1,721,032 research outputs found
Franco Montagna’s Work on Provability Logic and Many-valued Logic. Stud LogicaF
No full text[EN]Franco Montagna, a prominent logician and one of the leaders of the Italian school on Mathematical Logic, passed away on February 18, 2015. We survey some of his results and ideas in the two disciplines he greatly contributed along his career: provability logic and many-valued logic.Peer reviewe
Mixed Rational Assessments of Possibility and Probability Measures
No full textAbstractIn this paper we introduce the modal-fuzzy logic FPΠ(RŁΔ) for reasoning about probability and possibility at the same time. We will use such a logical formalism in order to treat mixed assessments of both those kinds of measures. The main result of this paper is a characterization of the coherence for rational mixed assessments by means of the logical consistency of a suitably defined FPΠ(RŁΔ)-theory. By means of this characterization, we will also prove that the problem of testing the coherence of a mixed assessment is NP-complete
T-norm-based logics with an independent involutive negation
No full textIn this paper we investigate the addition of arbitrary independent involutive 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 (finite) strong standard completeness. We will deal with both propositional and predicate logics
States of finite GBL-algebras with monoidal sum
No full textGeneralized BL-algebras, i.e. divisible residuated lattices, provide the semantics for a generalization of Basic Logic where the axiom of prelinearity does not hold. Informally, GBL-algebras generalize Heyting algebras in a similar way as MV-algebras generalize Boolean algebras. We introduce the operation of sum in finite GBL-algebras and we axiomatize the obtained finite structures, called GBL⊕-algebras. We hence define states of GBL⊕-algebras, extending MV-algebraic states, and we prove that they are determined by their restriction on the Heyting skeleton. Extremal states are also characterized in terms of densities concentrated in a unique join-prime idempotent
On the logical formalization of possibilistic counterparts of states over n-valued Łukasiewicz events
No full textPossibility 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) Sugeno integrals. For reasoning about these representable classes of possibilistic states, we introduce many-valued modal logics based on the Rational Łukasiewicz Logic, that are shown to be complete with respect to corresponding classes of Kripke models equipped with those states
Logics for belief functions on MV-algebras
No full textIn 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 of belief functions can be characterized in a quite uniform way, just by slightly modifying the complete axiomatization of one of the modal logics involved in the definition of our formalism
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