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On the law (a·b′)′=b+a′·b′ in de Morgan algebras and orthomodular lattices

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Abstract

This paper's goal is to prove that the only de Morgan algebras and the only orthomodular lattices in which the law (a·b′)′=b+a′·b′, posed by Charles Elkan in [1] holds, are those that are boolean algebras. That is, that among both families of de Morgan algebras and orthomodular lattices, Elkan's formula is only characteristic of boolean algebras.

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Authors and Affiliations

  1. Dep. Inteligencia Artificial, Universidad Politécnica de Madrid, Campus de Montegancedo, Boadilla del Monte, 28660, Madrid, Spain

    E. Renedo & E. Trillas

  2. Secció de Matemàtiques i Informàtica, Dept. d'Estructures a l'Arquitectura, Universitat Politècnica de Catalunya, Diagonal 649, 08028, Barcelona, Spain

    C. Alsina

Authors
  1. E. Renedo
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  2. E. Trillas
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  3. C. Alsina
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Corresponding author

Correspondence to E. Renedo.

Additional information

Authors are actually in debt with an anonymous referee that helped them to considerably improve the first version of this paper.

This paper has been partially supported by CICYT(Spain) under project TIC2000-1420

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Renedo, E., Trillas, E. & Alsina, C. On the law (a·b′)′=b+a′·b′ in de Morgan algebras and orthomodular lattices. Soft Computing 8, 71–73 (2003). https://doi.org/10.1007/s00500-003-0264-4

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  • DOI: https://doi.org/10.1007/s00500-003-0264-4

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