2022/04/22 by Ivan Chajda, Chajda, Ivan, Helmut Länger +1
Computer Science · Decision Sciences · #03G17 #06A11 #06C15 #81P10 #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Logic (math.LO) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2204.10794
openalex publication_date 2022/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.