Abstract
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.
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Acknowledgements
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.
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Communicated by A. Di Nola.
Research of the first author is supported 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 entitled Ordered structures for non-classical logics.
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Chajda, I., Kolařík, M. Reduced axioms for the propositional logics induced by basic algebras. Soft Comput 22, 1203–1207 (2018). https://doi.org/10.1007/s00500-017-2628-1
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DOI: https://doi.org/10.1007/s00500-017-2628-1