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

Quantum logics of idempotents of unital rings

Исследованы квантовые логики идемпотенто