic defined over (crisp) equivalence relations. Although the latter modal logics in general lack the finite model property with respect to their frame semantics, an alternative semantics is defined that has this property and used to establish co-NP-completeness results for the one-variable fragments of the corresponding intermediate logics both with and without constant domains

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

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