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|-...

Both soybean composition and processing conditions impact the nutritional quality of soybean meal. The objective of this experiment was to compare nutrient compositions of soybeans grown under diverse environmental conditions in a variety of locations. Dry matter, organic matter, and ash concentrations differed in soybeans collected within the countries of Brazil, China, and the United States, ...

The paper explores properties of the Lukasiewicz μ-calculus, or Lμ for short, an extension of Lukasiewicz logic with scalar multiplication and least and greatest fixed-point operators (for monotone formulas). We observe that Lμ terms, with n variables, define monotone piecewise linear functions from [0, 1]n to [0, 1]. Two effective procedures for calculating the output of Lμ terms on rational i...

In “Bulgarian Solitaire”, a player divides a deck of n cards into piles. Each move consists of taking a card from each pile to form a single new pile. One is concerned only with how many piles there are of each size. Starting from any division into piles, one always reaches some cycle of partitions of n. Brandt proved that for n = 1+2+ · · ·+k, the cycle is just the single partition into piles ...

The Loś-Tarski Theorem and the ChangLoś-Susko Theorem, two classical results in Model Theory, are extended to the infinitevalued Lukasiewicz logic. The latter is used to settle a characterisation of the class of generic structures introduced in the framework of model theoretic forcing for Lukasiewicz logic [1]. Key-words: First Order Many-Valued Logic, Lukasiewicz logic, Model Theory.

In this work we investigate bounded Lukasiewicz logics, characterised as the intersection of the k-valued Lukasiewicz logics for k = 2, . . . , n (n ≥ 2). These logics formalise a generalisation of Ulam’s game with applications in Information Theory. Here we provide an analytic proof calculus G LBn for each bounded Lukasiewicz logic, obtained by adding a single rule to G L, a hypersequent calcu...

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.

The paper deals with Lukasiewicz filters. It analyzes some of their possible constructions and their basic properties. The Cartesian product of Lukasiewicz filters is introduced.