Dynamic effect algebras

Mathematica Slovaca - Tập 62 Số 3 - Trang 379-388 - 2012
Ivan Chajda1, Miroslav Kolařík2
1Department of Algebra and Geometry Faculty of Science, Palacký University Olomouc, 17. listopadu 12, CZ-771 46, Olomouc, Czech Republic
2Department of Computer Science Faculty of Science, Palacký University Olomouc, 17. listopadu 12, CZ-771 46, Olomouc, Czech Republic

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Abstract We introduce the so-called tense operators in lattice effect algebras. 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 in the logic of quantum mechanics. We present an axiomatization of these tense operators and prove that every lattice effect algebra whose underlying lattice is complete can be equipped with tense operators. Such an effect algebra is called dynamic since it reflects changes of quantum events from past to future.

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Mathematica Slovaca

Tập 62 Số 3

379-388

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