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Displaying 21 – 36 of 36

On the concreteness of quantum logics

Pavel Pták, John David Maitland Wright (1985)

Aplikace matematiky

It is shown that for any quantum logic $L$ one can find a concrete logic $K$ and a surjective homomorphism $f$ from $K$ onto $L$ such that $f$ maps the centre of $K$ onto the centre of $L$ . Moreover, one can ensure that each finite set of compatible elements in $L$ is the image of a compatible subset of $K$ . This result is “best possible” - let a logic $L$ be the homomorphic image of a concrete logic under a homomorphism such that, if $F$ is a finite subset of the pre-image of a compatible subset of $L$ , then $F$ is compatible....

On the convergence and absolute continuity of signed states on a logic

Vladimír Palko (1985)

Mathematica Slovaca

On the homomorphisms of sum logics

S. Pulmannová, A. Dvurečenskij (1991)

Annales de l'I.H.P. Physique théorique

On the individual ergodic theorem on a logic

Anatolij Dvurečenskij, Beloslav Riečan (1980)

Commentationes Mathematicae Universitatis Carolinae

On the lattice structure of quantum logics

Wawrzyniec Guz (1978)

Annales de l'I.H.P. Physique théorique

On the products of quantum logics

Pulmannová, Sylvia (1984)

Proceedings of the 11th Winter School on Abstract Analysis

On the structure of numerical event spaces

Gerhard Dorfer, Dietmar W. Dorninger, Helmut Länger (2010)

Kybernetika

The probability $p (s)$ of the occurrence of an event pertaining to a physical system which is observed in different states $s$ determines a function $p$ from the set $S$ of states of the system to $[0, 1]$ . The function $p$ is called a numerical event or multidimensional probability. When appropriately structured, sets $P$ of numerical events form so-called algebras of $S$ -probabilities. Their main feature is that they are orthomodular partially ordered sets of functions $p$ with an inherent full set of states. A classical...

On the sum of observables in a logic

Anatolij Dvurečenskij, Sylvia Pulmannová (1980)

Mathematica Slovaca

On the tensor product of a Boolean algebra and an orthoalgebra

David J. Foulis, Pavel Pták (1995)

Czechoslovak Mathematical Journal

On the uniqueness problem for quite full logics

Vladimír Rogalewicz (1984)

Annales de l'I.H.P. Physique théorique

On two problems of quantum logics

Anatolij Dvurečenskij (1986)

Mathematica Slovaca

On σ-orthodistributivity

Janusz Czelakowski (1979)

Colloquium Mathematicae

Order properties of splitting subspaces in an inner product space

Pavel Pták, Hans Weber (2004)

Mathematica Slovaca

Ordering of observables and characterization of conditional expectation

Oľga Nánásiová (1987)

Mathematica Slovaca

Orthocomplemented difference lattices with few generators

Milan Matoušek, Pavel Pták (2011)

Kybernetika

The algebraic theory of quantum logics overlaps in places with certain areas of cybernetics, notably with the field of artificial intelligence (see, e. g., [19, 20]). Recently an effort has been exercised to advance with logics that possess a symmetric difference ([13, 14]) - with so called orthocomplemented difference lattices (ODLs). This paper further contributes to this effort. In [13] the author constructs an ODL that is not set-representable. This example is quite elaborate. A main result...

Orthomodular lattices with almost orthogonal sets of atoms

Sylvia Pulmannová, Vladimír Rogalewicz (1991)

Commentationes Mathematicae Universitatis Carolinae

The set $A$ of all atoms of an atomic orthomodular lattice is said to be almost orthogonal if the set ${b \in A : b ≰ a^{'}}$ is finite for every $a \in A$ . It is said to be strongly almost orthogonal if, for every $a \in A$ , any sequence $b_{1}, b_{2}, \dots$ of atoms such that $a ≰ b_{1}^{'}, b_{1} ≰ b_{2}^{'}, \dots$ contains at most finitely many distinct elements. We study the relation and consequences of these notions. We show among others that a complete atomic orthomodular lattice is a compact topological one if and only if the set of all its atoms is almost orthogonal.

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