How to Produce S-Tense Operators on Lattice Effect Algebras

Chajda, Ivan; Janda, Jiří; Paseka, Jan

doi:10.1007/s10701-014-9818-9

Cited by 1 publication

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“…It is well known [2] that this problem is easily solvable for Boolean algebras but it is not solvable e.g. for MV-algebras or effect algebras in general (see [1] and [4] for details). Hence, we are encouraged to find certain restrictions that are still in accordance with physical reality.…”

Section: Introductionmentioning

confidence: 99%

“…This means that we get a procedure how to construct a corresponding time frame to be in accordance with the canonical construction from [6]. Since any MV-algebra and any lattice effect algebra with q-tense operators is a q-effect algebra our approach covers the results from [1] and [4].…”

Section: Introductionmentioning

confidence: 99%

“…In Section 3 we introduce a powerful notion of a q-semi-state on a q-effect algebra and we also establish a relationship among various kinds of q-semi-states on q-effect algebras. Following [4] we introduce the notion of a Jauch-Piron q-semi-state. The advantage of this approach is that these semi-states reflect an important property of the logic of quantum mechanics, namely the so-called Jauch-Piron property (see [17] and [18]) saying that if the probability of propositions A and B being true is zero then there exists a proposition C covering both A and B.…”

Section: Introductionmentioning

confidence: 99%

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Galois connections and tense operators on q-effect algebras

Chajda

Paseka

2016

Fuzzy Sets and Systems

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Please cite this article in press as: I. Chajda, J. Paseka, Galois connections and tense operators on q-effect algebras, Fuzzy Sets and Systems (2015), http://dx.Abstract. 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.

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Section: Introductionmentioning

confidence: 99%