Abstract:

In this paper we present completeness results of several fuzzy logics trying to capture di?erent notions of necessity (in the sense of Possibility theory) for G¨odel logic formulas. In a ?rst attempt, based on di?erent 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 G¨odel logic is also introduced together with an algebraic semantics, the class of NG-algebras.

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