Safety- and liveness-properties in propositional temporal logic: characterizations and decidability
Satisfiability and computing van der Waerden numbers.
Self-dual binary and ternary connectives for m-valued propositional calculi.
Semantic analysis of topic and focus
Semantics based on states of affairs
Semantics for some intermediate logics.
Sémantika otázky v problémové situaci
Sémantique catégorique des types : comprendre le système F
Sémantique formelle des opérateurs d'un langage de listes
Semi-Boolean algebras and their applications to intuitionistic logic with dual operations
Semiring of Sets
Schmets [22] has developed a measure theory from a generalized notion of a semiring of sets. Goguadze [15] has introduced another generalized notion of semiring of sets and proved that all known properties that semiring have according to the old definitions are preserved. We show that this two notions are almost equivalent. We note that Patriota [20] has defined this quasi-semiring. We propose the formalization of some properties developed by the authors.
Semiring of Sets: Examples
This article proposes the formalization of some examples of semiring of sets proposed by Goguadze [8] and Schmets [13].
Sentences with three quantifiers are decidable in set theory
Separability of Real Normed Spaces and Its Basic Properties
In this article, the separability of real normed spaces and its properties are mainly formalized. In the first section, it is proved that a real normed subspace is separable if it is generated by a countable subset. We used here the fact that the rational numbers form a dense subset of the real numbers. In the second section, the basic properties of the separable normed spaces are discussed. It is applied to isomorphic spaces via bounded linear operators and double dual spaces. In the last section,...
Sequent Calculus, Derivability, Provability. Gödel's Completeness Theorem
Fifth of a series of articles laying down the bases for classical first order model theory. This paper presents multiple themes: first it introduces sequents, rules and sets of rules for a first order language L as L-dependent types. Then defines derivability and provability according to a set of rules, and gives several technical lemmas binding all those concepts. Following that, it introduces a fixed set D of derivation rules, and proceeds to convert them to Mizar functorial cluster registrations...
Set theory in predicate calculus with equality
Sheaf constructions in universal algebra and model theory
Signed states on a logic
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...
S-implications and -implications on a finite chain
This paper is devoted to the study of two kinds of implications on a finite chain : -implications and -implications. A characterization of each kind of these operators is given and a lot of different implications on are obtained, not only from smooth t-norms but also from non smooth ones. Some additional properties on these implications are studied specially in the smooth case. Finally, a class of non smooth t-norms including the nilpotent minimum is characterized. Any t-norm in this class...