# research

I have a rather broad range of research interests, which includes philosophical issues, technical work and more application-oriented topics. Below is an incomplete overview:

**:: logical geometry**: generalizing and re-analyzing the traditional square of opposition; connections and differences between the various types of logical diagrams (Aristotelian diagrams, opposition diagrams, implication diagrams, Hasse diagrams, duality diagrams, etc.); bitstring semantics; algebraic perspectives on duality in logic and language; the visual-cognitive properties of logic diagrams; etc. (for more information, see the project website)

**:: history of logic**: Aristotelian diagrams in specific historical authors (e.g. John Buridan, Nicole Oresme, Domingo Bañez, Juan Caramuel y Lobkowitz, Arthur Schopenhauer, Augustus De Morgan); development of a comprehensive digital database of Aristotelian diagrams used throughout history; the history of logic at the University of Leuven (with a special focus on the 15th and 16th centuries, e.g. John Fabri of Valenciennes); the development of vernacular logic in Dutch (1585 - 1685)

**:: philosophy of logic**: the various roles of Aristotelian diagrams in logical practice

**:: epistemic logic and formal epistemology**: probabilistic epistemic logic (with applications in game theory, e.g. Aumann's agreeing to disagree theorem); the Lockean thesis on belief vs. degrees of belief; the philosophical significance of the dynamic turn in epistemic logic

**:: natural language semantics and philosophy of language**: the semantics and pragmatics of indefinite/definite descriptions; generalized quantifier theory; vagueness; bitstring semantics for various lexical fields; scalar implicatures

**:: history of philosophy**: William of Ockham's theory of cognition

**:: mathematical modal logic**: algebraic and topological models for modal logic; probabilistic extensions of modal logic