2024/04/20 by Ivan Chajda, Miroslav Kolařík, Chajda, Ivan +3
Computer Science · Decision Sciences · #06B05 #06C15 #06D15 #06D25 #08A11 #Advanced Algebra and Logic #Combinatorics (math.CO) #FOS: Mathematics #Multi-Criteria Decision Making #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2404.13361
openalex publication_date 2024/04/20 · openalex created_date 2024/04/24 · openalex updated_date 2026/07/28
On an arbitrary meet-semilattice S with 0 we define an orthogonality relation and investigate the lattice Cl(S) of all subsets of S closed under this orthogonality. We show that if S is atomic then Cl(S) is a complete atomic Boolean algebra. If S is a pseudocomplemented lattice, this orthogonality relation can be defined by means of the pseudocomplementation. Finally, we show that if S is a complete pseudocomplemented lattice then Cl(S) is a complete Boolean algebra. For pseudocomplemented posets a similar result holds if the subset of pseudocomplements forms a complete lattice satisfying a certain compatibility condition.