85 research outputs found
Ts-Tribes andTs-Measures
AbstractWe show that any fundamental triangular norm-basedTs-tribe T,s∈(0,∞), is a weakly generated tribe. Consequently, T is aT-tribe for any measurable t-normTif and only if it is aTs-tribe for somes∈(0,∞). Further we prove that eachTs-measurem,s∈(0,∞], defined on aTs-tribe T, is a generated measure; i.e., the irreducible part in the Butnariu–Klement decomposition ofTs-measures is always trivial
A Novel Form of Contextuality Predicting Probabilistic Equivalence between Two Sets of Three Mutually Noncommuting Observables
A novel contextual quantum system of observables is introduced, which
predicts the state-independent equality of occurrence probabilities between two
sets of triple mutually noncommuting observables.Comment: 18 pages, 8 figures, 1 table, dedicated to the memory of Rene Maye
Boolean Subalgebras of Orthoalgebras
We develop a direct method to recover an orthoalgebra from its poset of
Boolean subalgebras. For this a new notion of direction is introduced.
Directions are also used to characterize in purely order-theoretic terms those
posets that are isomorphic to the poset of Boolean subalgebras of an
orthoalgebra. These posets are characterized by simple conditions defining
orthodomains and the additional requirement of having enough directions.
Excepting pathologies involving maximal Boolean subalgebras of four elements,
it is shown that there is an equivalence between the category of orthoalgebras
and the category of orthodomains with enough directions with morphisms suitably
defined. Furthermore, we develop a representation of orthodomains with enough
directions, and hence of orthoalgebras, as certain hypergraphs. This hypergraph
approach extends the technique of Greechie diagrams and resembles projective
geometry. Using such hypergraphs, every orthomodular poset can be represented
by a set of points and lines where each line contains exactly three points.Comment: 43 page
States on symmetric logics: extensions
Исследованы состояния на квантовых логиках множеств. Решена одна известная задача
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