On the -superposition of functions of a -valued logic.
Parametrized prime implicant-implicate computations for regular logics.
Prime implicant-implicate generating algorithms for multiple-valued logics (MVL's) are introduced. Techniques from classical logic not requiring large normal forms or truth tables are adapted to certain regular'' multiple-valued logics. This is accomplished by means of signed formulas, a meta-logic for multiple valued logics; the formulas are normalized in a way analogous to negation normal form. The logic of signed formulas is classical in nature. The presented method is based on path dissolution,...
Polyadic algebras over nonclassical logics
The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)'s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Łukasiewicz, modal logics that admit the rule of necessitation, BCK logic, etc.
Preboolean MV-algebras as bipartite MV-algebras.
In this note we characterize bipartite MV-algebras by introducing the notion of preboolean MV-algebras.
Precomplete classes of operations on an uncountable set
Probabilistic propositional calculus with doubled nonstandard semantics
The classical propositional language is evaluated in such a way that truthvalues are subsets of the set of all positive integers. Such an evaluation is projected in two different ways into the unit interval of real numbers so that two real-valued evaluations are obtained. The set of tautologies is proved to be identical, in all the three cases, with the set of classical propositional tautologies, but the induced evaluations meet some natural properties of probability measures with respect to nonstandard...
Putting together Lukasiewicz and product logics.
In this paper we investigate a propositional fuzzy logical system LΠ which contains the well-known Lukasiewicz, Product and Gödel fuzzy logics as sublogics. We define the corresponding algebraic structures, called LΠ-algebras and prove the following completeness result: a formula φ is provable in the LΠ logic iff it is a tautology for all linear LΠ-algebras. Moreover, linear LΠ-algebras are shown to be embeddable in linearly ordered abelian rings with a strong unit and cancellation law.
Relative sets and rough sets
In this paper, by defining a pair of classical sets as a relative set, an extension of the classical set algebra which is a counterpart of Belnap's four-valued logic is achieved. Every relative set partitions all objects into four distinct regions corresponding to four truth-values of Belnap's logic. Like truth-values of Belnap's logic, relative sets have two orderings; one is an order of inclusion and the other is an order of knowledge or information. By defining a rough set as a pair of definable...
Representation of logic formulas by normal forms
In this paper, we deal with the disjunctive and conjunctive normal forms in the frame of predicate BL-logic and prove theirs conditional equivalence to appropriate formulas. Our aim is to show approximation ability of special normal forms defined by means of reflexive binary predicate.
Representation theorem for finite quasi-boolean algebras
Representing Upper Probability Measures over Rational Lukasiewicz Logic.
Riemann average truth-value of Łukasiewicz formulas
Self-dual binary and ternary connectives for m-valued propositional calculi.
Simple games in Łukasiewicz calculus and their cores
We propose a generalization of simple coalition games in the context of games with fuzzy coalitions. Mimicking the correspondence of simple games with non-constant monotone formulas of classical logic, we introduce simple Łukasiewicz games using monotone formulas of Łukasiewicz logic, one of the most prominent fuzzy logics. We study the core solution on the class of simple Łukasiewicz games and show that cores of such games are determined by finitely-many linear constraints only. The non-emptiness...
Some Theorems For Model Theory Of Mixed-Valued Predicate Calculi
States on pseudo-effect algebras with general comparability
Sur le premier système de Lukasiewicz
Sur les systèmes déductifs dans la logique -valente
Temi geometrici e di teoria della dimostrazione nelle logiche proposizionali di Łukasiewicz
The algebra of first-order fuzzy logic