Programs in partial algebras

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 particula...

Pseudo-BCK algebras as partial algebras

It is well-known that the representation of several classes of residuated lattices involves lattice-ordered groups. An often applicable method to determine the representing group (or groups) from a residuated lattice is based on partial algebras: the monoidal operation is restricted to those pairs which fulfil a certain extremality condition, and else left undefined. The subsequent construction...

Collapsing Partial Combinatory Algebras

Partial combinatory algebras occur regularly in the literature as a framework for an abstract formulation of computation theory or re-cursion theory. In this paper we develop some general theory concerning homomorphic images (or collapses) of pca's, obtained by identiication of elements in a pca. We establish several facts concerning nal collapses (maximal identiication of elements). `En passan...

Extending partial combinatory algebras

Disjoint-union partial algebras

Disjoint union is a partial binary operation returning the union of two sets if they are disjoint and undefined otherwise. A disjoint-union partial algebra of sets is a collection of sets closed under disjoint unions, whenever they are defined. We provide a recursive first-order axiomatisation of the class of partial algebras isomorphic to a disjointunion partial algebra of sets but prove that ...