Operator residuation in orthomodular posets of finite height
Logic
2022-04-25 v1
Abstract
We show that for every orthomodular poset P of finite height there can be defined two operators forming an adjoint pair with respect to an order-like relation defined on the power set of P. This enables us to introduce the so-called operator residuated poset corresponding to P from which the original orthomodular poset P can be recovered. Moreover, this correspondence is almost one-to-one. We show that this construction of operators can be applied also to so-called weakly orthomodular and dually weakly orthomodular posets. Examples of such posets are included.
Keywords
Cite
@article{arxiv.2204.10794,
title = {Operator residuation in orthomodular posets of finite height},
author = {Ivan Chajda and Helmut Länger},
journal= {arXiv preprint arXiv:2204.10794},
year = {2022}
}