I have a rather broad range of research interests, which includes philosophical issues, technical work and more application-oriented topics. As you will see, much of my research is of an interdisciplinary nature, e.g. applying epistemic logic to game theory, or using corpus linguistics in the philosophy of mathematics. Below is an incomplete overview:
:: logical geometry generalizing and re-analyzing the traditional square of oppositions; the connections and differences between the various types of logical diagrams (Aristotelian diagrams, opposition diagrams, implication diagrams, Hasse diagrams, duality diagrams, etc.); opposition structures in public announcement logic; algebraic perspectives on duality in logic and language; the visual-cognitive properties of logic diagrams, etc. (for more information, see the project website)
:: epistemic logic: pretty much everything (dynamic turn, justification logics, etc.); research on probabilistic dynamic epistemic logic (with applications to game theory: Aumann's agreement theorem), on dynamifying neighborhood semantics, on connections with logical geometry, etc.
:: formal epistemology: research on (the dynamic perspective at) the Lockean thesis about (qualitative) belief vs (quantitative) degrees of belief; I'm also developing an interest in social epistemology (links with contemporary epistemic logic seem obvious: focus on multi-agent scenarios, testimony as public announcement, etc.)
:: philosophy of mathematics: mainly within the practice-based tradition: corpus-linguistic research on the function and historical development of specific mathematical phrases (in particular: "it is easy to see that..." and "let X be...")
:: history of philosophy and logic: research on William of Ockham's theory of cognition; active interest in the historical roots and development of dynamic epistemic logic and logical geometry
:: natural language semantics and philosophy of language: I published a paper on the semantics and pragmatics of indefinite/definite descriptions; my current interests are mainly in structured propositions (I claim this topic is related to the logical omniscience problem in epistemic logic), duality relations, the minimalism/contextualism debate, conditionals, generalized quantifier theory, and vagueness
:: mathematical modal logic: algebraic and topological models for modal logic; probabilistic extensions of modal logic (currently no active research)