Ein Henkin-Vollständigkeitsbeweis für die intuitionistische Prädikatelogik bezüglich der Kripke-Semantik.
Ein Satz über reproduktive Lösungen.
Ein starker Normalisationssatz für die bar-rekursiven Funktionale.
Ein starker Normalisationssatz für die intuitionistische Typentheorie.
Ein syntaktischer Beweis für die Zulässigkeit der Schnittregel im Kalkül von Schütte für die intuitionistische Typenlogik.
Ein Vollständigkeitsbeweis für schnittfreie Kalküle mit der Maximalisierungsmethode von Henkin.
Eine algebraische Konstruktion abzählbarer Modelle.
Eine Logik vager Sätze.
Eine Note zum System PC.
Eine semantische Charkterisierung der durch die Implikation allein darstellbaren Wahrheitsfunktionen.
Embedded Lattice and Properties of Gram Matrix
In this article, we formalize in Mizar [14] the definition of embedding of lattice and its properties. We formally define an inner product on an embedded module. We also formalize properties of Gram matrix. We formally prove that an inverse of Gram matrix for a rational lattice exists. Lattice of Z-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm [16] and cryptographic systems with lattice [17].
Embedding algebraic closure spaces in 2-ary closure spaces
Embedding relations in the lattice of recursively enumerable sets.
Embeddings of quasicells of iterative algebras.
Entropies of vague information sources
The information-theoretical entropy is an effective measure of uncertainty connected with an information source. Its transfer from the classical probabilistic information theory models to the fuzzy set theoretical environment is desirable and significant attempts were realized in the existing literature. Nevertheless, there are some open topics for analysis in the suggested models of fuzzy entropy - the main of them regard the formal aspects of the fundamental concepts. Namely their rather additive...
Entropy of -sums and -products of - fuzzy numbers
In the paper the entropy of – fuzzy numbers is studied. It is shown that for a given norm function, the computation of the entropy of – fuzzy numbers reduces to using a simple formula which depends only on the spreads and shape functions of incoming numbers. In detail the entropy of –sums and –products of – fuzzy numbers is investigated. It is shown that the resulting entropy can be computed only by means of the entropy of incoming fuzzy numbers or by means of their parameters without the...
Entropy on effect algebras with Riesz decomposition property II: MV-algebras
We study the entropy mainly on special effect algebras with (RDP), namely on tribes of fuzzy sets and sigma-complete MV-algebras. We generalize results from [RiMu] and [RiNe] which were known only for special tribes.
Entropy on effect algebras with the Riesz decomposition property I: Basic properties
We define the entropy, lower and upper entropy, and the conditional entropy of a dynamical system consisting of an effect algebra with the Riesz decomposition property, a state, and a transformation. Such effect algebras allow many refinements of two partitions. We present the basic properties of these entropies and these notions are illustrated by many examples. Entropy on MV-algebras is postponed to Part II.
Entscheidungsprobleme der Theorie zweier Äquivalenzrelationen mit beschränkter Zahl vоn Elementen in den Klassen
Enumerated type semantics for the calculus of looping sequences
The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. In this paper we enrich this calculus with a type discipline which preserves some biological properties depending on the minimum and the maximum number of elements of some type requested by the present elements. The type system enforces these properties and typed reductions guarantee that evolution preserves them. As an example, we model the hemoglobin structure and...