Lattice theory, ordered topological structures, and
related areas; applications in logic and computer science.
Specifically, my work has involved
Priestley duality for distributive lattices, topological dualities
for varieties of distributive lattices with additional operations
and the theory of natural dualities.
I have recent and current collaborative
projects
on natural dualities, including their connections to other constructions, with
For a number of years I have been working, in collaboration with
Mai Gehrke,
on duality and canonical extensions. In particular, we are preparing a
research monograph,n Lattices in Logic, for Oxford University Press.
A Research Case Study
Free Sugihara algebras: demonstrating the power of duality theory to solve problems in logic and algebra [.pdf] (November 2019)
Recent preprints and publications
(with L.M. Cabrer) Piggybacking over unbounded distributive lattices, pp. 21
(submitted; [arxiv preprint])
(with L.M. Cabrer) Sugihara algebras and monoids: free algebras
(manuscript)
(with L.M. Cabrer)
Sugihara algebras: admissibility algebras via the test space=s method (J. Pure Appl. Algebra
224 no.5 (May 2020)
[arxiv preprint])
(with L.M. Cabrer, B. Freisberg and G. Metcalfe)
Checking admissibility using the test spaces method (ACM Trans. Comput. Logic 20 (2019) , no.1, Art.2 (published
Dec. 2018)
[arxiv preprint]
(with L.M. Cabrer) Natural dualities through product representations: bilattices and beyond
(Studia Logica 104 (2016), 567-592) [preprint]
(with L.M. Cabrer) A general framework for product representations: bilattices and beyond
(Log. J. IGPL 23 (2015), 816-841) [arxiv preprint]
(with B.A.
Davey and M. Haviar) Piggyback dualities revisited (Algebra Universalis
76 (2016), 245-285. doi:10.1007/s00012-016-0395-y))
[arxiv preprint]
(with L.M. Cabrer) Gödel algebras: interactive dualities and their applications (Algebra Universalis
(a volume dedicated to Brian Davey for his 65th birthday)
74 (2015), 87-116)
[arxiv preprint]
(with L.M. Cabrer) A general framework for product representations: bilattices and beyond
(Log. J. IGPL 23 (2015), 816-841) [arxiv preprint]
(with L.M. Cabrer and A.P.K. Craig) Product representation for default bilattices: an application of natural duality theory (J. Pure Appl. Algebra 219
(2015),
2962-2988) [arxiv preprint]
(with L.M. Cabrer) Distributive bilattices from the perspective of natural duality theory
(Algebra Universalis,
(2015),
103-141)
[arxiv preprint]
GAIA 2013 (conference in honour of Brian Davey, Melbourne, July 2013): slides [pdf]
BLAST 2013 (Chapman University, California, August 2013): slides I
[pdf]; slides II [pdf]
George Boole Mathematical Sciences Conference, Theme 2: From Boole's Algebra of Logic to Boolean Algebra, and Beyond (University College Cork, August 2015): slides
[pdf]
TACL 2019 (Topology, Algebra and Categories in Logic, Nice, June 2019), Snapshots of duality theory, from 2019 and 50 years earlier: slides
[pdf]
Events organised
Research Workshops on Duality Theory in Algebra, Logic and
Computer Science, Oxford, 13-14 June and 15-17 August, 2012.
Sponsored by EPSRC and the British Logic Colloquium.
Workshop on Duality Theory, Oxford, 2-3 August 2011
Conference TANCL'07 (Algebraic and Topological Methods in Non-classical
Logics III)
This conference, sponsored by the London Mathematical Society and the British Logic
Colloquium, was held at the Mathematical
Institute, Oxford, 5-9 August, 2007. It was the third in the biennial series now using the acronym TACL
(Topology, Algebras and Categories in Logic)