Belief functions are generalized to formulas in Lukasiewicz logic. It is shown that they generalize probabilities on formulas (so-called states) and that they are completely monotone mappings with respect to the lattice operations.

In this paper, we define new decision procedures for Łukasiewicz logics. They are based on particular integer-labelled hypersequents and of logical proof rules for such hypersequents. These rules being proved strongly invertible our procedures naturally allow one to generate countermodels. From these results we define a “merge”-free calculus for the infinite version of Łukasiewicz logic and pro...

In his foundation of probability theory, Bruno de Finetti devised a betting scheme where a bookmaker offers bets on the outcome of events φ occurring in the future. He introduced a criterion for coherent bookmaking, and showed that coherent betting odds are given by some probability distribution. While de Finetti dealt with yes-no events and boolean propositional logic, Mundici generalized the ...

In this paper we summarize results on perfect MV-algebras and we show that the class of first order à Lukasiewicz formulas valid in all interpretations over perfect MV-chains is axiomatizable.

In this paper we are dealing with the construction of a fuzzy rule based classifier. A three-step method is proposed based on Lukasiewicz logic for the description of the rules and the fuzzy memberships to construct concise and highly comprehensible fuzzy rules. In our method, a genetic algorithm is applied to evolve the structure of the rules and then a gradient based optimization to fine tune...

This work describes a methodology that combines logic-based systems and connectionist systems. Our approach uses finite truth-valued Lukasiewicz logic, wherein every connective can be defined by a neuron in an artificial network [1]. This allowed the injection of first-order formulas into a network architecture, and also simplified symbolic rule extraction. For that we trained a neural networks...

In this paper, we investigate the Lukasiewicz’s 4-valued modal logic based on the Aristotele’s modal syllogistic. We present a new interpretation of the set of algebraic truth values by introducing the truth and knowledge orderings similar to those in Belnap’s 4-valued bilattice but by replacing the original Belnap’s negation with the lattice pseudo-complement instead. Based on it, we develop a...