Universal decomposition, performance and categorical properties will be presented for quantum automata in the form of three new theorems for the category of quantum automata [1][1], quantum computers [2] , Qa,c, and their related quantum logics based on an extension of n-Lukasiewicz algebra [3] as well as their applications [4]. The category of quantum automata and quantum computers is first de...

MV-algebras were introduced by Chang in 1958 preliminary to his providing an algebraic completeness proof for the K0-vaΓued Lukasiewicz propositional logic, LXo. In this paper a method is given for determining, for an arbitrary normal extension of LKo, an MV-algebra characteristic for the extension. The characteristic algebras are finite direct products of two sets of linearly ordered MV-algebr...

We investigated the mechanisms underlying the modulation of transmitter release from bipolar cells. Three currents, measured under whole-cell patch clamp in the tiger salamander retinal slice, were used to identify the sites of modulation and to establish their pharmacological profile. (1) A light-elicited inhibitory current was measured in bipolar cells that could be blocked by picrotoxin. Thi...

The conditional mean value has applications in regression analysis and financial mathematics, because they are used it. We can find papers from recent years that use the fuzzy cases. As intuitionstic sets an extension of sets, we will try to define a for intuitionistic case. crisp events was first studied by V. Valenčáková 2009. She Gödel connectives. Her approach only be special cases events, ...

The paper gives the systematic characterization of eigenspace in max-T algebra where T is equal to Łukasiewicz t-norm. Max-Łukasiewicz fuzzy algebra can be used for the description of the states of Discrete-event systems. The states can represent a balance of the resource unit expended during the evolution of the system (for example fuel or money). In the contribution, the classification of max...

In the present paper, we introduce topological notions defined by means of α-open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Lukasiewicz logic in [0, 1]). We introduce T 0 −, T 1 −, T 2 (αHausdorff)-, T 3 (α-regular)and T 4 (αnormal)-separation axioms. Furthermore, the R 0− and R 1− separation axioms are studied and their relations with the T 1 − ...

An approximate Herbrand theorem is proved and used to establish Skolemization for first-order Łukasiewicz logic. Proof systems are then defined in the framework of hypersequents. In particular, extending a hypersequent calculus for propositional Łukasiewicz logic with usual Gentzen quantifier rules gives a calculus that is complete with respect to interpretations in safe MV-algebras, but lacks ...

Hoop residuation algebras are the {→, 1}-subreducts of hoops; they include Hilbert algebras and the {→, 1}-reducts of MV-algebras (also known as Wajsberg algebras). The paper investigates the structure and cardinality of finitely generated algebras in varieties of kpotent hoop residuation algebras. The assumption of k-potency guarantees local finiteness of the varieties considered. It is shown ...

In classical propositional logic over finitely many variables no automorphism has any stochastic property, because the dual space is a finite discrete set. In this paper we show that the situation for the infinite-valued Lukasiewicz logic is radically different, by exhibiting a family of Bernoulli automorphisms over two variables. As dynamical systems, these are piecewiselinear area-preserving ...