Representations of synonymy and antonymy by automorphisms in fuzzy set theory.
Structures of automorphisms and automorphism groups in fuzzy set theory are studied in detail in view of applications to synonymy and antonymy representations.
Representations of the direct product of matrix algebras
Suppose B is a unital algebra which is an algebraic product of full matrix algebras over an index set X. A bijection is set up between the equivalence classes of irreducible representations of B as operators on a Banach space and the σ-complete ultrafilters on X (Theorem 2.6). Therefore, if X has less than measurable cardinality (e.g. accessible), the equivalence classes of the irreducible representations of B are labeled by points of X, and all representations of B are described (Theorem 3.3).
Representing free Boolean algebras
Partitioner algebras are defined in [2] and are natural tools for studying the properties of maximal almost disjoint families of subsets of ω. In this paper we investigate which free algebras can be represented as partitioner algebras or as subalgebras of partitioner algebras. In so doing we answer a question raised in [2] by showing that the free algebra with generators is represented. It was shown in [2] that it is consistent that the free Boolean algebra of size continuum is not a subalgebra...
Representing real numbers in denumerable Boolean algebras
Representing Upper Probability Measures over Rational Lukasiewicz Logic.
Residual implications and co-implications from idempotent uninorms
This paper is devoted to the study of implication (and co-implication) functions defined from idempotent uninorms. The expression of these implications, a list of their properties, as well as some particular cases are studied. It is also characterized when these implications satisfy some additional properties specially interesting in the framework of implication functions, like contrapositive symmetry and the exchange principle.
Residual quotient fuzzy subset in near-rings.
Residuation in twist products and pseudo-Kleene posets
M. Busaniche, R. Cignoli (2014), C. Tsinakis and A. M. Wille (2006) showed that every residuated lattice induces a residuation on its full twist product. For their construction they used also lattice operations. We generalize this problem to left-residuated groupoids which need not be lattice-ordered. Hence, we cannot use the same construction for the full twist product. We present another appropriate construction which, however, does not preserve commutativity and associativity of multiplication....
Résolution du problème de l'ellipse et du cercle par l'algorithme de Hörmander
Resolution Methods in Proving the Program Correctness
Resolvability in c.c.c. generic extensions
Every crowded space is -resolvable in the c.c.c. generic extension of the ground model. We investigate what we can say about -resolvability in c.c.c. generic extensions for . A topological space is monotonically -resolvable if there is a function such that for each . We show that given a space the following statements are equivalent: (1) is -resolvable in some c.c.c. generic extension; (2) is monotonically -resolvable; (3) is -resolvable in the Cohen-generic extension ....
Restricted ideals and the groupability property. Tools for temporal reasoning
In the field of automatic proving, the study of the sets of prime implicants or implicates of a formula has proven to be very important. If we focus on non-classical logics and, in particular, on temporal logics, such study is useful even if it is restricted to the set of unitary implicants/implicates [P. Cordero, M. Enciso, and I. de Guzmán: Structure theorems for closed sets of implicates/implicants in temporal logic. (Lecture Notes in Artificial Intelligence 1695.) Springer–Verlag, Berlin 1999]....
Restrictions on the degree spectra of algebraic structures.
Resultats sur la comparaison des types d΄ordres
Results on automorphisms of recursively saturated models of PA
Retraceable homogeneous sets
Rétractions et interprétation interne du polymorphisme : le problème de la rétraction universelle
Revealed automorphisms
We study automorphisms in the alternative set theory. We prove that fully revealed automorphisms are not closed under composition. We also construct some special automorphisms. We generalize the notion of revealment and Sd-class.
Revealments
Reversals-space-parallelism tradeoffs for language recognition