Exploring Extensions of Possibilistic Logic over Gödel Logic

Authors:
Pilar Dellunde;Lluís Godo;Enrico Marchioni
Affiliations:
Universitat Autònoma de Barcelona, Bellaterra, Spain 08193 and IIIA --- CSIC, Bellaterra, Spain 08193;IIIA --- CSIC, Bellaterra, Spain 08193;IIIA --- CSIC, Bellaterra, Spain 08193
Venue:
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Year:
2009

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Abstract

In this paper we present completeness results of several fuzzy logics trying to capture different notions of necessity (in the sense of Possibility theory) for Gödel logic formulas. In a first attempt, based on different characterizations of necessity measures on fuzzy sets, a group of logics, with Kripke style semantics, are built over a restricted language, indeed a two level language composed of non-modal and modal formulas, the latter moreover not allowing for nested applications of the modal operator N . Besides, a full fuzzy modal logic for graded necessity over Gödel logic is also introduced together with an algebraic semantics, the class of NG-algebras.