151 citations · 163 across the 9 of their papers we have counts for
5 papers · 1 filter
Dual Ploščica spaces of ortholattices
Andrew Craig, Miroslav Haviar
We describe digraphs with topology which give dual representations of ortholattices. This is done via so-called dual Ploščica spaces of lattices. First, we improve the definition o…
Dual spaces of lattices and semidistributive lattices
Andrew Craig, Miroslav Haviar, José São João
Birkhoff's 1937 dual representation of finite distributive lattices via finite posets was in 1970 extended to a dual representation of arbitrary distributive lattices via compact t…
Dual digraphs of finite meet-distributive and modular lattices
Andrew Craig, Miroslav Haviar, Klarise Marais
We describe the digraphs that are dual representations of finite lattices satisfying conditions related to meet-distributivity and modularity. This is done using the dual digraph r…
Product representation for default bilattices: an application of natural duality theory
L. M. Cabrer, A. P. K. Craig, H. A. Priestley
Bilattices (that is, sets with two lattice structures) provide an algebraic tool to model simultaneously the validity of, and knowledge about, sentences in an appropriate language.…
A fresh perspective on canonical extensions for bounded lattices
A. P. K. Craig, M. Haviar, H. A. Priestley
This paper presents a novel treatment of the canonical extension of a bounded lattice, in the spirit of thetheory of natural dualities. At the level of objects, this can be achieve…