A general theory of optimal natural dualities is presented, built on the test algebra technique introduced in an earlier paper. Given that a set R of finitary algebraic relations yields a duality on a class of algebras A = ISP(M), those subsets R of R which yield optimal dualities are char-acterised. Further, the manner in which the relations in R are… (More)
These notes deal with an interconnecting web of mathematical techniques all of which deserve a place in the armoury of the well-educated computer scientist. The objective is to present the ideas as a self-contained body of material, worthy of study in its own right, and at the same time to assist the learning of algebraic and coalgebraic methods , by giving… (More)
A backtracking algorithm with element order selection is presented, and its eeciency discussed in relation both to standard examples and to examples concerning relation-preserving maps which the algorithm was derived to solve.
A b s t r a c t. The purpose of this note is to expose a new way of viewing the canonical extension of posets and bounded lattices. Specifically, we seek to expose categorical features of this completion and to reveal its relationship to other completion processes. The theory of canonical extensions is introduced by Jónsson and Tarski [15, 16] for Boolean… (More)
The context for this paper is a class of distributive lattice expansions, called double quasioperator algebras (DQAs). The distinctive feature of these algebras is that their operations preserve or reverse both join and meet in each coordinate. Algebras of this type provide algebraic semantics for certain non-classical propositional logics. In particular,… (More)
This paper presents a unified account of a number of dual category equivalences of relevance to the theory of canonical extensions of distributive lattices. Each of the categories involved is generated by an object having a 2-element underlying set; additional structure may be algebraic (lattice or complete lattice operations) or relational (order) and, in… (More)