Tense Operators on Basic Algebras |
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Authors: | M Botur I Chajda R Hala? M Kola?ík |
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Institution: | 1.Department of Algebra and Geometry,Palacky University Olomouc,Olomouc,Czech Republic;2.Department of Computer Science,Palacky University Olomouc,Olomouc,Czech Republic |
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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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Keywords: | |
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