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Dynamic effect algebras. (English) Zbl 1324.03026
Summary: 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.

MSC:
03G12 Quantum logic
03G25 Other algebras related to logic
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
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