Soft Computing

, Volume 22, Issue 4, pp 1203–1207 | Cite as

Reduced axioms for the propositional logics induced by basic algebras

  • Ivan ChajdaEmail author
  • Miroslav Kolařík


A certain logic induced by basic algebras was already studied by the first author in Chajda (Int J Theor Phys 54:4306–4312, 2015) and, for the particular case of the so-called commutative basic algebras, axiom system was established by Botur and Halaš (Arch Math Logic 48:243–255, 2009). In Kolařík (Discuss Math Gen Algebra Appl 36:113–116, 2016) the just mentioned axiom system was essentially reduced. The aim of this paper is to reduce the original axiom system from Chajda (Int J Theor Phys 54:4306–4312, 2015) and to show that it is the best possible reduction in the sense that the remaining axioms are independent.


Basic algebra Commutative basic algebra Orthomodular lattice The logic of quantum mechanics Axiom system 



This study was funded by the project New Perspectives on Residuated Posets, Project I 1923–N25 by Austrian Sci. Fund (FWF) and 15–34697L by Czech Grant Agency (GAČR), and by ÖAD, Project CZ 04/2017.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interests.

Human and animal participants

This article does not contain any studies with human participants performed by any of the authors.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Algebra and Geometry, Faculty of SciencePalacký University OlomoucOlomoucCzech Republic
  2. 2.Department of Computer Science, Faculty of SciencePalacký University OlomoucOlomoucCzech Republic

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