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Tense operators on basic algebras. (English) Zbl 1246.81014
Effect algebras were introduced ca. 20 years ago to generalize the set of all Hermitian operators between zero and the identity operator of a Hilbert space. They are simply partial algebras with a primary operation \(+\) of addition. They cannot be studied completely using methods of universal algebras. Therefore, the first three authors introduced basic algebras [Soft Comput. 14, No. 3, 251–255 (2010; Zbl 1188.03048)]. The aim of the present paper is to introduce tense operators for basic algebras and to study their basic properties. They have also connection with the so-called dynamic effect algebras.

MSC:
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
03G25 Other algebras related to logic
06F35 BCK-algebras, BCI-algebras
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