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Start Over Subject orthomodular lattice

1. On systems of congruences on principal filters of orthomodular implication algebras

Creator:
Halaš, Radomír and Plojhar, Luboš
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
orthoimplication algebra, orthomodular lattice, and p-filter
Language:
English
Description:
Orthomodular implication algebras (with or without compatibility condition) are a natural generalization of Abbott’s implication algebras, an implication reduct of the classical propositional logic. In the paper deductive systems (= congruence kernels) of such algebras are described by means of their restrictions to principal filters having the structure of orthomodular lattices.
Rights:
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2. Orthocomplemented difference lattices with few generators

Creator:
Matoušek, Milan and Pták, Pavel
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
orthomodular lattice, quantum logic, symmetric difference, Gödel´s coding, Boolean algebra, and free algebra
Language:
English
Description:
The algebraic theory of quantum logics overlaps in places with certain areas of cybernetics, notably with the field of artificial intelligence (see, e. g., \cite{pp:book,wata}). Recently an effort has been exercised to advance with logics that possess a symmetric difference (\cite{matODL,MP1}) - with so called orthocomplemented difference lattices (ODLs). This paper further contributes to this effort. In \cite{matODL} the author constructs an ODL that is not set-representable. This example is quite elaborate. A main result of this paper somewhat economizes on this construction: There is an ODL with 3 generators that is not set-representable (and so the free ODL with 3 generators cannot be set-representable). The result is based on a specific technique of embedding orthomodular lattices into ODLs. The ODLs with 2 generators are always set-representable as we show by characterizing the free ODL with 2 generators - this ODL is MO3×24.
Rights:
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3. Orthomodular lattices with state-separated noncompatible pairs

Creator:
Mayet, R. and Pták, Pavel
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
orthomodular lattice, state, noncompatible pairs, and (quasi)variety
Language:
English
Description:
In the logico-algebraic foundation of quantum mechanics one often deals with the orthomodular lattices (OML) which enjoy state-separating properties of noncompatible pairs (see e.g. [18], [9] and [15]). These properties usually guarantee reasonable “richness” of the state space—an assumption needed in developing the theory of quantum logics. In this note we consider these classes of OMLs from the universal algebra standpoint, showing, as the main result, that these classes form quasivarieties. We also illustrate by examples that these classes may (and need not) be varieties. The results supplement the research carried on in 1], [3], [4], [5], [6], [11], [12], [13] and [16].
Rights:
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4. Quantum logics and bivariable functions

Creator:
Drobná, Eva, Nánásiová, Oľga, and Valášková, Ľubica
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
finite atomistic quantum logic, orthomodular lattice, conditional state, s-map, d-map, bivariable functions, modeling infimum measure, supremum measure, and simultaneous measurements
Language:
English
Description:
New approach to characterization of orthomodular lattices by means of special types of bivariable functions G is suggested. Under special marginal conditions a bivariable function G can operate as, for example, infimum measure, supremum measure or symmetric difference measure for two elements of an orthomodular lattice.
Rights:
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5. Quotient structures in lattice effect algebras

Creator:
Sharafi, Amir Hossein and Borzooei, Rajb Ali
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
MV-effect algebra, orthomodular lattice, Lattice effect algebra, CI-lattice, Sasaki arrow, (strong, fantastic, implicative, positive implicative) filter, Riesz ideal, and D-ideal
Language:
English
Description:
In this paper, we define some types of filters in lattice effect algebras, investigate some relations between them and introduce some new examples of lattice effect algebras. Then by using the strong filter, we find a CI-lattice congruence on lattice effect algebras, such that the induced quotient structure of it is a lattice effect algebra, too. Finally, under some suitable conditions, we get a quotient MV-effect algebra and a quotient orthomodular lattice, by this congruence relation.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public