Closures in Binary Partial Algebras

Two procedures for computing closures in binary partial algebras (BPA) are introduced: a Fibonacci-style procedure for closures in associative BPAs, and a multistage procedure for closures in associative, commutative and idempotent BPAs. Ramifications in areas such as resolution theorem proving, graph-theoretic algorithms, formal languages and formal concept analysis are discussed. In particular, the multistage procedure, when applied to formal concept analysis, results in a new algorithm outperforming leading algorithms for computing concept sets.