A Logical Framework for Graded Deontic Reasoning

* Wider research context / theoretical framework

Graded obligations and permissions are discussed in various disciplines: Philosophy, linguistics, logic and computer science. With the advance of autonomous agents comes the need to specify, formalize and automate logical reasoning via deontic modalities. These modalities often vary in strength, so that combinations of deontic and many-valued logics are required.

* Hypotheses / research questions / objectives

Our main goal is to explore and evaluate a number of different options for formalizing reasoning about graded obligations and permissions. We aim to provide a logical framework that allows us to systematically explore appropriate goodness relations, connections between degrees of goodness and truth, and the suitability of various many-valued logics as base formalism. We also plan to incorporate reasoning about uncertainty and develop corresponding proof systems. To test the resulting framework, we have chosen two application areas that fit our current research focus: many-valued judgment aggregation and degrees of consistency of deontic situations with given sets of (possibly) graded norms.

* Approach / methods

Drawing on our expertise in mathematical fuzzy logic, deontic logic and many-valued judgment aggregation, we pursue our research objectives in three work packages (WPs). WP1 will develop the aforementioned logical framework, informed by recent developments in fuzzy and deontic logic, but also by linguistic and philosophical research. WP2 is devoted to judgment aggregation, extending research on classical aggregation to scenarios in which deontic propositions are to be aggregated and in which agents’ individual and collective judgments admit different degrees of agreement or disagreement. WP3 focuses on the consistency of graded deontic situations. It builds on current research on choice logics and will use evaluation games to refine the semantics of the choice operator.

* Level of originality / innovation

Graded deontic logic is a surprisingly under-researched topic. We approach this area in an innovative way, not only by defining multi-valued versions of deontic logics, but rather by creating a flexible formal framework that is also informed by linguistic and philosophical research. The two application areas mentioned above - graded judgment aggregation and grading deontic situations - are at the forefront of current research.

* Primary researchers involved

The applicant, Chris Fermüller, is known for his work on models of graded reasoning, proof theory, automatic reasoning, and game semantics. He will work closely with Agata Ciabattoni and Xavier Parent, who are leading experts in the field of deontic logic. The project allows Robert Freiman to join as a postdoctoral researcher after completing a very promising PhD programme.