Extending possibilistic logic over Gödel logic

Authors:
Pilar Dellunde;Lluís Godo;Enrico Marchioni
Affiliations:
Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain and IIIA -- CSIC, 08193 Bellaterra, Spain;IIIA -- CSIC, 08193 Bellaterra, Spain;IIIA -- CSIC, 08193 Bellaterra, Spain
Venue:
International Journal of Approximate Reasoning
Year:
2011

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Abstract

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.