Talks

Recent invited talks

1. The variety generated by completions of representable relation algebras.   LLF seminar, Birkbeck, 17 July 2019.   Abstract
2. A shorter proof that wRRA is a variety.   LLF seminar, Birkbeck, 26 Jan 2018.   Abstract
3. RaMICS, Braga, Portugal, Sept 2015.   Slides
4. LogIC seminar, Imperial College, Feb 2015
5. School of Computer Science and Software Engineering, University of Western Australia, Apr 2014.
6. Departamento de Matematica, Universidade de Aveiro, Portugal, Apr 2012 (3 talks).
7. 12th Asian Logic Conference Victoria University of Wellington, NZ, Dec 2011.
8. Logic Seminar, Dept of Mathematics, University of Leeds, March 2011.
9. TIME-10, Paris, 2010.
10. Workshop on Lattices and Binary Relations, UCL, September 2010.
11. Logic Colloquium, Paris, 2010.
12. Invited workshop ICLA 2009, Chennai. Two 90-min lectures.
13. International Workshop on Topological Methods in Logic, Tbilisi, Georgia, June 08.
14. University of Leicester, Mar 08. Workshop.
15. Hybrid Logic workshop (part of ESSLLI), Dublin, Aug 07.

Slides from talks

1. RaMICS, Braga, Sept 2015
   
   
2. Sahlqvist fixed point formulas
   12th Asian Logic Conference, Wellington, New Zealand, December 2011
   Recent results on Sahlqvist's theorem for the modal mu-calculus - joint work with Johan van Benthem and Nick Bezhanishvili.
   
   
3. Interval temporal logics with chop-like operators
   TIME'10, Paris, September 2010
   Some expressivity, decidability and axiomatisability results for temporal logics of intervals.
   
   
4. Algebras of relations: some results and methods
   Logic Colloquium 2010, Paris, July 2010
   A survey.
   
   
5. Axiomatising modal logics of elementary classes of Kripke frames
   Analytic Topology in Mathematics and Computer Science seminar, Oxford, November 2006
   The modal logics of elementary classes of Kripke frames have been of some longstanding interest in modal logic.  Sahlqvist (1973) gave a syntactic form of axiom that serves to axiomatise many but not all of them.  His work has been extended, and other ways to capture some of these logics are known.  I will survey some of this in the talk, and then go on to discuss one way to axiomatise the modal logic of an arbitrary elementary frame class.  The method is to translate the first-order definition into the 'quasipositive' fragment of hybrid logic, using results of Goldblatt on 'pseudo-equational' first-order sentences.  One then computes modal 'approximants' to each hybrid formula, which can be shown to axiomatise the original modal logic.  This process is analogous to standard proofs of Sahlqvist's theorem.
   
   See also slides for talk in HyLo workshop, ESSLLI, Dublin, August 2007
   
   
6. Fine's canonicity theorem and its converse
   British Logic Colloquium, Oxford, September 2006
   In a 1975 paper, Kit Fine proved that if L is the modal logic of an elementary class of Kripke frames, then L is canonical.  This was generalised by several authors, including van Benthem, Goldblatt, and Gehrke-Harding-Venema.  It is a central result in canonicity.  Fine asked in his paper whether the converse holds.  I will try to show how probabilistic and model-theoretic methods contribute to resolving this problem.  This is joint work with Rob Goldblatt (Wellington, New Zealand) and Yde Venema (Amsterdam).
   
   
7. Axiomatising the Modal Logic of Affine Planes
   Modal Logic, Stone Duality and Coalgebras, Leicester, June 2006
   In a 1999 paper, Yde Venema proposed to model projective planes by two-sorted Kripke frames, with a sort for points, another sort for lines, and an 'incidence' accessibility relation between them.  Among other things, he showed how to axiomatise the modal logic of projective planes.  Affine planes can be similarly modeled, using an additional accessibility relation of 'parallel' - two lines are parallel if and only if they are equal or have no points in common.  I will discuss recent joint work with Altaf Hussain on axiomatising the modal logic of affine planes, which, surprisingly, turns out to be more difficult than in the projective case.
   
   
8. Modal Logics of Elementary Classes of Kripke Frames via Hybrid Logic
   Amsterdam-London Workshop on Modal Logic, March 2006
   The modal logics of elementary classes of Kripke frames are precisely those logics that can be captured by sets of pure positive hybrid logic sentences with arbitrary existential and relativised universal quantification over nominals.  Each such hybrid sentence H syntactically generates an infinite set of modal formulas called 'approximants', which together axiomatise the modal logic of the class of frames validating H.  This generalises to sets of hybrid sentences.  The proof is analogous to standard proofs of Sahlqvist's theorem, combined with results of van Benthem and Goldblatt on 'pseudo-equational' first-order sentences.
   
   
9. Canonicity and representable relation algebras
   Logic in Hungary, Budapest, Aug 2005
   In the 1960s, Monk proved that the variety RRA of representable relation algebras is canonical. This is an instance of general results on canonical varieties due to Fine, van Benthem, and Goldblatt (1975-89). Recent work has shown that RRA only just manages to be canonical: it has no canonical axiomatisation, and any first-order axiomatisation of it has infinitely many non-canonical axioms. This is connected to a recent counterexample to the converse of the Fine-van Benthem-Goldblatt theorems. The talk outlined this material.
   
   
10. Finite model property for guarded fragments
    3 lectures, Logic and Computation Workshop, Nelson, New Zealand, Jan 2004
    Abstract  |  Workshop's copy of slides
    I aim to prove that some guarded fragments of first-order logic have the finite model property.
    
    
11. Finite model property for guarded fragments, and extending partial isomorphisms
    Leeds Logic Seminar, 5 Feb 2003
    I aim to explain the context and proof of a recent theorem of M. Otto--I.H. on extending partial isomorphisms of relational structures.
    
    
12. Monodic fragments of first-order temporal logics
    Advances in Modal Logic (Toulouse, Oct 2002)
    Most propositional temporal logics are decidable.  But the decision problem in predicate (first-order) temporal logics has seemed near-hopeless.  I will report on some recent work on this problem.  I will consider monodic fragments of the first-order temporal language, in which formulas beginning with a temporal operator have at most one free variable.  The first-order part is also restricted.  Validity of formulas in these fragments can be decided by combining an algorithm to decide the first-order part of the formula, with an algorithm deciding monadic second-order logic over the given flow of time.  It works for linear and (with additional restrictions) for branching time.
    
    
13. Aspects of relation algebras: slides for lectures given at the Third International Tbilisi Symposium on Language, Logic and Computation, Batumi, Georgia, September 1999.
    Article version in proceedings.