MV-algebras were introduced by Chang as an algebraic counterpart of the Lukasiewicz infinite-valued logic. D. Mundici proved that the category of MV-algebras is equivalent to the category of abelian l-groups with strong unit. A. Di Nola and A. Lettieri established a categorical equivalence between the category of perfect MV-algebras and the category of abelian l-groups. In this paper we investi...

We provide a methodology to introduce proof search oriented calculi for a large class of many-valued logics, and a sufficient condition for their Co-NP completeness. Our results apply to many well known logics including Gödel, Lukasiewicz and Product Logic, as well as Hájek’s Basic Fuzzy Logic.

We explore some links between abstract argumentation, logic and kernels in digraphs. Viewing argumentation frameworks as propositional theories in graph normal form, we observe that the stable semantics for argumentation can be given equivalently in terms of satisfaction and logical consequence in classical logic. We go on to show that the complete semantics can be formulated using Lukasiewicz ...

The Cai δ-equality of fuzzy sets corresponds to the Lukasiewicz t-norm. In this paper we study the notion of (∗, δ)-equality, a concept which generalizes the δ-equality to the case of the fuzzy set theory based on an arbitrary continuous t-norm ∗. We investigate the robustness of some fuzzy implication operators in terms of (∗, δ)-equality.

In this paper, we develop a duality for the varieties of a Lukasiewicz n + 1-valued modal system. This duality is an extension of Stone duality for modal algebras. Some logical consequences (such as completeness results, correspondence theory. . . ) are the derived and we propose some ideas for future research.

This paper presents an application of an optimized implementation of a probabilistic description logic defined by Giugno and Lukasiewicz [9] to the domain of image interpretation. This approach extends a description logic with so-called probabilistic constraints to allow for automated reasoning over formal ontologies in combination with probabilistic knowledge. We analyze the performance of cur...

We explain Giles’s characterization of Lukasiewicz logic via a dialogue game combined with bets on results of experiments that may show dispersion. The game is generalized to other fuzzy logics and linked to recent results in proof theory. We argue that these results allow one to place t-norm based fuzzy logics in a common framework with supervaluation as a theory of vagueness.

In Artificial Intelligence, as well as in data base updating or in the design of intelligent agents, it is necessary the use of contradictory information. For that, it is useful to direct our attention to paraconsistent logics. The goal of the present survey is to offer an initial analysis on paraconsistency in some logics like Pac, RM3, Lukasiewicz, G ′ 3.

The aim of this work is to study a class of non-archimedean valued measures on MV-algebras. We call them hyperreal states and their definition naturally arise from (the uniform version of) Di Nola representation theorem for MV-algebras (cf [5, 6]): for any MV-algebra A = (A,⊕,¬,>,⊥) there exists a ultrafilter U on the cardinality of A such that A embeds into (∗[0, 1]U) Spec(A) (where as usual S...