The generalized orthomodularity property: configurations and pastings. (23rd June 2020)

• Record Type: Journal Article
• Authors: Chajda, Ivan; Fazio, Davide; Ledda, Antonio
• Is Part Of: Journal of logic and computation. Volume 30:Number 5(2020)
• Page Start: 991
• Page End: 1022
• Publication Date: 2020-06-23
• Subjects: Generalized ortomodularity -- effect algebras -- orthoalgebras -- pastings -- forbidden configurations; Logic programming -- Periodicals; Logic, Symbolic and mathematical -- Periodicals; Computational complexity -- Periodicals; 005.115
• DOI: 10.1093/logcom/exaa028
• Languages: English
• ISSNs: 0955-792X

Abstract

Abstract: In this paper, we consider a generalization of the notion of orthomodularity for posets to the concept of the generalized orthomodularity property (GO-property) by considering the $LU$ -operators. This seemingly mild generalization of orthomodular posets and its order theoretical analysis yield rather strong application to effect algebras and orthomodular structures. Also, for several classes of orthoalgebras, the GO-property yields a completely order-theoretical characterization of the coherence law, and, in turn, of proper orthoalgebras.