in the present paper, a partial order on a non- archimedean fuzzymetric space under the  lukasiewicz t-norm is introduced and fixed point theoremsfor single and multivalued mappings are proved.

In this paper we study generic expansions of logics of continuous t-norms with truth-constants, taking advantage of previous results for Lukasiewicz logic and more recent results for Gödel and Product logics. Indeed, we consider algebraic semantics for expansions of logics of continuous t-norms with a set of truth-constants {r | r ∈ C}, for a suitable countable C ⊆ [0, 1], and provide a full de...

As it is well-known, Lukasiewicz developed in [2] the many-valued propositional calculi based on two primitive connectives, negation N and implication C, which were defined semantically. Complete axiomatizations followed later on. Among the works on this argument, we mention Wajsberg [9], Rosser and Turquette [8], Mc Naughton [3], Rose and Rosser [7], Meredith [4], Chang [1], Rose [5], [6]. It ...

If logic programs are interpreted over a three-valued logic, then often Kleene’s strong three-valued logic with complete equivalence and Fitting’s associated immediate consequence operator is used. However, in such a logic the least fixed point of the Fitting operator is not necessarily a model for the program under consideration. Moreover, the model intersection property does not hold. In this...

This work describes a methodology to combine logic-based systems and connectionist systems. Our approach uses finite truth valued Lukasiewicz logic, where we take advantage of fact, presented by Castro in [6], what in this type of logics every connective can be define by a neuron in an artificial network having by activation function the identity truncated to zero and one. This allowed the inje...

In the 1970s, Robin Giles introduced a game combining Lorenzen-style dialogue rules with a simple scheme for betting on the truth of atomic statements, and showed that the existence of winning strategies for the game corresponds to the validity of formulas in Lukasiewicz logic. In this paper, it is shown that ‘disjunctive strategies’ for Giles’s game, combining ordinary strategies for all insta...