Intuitionistic Fuzzy Sets (IFS) are defined as pairs of mutually orthogonal fuzzy sets. We discuss this approach from an algebraic point of view. As a result we characterize two implication operators on the collection of IFS, which on a particular subset of IFS behave as a Lukasiewicz and a Gödel implication.

We investigate the computational complexity of admissibility of inference rules in infinite-valued Lukasiewicz propositional logic ( L). It was shown in [13] that admissibility in L is checkable in PSPACE. We establish that this result is optimal, i.e., admissible rules of L are PSPACE-complete. In contrast, derivable rules of L are known to be coNP-complete.

In this paper we shall describe a correspondence between Rational à Lukasiewicz formulas and neural networks in which the activation function is the truncated identity and synaptic weights are rational numbers. On one hand to have a logical representation (in a given logic) of neural networks could widen the interpretability, amalgamability and reuse of these objects. On the other hand, neural ...

Although it is well-known that every satisfiable formula in Lukasiewicz’ infinite-valued logic L∞ can be satisfied in some finitevalued logic, practical methods for finding an appropriate number of truth degrees do currently not exist. As a first step towards efficient reasoning in L∞, we propose a method to find a tight upper bound on this number which, in practice, often significantly improve...

Received 22 November 2004 This work was partially supported by the Universidad Nacional del Sur, Bah́ıa Blanca, Argentina.

The unit square is regarded as a special kind of dynamical system. It is proved that the square is an MV-algebra, hence the recent results on MValgebra entropy theory can be applied to it.

In this paper I study Lukasiewicz-style refutation procedures (cf. [8], also [3]) for intermediate logics as a method of obtaining decidability results. This method proves to be more general than Harrop’s criterion (cf. [4]) saying that every finitely axiomatizable logic with the finite model property is decidable. There are 2א0 intermediate logics without the f.m.p. (cf. [1], [2]). I give a mo...

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...

It is well-known that satisfiability (and hence validity) in the minimal classical modal logic is a PSPACE-complete problem. In this paper we consider the satisfiability and validity problems (here they are not dual, although mutually reducible) for the minimal modal logic over a finite Lukasiewicz chain, and show that they also are PSPACE-complete. This result is also true when adding either t...