Errata to the article ``Topologies on quantum logics induced by measures''
Every uniformly Archimedean atomic MV-effect algebra is sharply dominating
Following the study of sharp domination in effect algebras, in particular, in atomic Archimedean MV-effect algebras it is proved that if an atomic MV-effect algebra is uniformly Archimedean then it is sharply dominating.
Extending Coarse-Grained Measures
In [4] it is proved that a measure on a finite coarse-grained space extends, as a signed measure, over the entire power algebra. In [7] this result is reproved and further improved. Both the articles [4] and [7] use the proof techniques of linear spaces (i.e. they use multiplication by real scalars). In this note we show that all the results cited above can be relatively easily obtained by the Horn-Tarski extension technique in a purely combinatorial manner. We also characterize the pure measures...
Extension theorems (vector measures on quantum logics)
Extensions of partially ordered partial abelian monoids
The notion of a partially ordered partial abelian monoid is introduced and extensions of partially ordered abelian monoids by partially ordered abelian groups are studied. Conditions for the extensions to exist are found. The cases when both the above mentioned structures have the Riesz decomposition property, or are lattice ordered, are treated. Some applications to effect algebras and MV-algebras are shown.
Filter theory and covering law
Fractal construction of an atomic Archimedean effect algebra with non-atomic subalgebra of sharp elements
Does there exist an atomic Archimedean lattice effect algebra with non-atomic subalgebra of sharp elements? An affirmative answer to this question is given.
Fuzzy quantum logics.
Quantum logic is a particular example of a fuzzy quantum logic. QL is semantically characterized by the class of all quantum MV algebras. The standard quantum MV algebra is based on the set of all effects in a Hilbert space. From the physical point of view, effects represent physical properties that may be noisy and ambiguous.
Generalized homogeneous, prelattice and MV-effect algebras
We study unbounded versions of effect algebras. We show a necessary and sufficient condition, when lattice operations of a such generalized effect algebra are inherited under its embeding as a proper ideal with a special property and closed under the effect sum into an effect algebra. Further we introduce conditions for a generalized homogeneous, prelattice or MV-effect effect algebras. We prove that every prelattice generalized effect algebra is a union of generalized MV-effect algebras and...
Group-valued measures on coarse-grained quantum logics
In it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure, over the entire power algebra. Later () this result was re-proved (and further improved on) and, moreover, the non-negative measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained...
“Hidden variables” on concrete logics (extensions)
Hilbert-space-valued states on quantum logics
Individual ergodic theorem on a logic
Integration on generalized measure spaces
Joint distributions and compatibility of observables in quantum logics
Kvantová teorie a operace spojení v teorii svazů
Lattice effect algebras densely embeddable into complete ones
An effect algebraic partial binary operation defined on the underlying set uniquely introduces partial order, but not conversely. We show that if on a MacNeille completion of there exists an effect algebraic partial binary operation then need not be an extension of . Moreover, for an Archimedean atomic lattice effect algebra we give a necessary and sufficient condition for that existing on is an extension of defined on . Further we show that such extending exists at most...
Local transition functions of quantum Turing machines
Local Transition Functions of Quantum Turing Machines
Foundations of the notion of quantum Turing machines are investigated. According to Deutsch's formulation, the time evolution of a quantum Turing machine is to be determined by the local transition function. In this paper, the local transition functions are characterized for fully general quantum Turing machines, including multi-tape quantum Turing machines, extending the results due to Bernstein and Vazirani.
Logical cover spaces