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Foundations of Physics

, Volume 44, Issue 7, pp 792–811 | Cite as

How to Produce S-Tense Operators on Lattice Effect Algebras

  • Ivan Chajda
  • Jiří  Janda
  • Jan Paseka
Article

Abstract

Tense operators in effect algebras play a key role for the representation of the dynamics of formally described physical systems. For this, it is important to know how to construct them on a given effect algebra \( E\) and how to compute all possible pairs of tense operators on \( E\). However, we firstly need to derive a time frame which enables these constructions and computations. Hence, we usually apply a suitable set of states of the effect algebra \( E\) in question. To approximate physical reality in quantum mechanics, we use only the so-called Jauch–Piron states on \( E\) in our paper. To realize our constructions, we are restricted on lattice effect algebras only.

Keywords

Effect algebra MV-algebra Complete lattice Tense operator S-tense operator Jauch–Piron E-state Jauch–Piron E-semi-state 

Mathematics Subject Classification

Primary 03B44 03G25 06A11 06B23 

Notes

Acknowledgments

We thank the anonymous referees for the careful reading of the paper and the suggestions on improving its presentation. All authors acknowledge the support by ESF Project CZ.1.07/2.3.00/20.0051 Algebraic methods in Quantum Logic of the Masaryk University.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Algebra and Geometry, Faculty of SciencePalacký University OlomoucOlomoucCzech Republic
  2. 2.Department of Mathematics and Statistics, Faculty of ScienceMasaryk UniversityBrnoCzech Republic

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