In this paper we investigate special types of Lukasiewicz filters. We show their connection to crisp filters. Further, we introduce the notion of Lukasiewicz ideal as a set-function which is in some sense complementary to Lukasiewicz filters.

Lukasiewicz implication algebras are the {→, 1}-subreducts of MV algebras. They are the algebraic counterpart of SuperLukasiewicz Implicational Logics. We give a description of free Lukasiewicz implication algebras in the context of McNaughton functions. More precisely, we show that the |X|-free Lukasiewicz implication algebra is isomorphic to ⋃ x∈X [xθ) for a certain congruence θ over the |X|-...

Lukasiewicz logic arrays (LLAs) are analog VLSI circuits structured as trees of continuous-valued implications. First described in 1990, LLAs are now nding uses as applicationspeci c array processors for image processing, fuzzy inference, and robotic control. Yet an early question persists: Why do LLAs work? Intuitively, a small error should build up through successive implications of an arbitr...

Basic Logic was introduced by Petr Hájek to provide a uni ed approach to fuzzy logics, and judging by its rapid adoption in the research community, it has enjoyed considerable success in this regard. One of the reasons is that while it is a very general logic, it has elegant semantics with respect to the real unit interval, which allow for practical applications and use of standard software too...

From 1920, when Lukasiewicz established the 3-valued logic, many other versions have been made, with the purpose of improving or generalizing the precedent system. Fuzzy Logic departs from the multi-valued logic point of view, with real truth values in the closed unit interval. Our paper deals, basically, with analogies and differences between fuzzy and rough characters. Therefore, it belongs t...

First order Gödel logic G∞, enriched with the projection operator 4—in contrast to other important t-norm based fuzzy logics, like Lukasiewicz and Product logic—is well known to be recursively axiomatizable. However, unlike in classical logic, testing (1-)unsatisfiability, i.e., checking whether a formula has no interpretation that assigns the designated truth value 1 to it, cannot be straightf...

Definition 1. An algebra (A,⊕,∗ , 0) with a binary operation ⊕ : A×A → A and with a unary operation ∗ : A → A and a constant 0, is said to be an MV -algebra iff satisfies the following conditions for all a, b, c ∈ A: (1) (A,⊕, 0) is a commutative monoid; (2) x⊕ 0∗ = 0∗ for every x ∈ A; (3) (x∗)∗ = x for every x ∈ A; (4) (x∗ ⊕ y)∗ ⊕ y = (x⊕ y∗)∗ ⊕ x for every x, y ∈ A. ¿From (4), setting y = 0∗,...

MV-algebras were introduced by Chang in 1958 preliminary to his providing an algebraic completeness proof for the K0-vaΓued Lukasiewicz propositional logic, LXo. In this paper a method is given for determining, for an arbitrary normal extension of LKo, an MV-algebra characteristic for the extension. The characteristic algebras are finite direct products of two sets of linearly ordered MV-algebr...

Publicado originalmente em 1974, este breve artigo de John Corcoran analisa algumas passagens da obra Jan Lukasiewicz dedicada à silogística Aristóteles, refutando a tese do lógico polonês que os silogismos aristotélicos seriam condicionais universalizados.

Complete deductive systems are constructed for the non-valid (refutable) formulae and sequents of some propositional modal logics. Thus, complete syntactic characterizations in the sense of Lukasiewicz are established for these logics and, in particular, purely syntactic decision procedures for them are obtained. The paper also contains some historical remarks and a general discussion on refuta...