On the representation of S5 algebras and their automorphism groups.
On the restricted equivalence for subclasses of propositional logic
On the structure and classification of SOMAs: Generalizations of mutually orthogonal Latin squares.
On the structure of continuous uninorms
Uninorms were introduced by Yager and Rybalov [13] as a generalization of triangular norms and conorms. We ask about properties of increasing, associative, continuous binary operation in the unit interval with the neutral element . If operation is continuous, then or . So, we consider operations which are continuous in the open unit square. As a result every associative, increasing binary operation with the neutral element , which is continuous in the open unit square may be given in ...
On the syntactico-semantical completeness of first-order fuzzy logic. I. Syntax and semantics
On the syntactico-semantical completeness of first-order fuzzy logic. II. Main results
On the -conditionality of -power based implications
It is well known that, in forward inference in fuzzy logic, the generalized modus ponens is guaranteed by a functional inequality called the law of -conditionality. In this paper, the -conditionality for -power based implications is deeply studied and the concise necessary and sufficient conditions for a power based implication being -conditional are obtained. Moreover, the sufficient conditions under which a power based implication is -conditional are discussed, this discussions give an...
On the t-closure Condition of Martin.
On the -superposition of functions of a -valued logic.
On universal theories of metabelian groups and the Shmel'kin embedding.
On weaker forms of choice in second order arithmetic
One of the Possible Formal Desribtions of Deducubility
Open problems posed at the eighth international conference on fuzzy set theory and applications
Several open problems posed during FSTA 2006 (Liptovský Ján, Slovakia) are presented. These problems concern the classification of strict triangular norms, Lipschitz t-norms, interval semigroups, copulas, semicopulas and quasi- copulas, fuzzy implications, means, fuzzy relations, MV-algebras and effect algebras.
Opérateurs de mise en mémoire et types -positifs
Order with successors is not interprétable in RCF
Using the monotonicity theorem of L. van den Dries for RCF-definable real functions, and a further result of that author about RCF-definable equivalence relations on ℝ, we show that the theory of order with successors is not interpretable in the theory RCF. This confirms a conjecture by J. Mycielski, P. Pudlák and A. Stern.
Ordered Rings and Fields
We introduce ordered rings and fields following Artin-Schreier’s approach using positive cones. We show that such orderings coincide with total order relations and give examples of ordered (and non ordered) rings and fields. In particular we show that polynomial rings can be ordered in (at least) two different ways [8, 5, 4, 9]. This is the continuation of the development of algebraic hierarchy in Mizar [2, 3].
Orthogonality as single primitive notion for metric planes.
Parametric families of fuzzy consequence operators.
In a previous paper we explored the notion of coherent fuzzy consequence operator. Since we did not know of any example in the literature of non-coherent fuzzy consequence operator, we also showed several families of such operators. It is well-known that the operator induced by a fuzzy preorder through Zadeh's compositional rule is always a coherent fuzzy consequence operator. It is also known that the relation induced by a fuzzy consequence operator is a fuzzy preorder if such operator is coherent....
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,...
Peano-Systeme.