2020/04/29 by Ivan Chajda, Miroslav Kolařík, Chajda, Ivan +3
Computer Science · #03B47 #03B52 #06A11 #06B05 #Advanced Algebra and Logic #FOS: Mathematics #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2004.14127
openalex publication_date 2020/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that every not necessarily bounded poset P=(P,\≤,') with an\nantitone involution can be extended to a residuated poset\nE(P)=(E(P),\≤, odot,\→,1) where x'=x\→0 for all x\∈ P. If P\nis a lattice with an antitone involution then E(P) is a lattice, too. We show\nthat a poset can be extended to a residuated poset by means of a finite chain\nand that a Boolean algebra (B, vee, wedge,',p,q) can be extended to a\nresiduated lattice (Q, vee, wedge, odot,\→,1) by means of a finite\nchain in such a way that x odot y=x wedge y and x\→ y=x' vee y for all\nx,y\∈ B.\n