Soft Computing

, Volume 21, Issue 10, pp 2513–2519

Notes on quantum logics and involutive bounded posets

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DOI: 10.1007/s00500-017-2579-6

Cite this article as:
Wu, Y. & Yang, Y. Soft Comput (2017) 21: 2513. doi:10.1007/s00500-017-2579-6
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Abstract

In this paper, we study the exclusion problem concerning the classes of involutive bounded lattices, logics, and quantum logics (i.e., orthomodular lattices). We also obtain that a logic is a quantum logic if and only if it is a paraconsistent logic. Moreover, we give some considerations on an open question to find sufficient conditions for the existence of an orthomodular orthocomplementation on lattices. Furthermore, we revisit the Dedekind–MacNeille completion of involutive bounded posets and correct a widely cited error in quantum logics.

Keywords

Involutive bounded poset Ortholattice Orthomodular lattice (quantum logic) Dedekind–MacNeille completion 

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Mathematics and System SciencesBeihang UniversityBeijingChina

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