The Structure of Practical Reasons
Reasons are central both in everyday normative reasoning and in normative theorizing, regardless of whether they are the fundamental (or one of the fundamental) normative notions.
Having precise models of how reasons are structured and how to reason with them is crucial to advance our understanding of substantive normative questions. The general aim of this project is to investigate the structure of practical reasons. This aim will be realized by giving a unified formal account, to serve as the semantic backdrop to construct natural logical systems to reason with reasons, based on justification logic with a novel truthmaker semantics.
Proof and Model Theory of Intuitionistic Temporal Logic
Intuitionistic logic enjoys a myriad of interpretations based on computation, information or topology, making it a natural framework to reason about dynamic processes in which these phenomena play a crucial role. Yet there is a large gap to be filled regarding our understanding of the computational behaviour of intuitionistic temporal logics. The aim of this project is to cement our understanding of intuitionistic temporal logics by developing their model theory based on dynamic topological systems, and their proof theory based on prominent paradigms such as Gentzen-style calculi as well as cyclic proofs. Further information can be found here:
https://users.ugent.be/~dfernnde/itl.html
Modalities in Substructural Logics: Theory, Methods and Applications
Modal logics are a family of formal systems based on classical logic which aim at improving the expressive power of the classical calculus allowing to reason about “modes of truth”. The aim of the present proposal is to put forward a systematic study of substructural modal logics, understood as those modal logics in which the modal operators are based upon the general ground of substructural logics, weaker deductive systems than classical logic. Our aim is also to explore the applications of substructural modal logics outside the bounds of mathematical logic and, in particular, in the areas of knowledge representation; legal reasoning; data privacy and security; logical analysis of natural language.
Explicit reasons
This project is concerned with reasons why one believes something, reasons why one knows something, and reasons why one ought to do something. We develop formal languages in which reasons can be represented explicitly and investigate the logical properties of explicit reasons. To achieve this, we rely on the framework of justification logic.
In particular, we present non-normal deontic logics with justifications. Further, we develop a semiring framework for justifications, and we engineer a possible world semantics for justifications that supports additional structure like graded justifications or probability distributions on justifications.
