In this paper, we introduce generalized connectivity in L-fuzzy topological spaces by à Lukasiewicz logic and prove K. Fan’s theorem.

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...

Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr(x) saying \x is true" and satisfying the \dequotation schema" ' Tr(') for all sentences '? This problem is investigated in the frame of Lukasiewicz innnitely valued logic.

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.

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...

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 fuzzy logic in wider sense, i.e. in the field of fuzzy sets applications, t-norms got a prominent rôle in recent times. In many-valued logic, the Lukasiewicz systems, the Gödel sytems, and also the product logic all are t-norm based systems. The present paper discusses the more general problem of the adequate axiomatizability for such t-norm based logical systems in general, surveying result...

We present logic programming style “goal-directed” proof methods for Lukasiewicz logic L that both have a logical interpretation, and provide a suitable basis for implementation. We introduce a basic version, similar to goal-directed calculi for other logics, and make refinements to improve efficiency and obtain termination. We then provide an algorithm for fuzzy logic programming in Rational P...

We present two embeddings of in nite-valued Lukasiewicz logic L into Meyer and Slaney’s abelian logic A, the logic of lattice-ordered abelian groups. We give new analytic proof systems for A and use the embeddings to derive corresponding systems for L. These include: hypersequent calculi for A and L and terminating versions of these calculi; labelled single sequent calculi for A and L of comple...