151 citations · 163 across the 9 of their papers we have counts for
12 papers
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…
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…
Modelling competing theories
Willem Conradie, Andrew Craig, Alessandra Palmigiano +1
We introduce a complete many-valued semantics for two normal lattice-based modal logics. This semantics is based on reflexive many-valued graphs. We discuss an interpretation and p…
Modelling informational entropy
Willem Conradie, Andrew Craig, Alessandra Palmigiano +1
By 'informational entropy', we understand an inherent boundary to knowability, due e.g. to perceptual, theoretical, evidential or linguistic limits. In this paper, we discuss a log…
Microarcsecond VLBI pulsar astrometry with PSR II. parallax distances for 57 pulsars
A. T. Deller, W. M. Goss, W. F. Brisken +8
We present the results of PSR, a large astrometric project targeting radio pulsars using the Very Long Baseline Array (VLBA). From our astrometric database of 60 pulsars, we hav…
Constructive canonicity for lattice-based fixed point logics
Willem Conradie, Andrew Craig, Alessandra Palmigiano +1
We prove the algorithmic canonicity of two classes of -inequalities in a constructive meta-theory of normal lattice expansions. This result simultaneously generalizes Conradie a…
Canonicity results for mu-calculi: an algorithmic approach
Willem Conradie, Andrew Craig
We investigate the canonicity of inequalities of the intuitionistic mu-calculus. The notion of canonicity in the presence of fixed point operators is not entirely straightforward.…
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…