Publication details

Galois connections and tense operators on q-effect algebras

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Year of publication 2016
Type Article in Periodical
Magazine / Source Fuzzy Sets and Systems
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Effect algebra; q-Effect algebra; Galois q-connection; q-Tense operators; q-Jauch-Piron q-effect algebra; q-Representable q-effect algebra
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Description For effect algebras, the so-called tense operators were already introduced by Chajda and Paseka. They presented also a canonical construction of them using the notion of a time frame. Tense operators express the quantifiers "it is always going to be the case that" and "it has always been the case that" and hence enable us to express the dimension of time both in the logic of quantum mechanics and in the many-valued logic. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a time frame such that each of these operators can be obtained by the canonical construction. To approximate physical real systems as best as possible, we introduce the notion of a q-effect algebra and we solve this problem for q-tense operators on q-representable q-Jauch-Piron q-effect algebras. (c) 2015 Elsevier B.V. All rights reserved.
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