One main research focus is on foundational issues in natural language semantics related to  compositionality, content, and context-dependence. A related project is on the semantics of quantification and binding, and issues in the vicinity of Russell's antinomy of the variable—the historical issues, the logical issues, and the relations to linguistics.

I've recently been thinking about the semantics of diagrams, and especially  diagrams used in logic such as quantificational diagrams and the diagrams associated with Peirce and Venn. 

I'm also interested in traditional philosophical problems, and in the deployment of formal methods in the service of addressing such problems, so think about puzzles and paradoxes having to do with truth, knowledge, modality, time, grounding, etc. For example, I'm currently working on develoments of counterpart theory in relation to de re epistemic modality. I am co-organiser of the Edinburgh Meaning Sciences Group.