151 citations · 152 across the 8 of their papers we have counts for
10 papers
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…
Expanding Belnap 2: the dual category in depth
Andrew Craig, Brian A. Davey, Miroslav Haviar
Bilattices, which provide an algebraic tool for simultaneously modelling knowledge and truth, were introduced by N.D. Belnap in a 1977 paper entitled 'How a computer should think'.…
Canonical extensions of lattices are more than perfect
Andrew P. K. Craig, Maria J. Gouveia, Miroslav Haviar
In \cite{CGH15} we introduced TiRS graphs and TiRS frames to create a new natural setting for duals of canonical extensions of lattices. In this continuation of \cite{CGH15} we ans…
On selected developments in the theory of natural dualities
Miroslav Haviar
This is a survey on selected developments in the theory of natural dualities where the author had the opportunity to make with his foreign colleagues several breakthroughs and move…
Congruence pairs of principal MS-algebras and perfect extensions
Abd El-Mohsen Badawy, Miroslav Haviar, Miroslav Ploščica
The notion of a congruence pair for principal MS-algebras, simpler than the one given by Beazer for -algebras \cite{6}, is introduced. It is proved that the congruences of the…
Perfect extensions of de Morgan algebras
Miroslav Haviar, Miroslav Ploščica
An algebra is called a perfect extension of its subalgebra if every congruence of has a unique extension to . This terminology was us…