2025/05/12 by Andrew Craig, Craig, Andrew, Peter Jipsen +3
Computer Science · Decision Sciences · #Advanced Algebra and Logic #FOS: Computer and information sciences #Fuzzy and Soft Set Theory #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.2505.07789
openalex publication_date 2025/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop dualities for complete perfect distributive quasi relation algebras and complete perfect distributive involutive FL-algebras. The duals are partially ordered frames with additional structure. These frames are analogous to the atom structures used to study relation algebras. We also extend the duality from complete perfect algebras to all algebras, using so-called doubly-pointed frames with a Priestley topology. We then turn to the representability of these algebras as lattices of binary relations. Some algebras can be realised as term subreducts of representable relation algebras and are hence representable. We provide a detailed account of known representations for all algebras up to size six.