Duality for Quasilattices and Galois Connections
Anna B. Romanowska, Jonathan D. H. Smith · Fundamenta Informaticae · 2017
The primary goal of the paper is to establish a duality for quasilattices. The main ingredients are duality for semilattices and their representations, the structural analysis of quasilattices as Płonka sums of lattices, and the duality for lattices developed by Hartonas and Dunn. Lattice duality t reats the identity function on a lattice as a Galois connection between its meet and join semilattice reducts, and then invokes a duality between Galois connections and polarities. A second goal of the paper is a further examination of this latter duality, using the concept of a pairing to provide an algebraic equivalent to the relational structure of a polarity.