STATES, UNIFORMITIES AND METRICS ON LATTICE EFFECT ALGEBRAS
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2002We show that every state ω on a lattice effect algebra E induces a uniform topology on E. If ω is subadditive this topology coincides with pseudometric topology induced by ω. Further, we show relations between the interval and order topology on E and topologies induced by states.
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Lattice ordered effect algebras
Algebra Universalis, 2003The purpose of this paper is to discuss some structural properties of lattice ordered effect algebras. We will use these structural properties to find certain lattices and classes of lattices that do not admit an effect algebra structure. Finally, using these structural properties, we will show that if L is the face lattice of a convex polytope in $ R ...
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Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras
International Journal of Theoretical Physics, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Paseka, Jan, Riečanová, Zdenka
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Generalization of Blocks for D-Lattices and Lattice-Ordered Effect Algebras
International Journal of Theoretical Physics, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A triple representation of lattice effect algebras
Mathematica Slovaca, 2016Abstract A mutual relationship between MV-algebras and coupled semirings as established by L. P. Belluce, A. Di Nola, A. R. Ferraioli and B. Gerla is extended to lattice effect algebras and so-called characterizing triples. We show that this correspondence is in fact one-to-one and hence every lattice effect algebra can be considered as ...
Chajda, Ivan, Länger, Helmut
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Effectively inseparable Boolean algebras in lattices of sentences
Archive for Mathematical Logic, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Pseudocomplemented lattice effect algebras and existence of states
Information Sciences, 2009The author studies pseudocomplemented lattice effect algebras. In particular, it is shown that the set of sharp elements in a pseudocomplemented lattice effect algebra forms a Boolean algebra (with the inherited pseudocomplementation as an orthocomplementation) and that every pseudocomplemented complete atomic lattice effect algebra admits a state.
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Observables on \(\sigma\)-MV algebras and \(\sigma\)-lattice effect algebras
Kybernetika, 2011The paper deals with observables on lattice ordered \(\sigma\)-effect algebras and introduces their \textit{smearings} with respect to (weak) Markov kernels. Using generalized Loomis-Sikorski theorem for \(\sigma\)-MV-algebras, the authors prove that every observable is defined by a smearing of a sharp observable. However, the smearing of an observable
Anna Jencová +2 more
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The sum of observables on a $$\sigma $$ σ -distributive lattice effect algebra
Soft Computing, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jirí Janda, Yongming Li 0001
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Some Ideal Lattices in Partial Abelian Monoids and Effect Algebras
Order, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
G. Chevalier, Sylvia Pulmannová
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