Using the possibility theory in fuzzy temporal reasoning
Validation sets in fuzzy logics
The validation set of a formula in a fuzzy logic is the set of all truth values which this formula may achieve. We summarize characterizations of validation sets of -fuzzy logics and extend them to the case of -fuzzy logics.
Validity up to complementation in graph theory
Veblen Hierarchy
The Veblen hierarchy is an extension of the construction of epsilon numbers (fixpoints of the exponential map: ωε = ε). It is a collection φα of the Veblen Functions where φ0(β) = ωβ and φ1(β) = εβ. The sequence of fixpoints of φ1 function form φ2, etc. For a limit non empty ordinal λ the function φλ is the sequence of common fixpoints of all functions φα where α < λ.The Mizar formalization of the concept cannot be done directly as the Veblen functions are classes (not (small) sets). It is done...
Very true operators on MTL-algebras
The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized...
Vollständigkeit und Schnittelimination in der intuitionistischen Typenlogik.
Wajsberg algebras.
We present the basic theory of the most natural algebraic counterpart of the ℵ0-valued Lukasiewicz calculus, strictly logically formulated. After showing its lattice structure and its relation to C. C. Chang's MV-algebras we study the implicative filters and prove its equivalence to congruence relations. We present some properties of the variety of all Wajsberg algebras, among which there is a representation theorem. Finally we give some characterizations of linear, simple and semisimple algebras....
Weak Completeness Theorem for Propositional Linear Time Temporal Logic
We prove weak (finite set of premises) completeness theorem for extended propositional linear time temporal logic with irreflexive version of until-operator. We base it on the proof of completeness for basic propositional linear time temporal logic given in [20] which roughly follows the idea of the Henkin-Hasenjaeger method for classical logic. We show that a temporal model exists for every formula which negation is not derivable (Satisfiability Theorem). The contrapositive of that theorem leads...
Weak Convergence and Weak Convergence
In this article, we deal with weak convergence on sequences in real normed spaces, and weak* convergence on sequences in dual spaces of real normed spaces. In the first section, we proved some topological properties of dual spaces of real normed spaces. We used these theorems for proofs of Section 3. In Section 2, we defined weak convergence and weak* convergence, and proved some properties. By RNS_Real Mizar functor, real normed spaces as real number spaces already defined in the article [18],...
Weak cylindric probability algebras.
Weak decidability of some modal extention of trigonometry
Weakly maximal decidable structures
We prove that there exists a structure M whose monadic second order theory is decidable, and such that the first-order theory of every expansion of M by a constant is undecidable.
What Is A Mathematical Theory?
What the finitization problem is not
Wide sets, deep many-valuedness and sorites arguments.
In this article I show how to obtain a powerful and truthful explanation of the failure of sorites arguments combining an adaptation of the Wide Set Theory formulated by Formato and Gerla and the concept of deep many valuedness established by Marraud. It is shown that if the premises of a sorites argument are conceived as a succession of indexed consequence operators (where indices express the accuracy of the inferences) prefixing sentences, the argument fails because the transitive property for...
Yager’s classes of fuzzy implications: some properties and intersections
Recently, Yager in the article “On some new classes of implication operators and their role in approximate reasoning” [Yager2004] has introduced two new classes of fuzzy implications called the -generated and -generated implications. Along similar lines, one of us has proposed another class of fuzzy implications called the -generated implications. In this article we discuss in detail some properties of the above mentioned classes of fuzzy implications and we describe their relationships amongst...
Základové arithmetiky. [I.]
Zum L(Q)-Interpolationsproblem.
Zur Konstruktiven Deutung der semantischen Vollständigkeit klassischer Quantoren- und Modalkalküle.
Zur Theorie der spektralen Darstellung von Prädikaten durch Ausdrücke der Prädikatenlogik 1. Stufe.