Representation of observables in quantum mechanical models
Representation theorem for finite quasi-boolean algebras
Representations of Reals in Reverse Mathematics
Working in the framework of reverse mathematics, we consider representations of reals as rapidly converging Cauchy sequences, decimal expansions, and two sorts of Dedekind cuts. Converting single reals from one representation to another can always be carried out in RCA₀. However, the conversion process is not always uniform. Converting infinite sequences of reals in some representations to other representations requires the use of WKL₀ or ACA₀.
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.
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....
Resolution Methods in Proving the Program Correctness
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]....
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...