Non-deterministic semantics as a tool for modeling negation and modality.

01 October 2023 → 30 September 2026
Research Foundation - Flanders (FWO)
Research disciplines
  • Humanities
    • Logic
    • Philosophy of mathematics
    • Analytical philosophy
Modal logic Paraconsistent negations Non-deterministic semantics
Project description

My research proposal provides a new perspective on the question of whether negation is a modality. According to one of the most popular approaches by Berto, negation is a particular kind of modality. He developed a formal framework based on possible worlds semantics. The first objective of this project is to use instead non-deterministic semantics and to develop an alternative framework that incorporates both negation and modality. To do so, I will further extend and adapt the existing results for non-deterministic modal logics. In particular, the non-deterministic approach that handles both weak modal logics (that do not have the standard possible world semantics) and various types of philosophically relevant negations (Boolean, paraconsistent) needs to be constructed. The project's ultimate goal is to compare the resulting framework with the one proposed by Berto. Such a comparison will be twofold: philosophical and technical. From the technical perspective, I will not only look at the limits of both frameworks, but also at their fine graininess, i.e., what logics can be captured in which framework and why. From the philosophical perspective, I will see in what sense one could consider the framework as modal and how it impacts on the interplay between negation and modality.