My research has focused on the theory of binary relations.  The principal algebraic formalism for binary relations is relation algebra, I have written the key textbook on this topic.  Binary relations are much harder to deal with than unary relations, my approach (jointly with Ian Hodkinson) is based on a simple two player game to test consistency of assertions about binary relations.  Using these games I have established various complexity results, including the undecidability of the representation problem for finite relation algebras.  I have extensive research in other algebras of relations, e.g. cylindric, polyadic, domain, kleene algebras, etc. 

I have published research in a wide range of fields including graph theory, relativity theory, argumentation, constraint satisfaction and planning.

I am director of the London Logic Forum which brings together eminent logicians from various academic institutions in London.