Compatibility in D-posets

Kōpka, František

doi:10.1007/bf00676263

Cited by 40 publications

(12 citation statements)

References 4 publications

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“…A D-poset has been introduced in Kôpka and Chovanec (1994) and studied in Chovanec and Kôpka (2007), Chovanec and Rybáriková (1998), Kôpka (1995).…”

Section: Introductionmentioning

confidence: 99%

Conditional states and independence in D-posets

et al. 2009

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“…A D-poset has been introduced in Kôpka and Chovanec (1994) and studied in Chovanec and Kôpka (2007), Chovanec and Rybáriková (1998), Kôpka (1995).…”

Section: Introductionmentioning

confidence: 99%

Conditional states and independence in D-posets

et al. 2009

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“…Elements x and y of a lattice effect algebra E are called compatible (x ↔ y for short) if x ∨ y = x ⊕ (y (x ∧ y)) (see [11,19]). …”

Section: Preliminaries and Basic Factsmentioning

confidence: 99%

MacNeille completion of centers and centers of MacNeille completions of lattice effect algebras: Generic scheme behind

Niederle

Paseka

2012

Mathematica Slovaca

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“…From the point of view of applications in physics, the compatibility relation in D-posets [13] is rather important.…”

Section: Proposition 1 Let a B C Be Elements Of A Boolean D-poset Pmentioning

confidence: 99%

Quasi Product on Boolean D-Posets

Kōpka

2007

Int J Theor Phys

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The pointwise multiplication on a full tribe and the product operation on an MValgebra play a crucial role in the construction of a joint observable. In the present paper we introduce a quasi product operation on Boolean D-posets and describe its properties. Our quasi product generalizes product on MV-algebras and in some cases also t-norms.Keywords Boolean D-poset · MV-algebra · Quasi product · t-norm 1 Basic notions D-posets [14] and, equivalently, effect algebras [10] generalize various classical algebraic structures modeling quantum mechanics and the fuzzy sets theory systems. The two structures are based on different approaches. The primary operation on effect algebras is a sum and the primary operation on D-posets is a difference of two comparable elements.A D-poset is a partially ordered set P , with a greatest element 1 and a smallest element 0, on which a partial binary operation difference b a is defined if and only if a ≤ b; it fulfills the following conditions:In every D-poset P the following three statements are equivalent [13]:(c1) For every two elements a and b from P there exist c, d ∈ P such that d ≤ a ≤ c, d ≤ b ≤ c and c a = b d;

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Compatibility in D-posets

Cited by 40 publications

References 4 publications

Conditional states and independence in D-posets

Conditional states and independence in D-posets

MacNeille completion of centers and centers of MacNeille completions of lattice effect algebras: Generic scheme behind

Quasi Product on Boolean D-Posets

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