Rétractions et interprétation interne du polymorphisme : le problème de la rétraction universelle
Riemann average truth-value of Łukasiewicz formulas
Riemann Integral of Functions from ℝ into Real Banach Space
In this article we deal with the Riemann integral of functions from R into a real Banach space. The last theorem establishes the integrability of continuous functions on the closed interval of reals. To prove the integrability we defined uniform continuity for functions from R into a real normed space, and proved related theorems. We also stated some properties of finite sequences of elements of a real normed space and finite sequences of real numbers. In addition we proved some theorems about the...
Riemann-Stieltjes Integral
In this article, the definitions and basic properties of Riemann-Stieltjes integral are formalized in Mizar [1]. In the first section, we showed the preliminary definition. We proved also some properties of finite sequences of real numbers. In Sec. 2, we defined variation. Using the definition, we also defined bounded variation and total variation, and proved theorems about related properties. In Sec. 3, we defined Riemann-Stieltjes integral. Referring to the way of the article [7], we described...
Right and left invertibility in -calculus
Rough membership functions: a tool for reasoning with uncertainty
A variety of numerical approaches for reasoning with uncertainty have been investigated in the literature. We propose rough membership functions, rm-functions for short, as a basis for such reasoning. These functions have values in the interval [0,1] and are computable on the basis of the observable information about the objects rather than on the objects themselves. We investigate properties of the rm-functions. In particular, we show that our approach is intensional with respect to the class of...
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,...