Publication details

Dynamic effect algebras and their representations



Year of publication 2012
Type Article in Periodical
Magazine / Source Soft computing
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Effect algebra; Lattice effect algebra; Tense operators; Dynamic effect algebra
Description For lattice effect algebras, the so-called tense operators were already introduced by Chajda and KolaA (TM) ik. 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 in every effect algebra can be introduced tense operators which, for non-complete lattice effect algebras, can be only partial mappings. An effect algebra equipped with tense operators reflects changes of quantum events from past to future. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a frame such that each of these operators can be obtained by our construction. We solve this problem for (strict) dynamic effect algebras having a full set of homorphisms into a complete lattice effect algebra.

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