Abstract
The concept of tense operators on a basic algebra is introduced. Since basic algebras can serve as an axiomatization of a many-valued quantum logic (see e.g. Chajda et al. in Algebra Univer. 60(1):63–90, 2009), these tense operators are considered to quantify time dimension, i.e. one expresses the quantification “it is always going to be the case that” and the other expresses “it has always been the case that”. We set up the axiomatization and basic properties of tense operators on basic algebras and involve a certain construction of these operators for left-monotonous basic algebras. Finally, we relate basic algebras with tense operators with another quantum structures which are the so-called dynamic effect algebras.
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This work is supported by the Research and Development Council of the Czech Government via the project MSM6198959214.
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Botur, M., Chajda, I., Halaš, R. et al. Tense Operators on Basic Algebras. Int J Theor Phys 50, 3737–3749 (2011). https://doi.org/10.1007/s10773-011-0748-4
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DOI: https://doi.org/10.1007/s10773-011-0748-4