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.

The generalized orthomodularity property: configurations and pastings

Chajda Ivan;Fazio Davide;Ledda Antonio
2020-01-01

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.
2020
Generalized ortomodularity; Effect algebras; Orthoalgebras; Pastings; Forbidden configurations
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/295627
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