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On representation of dynamic algebras with reversion

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Mathematical Foundations of Computer Science 1981 (MFCS 1981)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 118))

Abstract

We investigate the role of the reversion operator in dynamic algebras. We show that all actions in a dynamic algebra with reversion are completely additive. So the considering of the reversion is a way how to axiomatize complete additivity by purely algebraic means. Our main result states that every separable *-continuous dynamic algebra with reversion can be represented as a subalgebra of a full complete dynamic algebra consisting of all completely additive functions on a complete Boolean algebra. We give some corollaries related to the problem of representability of dynamic algebras by Kripke structures. We generalize some results from dynamic algebras with reversion to dynamic algebras with completely additive actions.

Section 1 deals with basic definitions. In Section 2 we introduce and investigate invertible functions. Section 3 contains main results. In Section 4 we discuss generalizations to dynamic algebras without reversion.

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Author information

Authors and Affiliations

  1. Faculty of Nuclear Science and Technical Engineering, Technical University of Prague, Husova 5, Prague 1, Czechoslovakia

    Jan Reiterman & Věra Trnková

  2. Faculty of Mathematics and Physics, Charles University Prague, Sokolovská 83, Prague 8, Czechoslovakia

    Jan Reiterman & Věra Trnková

Authors
  1. Jan Reiterman
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  2. Věra Trnková
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Editor information

Jozef Gruska Michal Chytil

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© 1981 Springer-Verlag Berlin Heidelberg

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Reiterman, J., Trnková, V. (1981). On representation of dynamic algebras with reversion. In: Gruska, J., Chytil, M. (eds) Mathematical Foundations of Computer Science 1981. MFCS 1981. Lecture Notes in Computer Science, vol 118. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10856-4_114

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  • DOI: https://doi.org/10.1007/3-540-10856-4_114

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10856-6

  • Online ISBN: 978-3-540-38769-5

  • eBook Packages: Springer Book Archive

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