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Possibility and necessity measures are commonly defined over Boolean algebras. This work considers a generalization of these kinds of measures over MV-algebras as a possibilistic counterpart of the (probabilistic) notion of state on MV-algebras. Two classes of possibilistic states over MV-algebras of functions are characterized in terms of (generalized)… (More)

In this paper we investigate the addition of arbitrary independent in-volutive negations to t-norm based logics. We deal with several extensions of MTL and establish general completeness results. Indeed, we will show that, given any t-norm based logic satisfying some basic properties, its extension by means of an involutive negation preserves algebraic and… (More)

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 are built over a restricted language, namely a two level language composed of… (More)

- Tommaso Flaminio, Lluís Godo, Enrico Marchioni
- 2012

In this paper we present a generalization of belief functions over fuzzy events. In particular we focus on belief functions defined in the algebraic framework of finite MV-algebras of fuzzy sets. We introduce a fuzzy modal logic to formalize reasoning with belief functions on many-valued events. We prove, among other results, that several different notions… (More)

Recently Kroupa has proposed a generalization of belief functions on MV-algebras, the latter being the chosen algebraic setting for fuzzy (or many-valued) events. However, Kroupa's belief functions evaluate the degree of belief in the occurrence of fuzzy events by taking into account (weighted) evidence on classical subsets. In other words, the focal… (More)

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… (More)

Very recently, a (fuzzy modal) logic to reason about coherent conditional probability, in the sense of de Finetti, has been introduced by the authors. Under this approach, a conditional probability ðÁ j ÁÞ is taken as a primitive notion defined over conditional events of the form ''' given '', 'j for short, where is not the impossible event. The logic,… (More)