A Logical Framework for Graded Deontic Reasoning

Deontic reasoning deals with the logical relationships between normative obligations, permissions and prohibitions. For example, the fact that something is forbidden if it is not permitted and that something whose opposite is not obligated represents a permission, represents a simple logical relationship between deontic statements. Accordingly, so-called deontic logics have been formulated and analyzed for many decades. However, these have so far almost exclusively referred to classical propositions, i.e. statements that are either simply true or false. However, many applications require a broader approach in which different norms can be given different weights. In addition, one should also be able to be taken into account statements that - due to vagueness or uncertainty - do not understand normative validity as a binary yes/no decision, but allow for degrees of truth or validity. There are many options for formulating corresponding graded deontic logics, which are created by a number of different components and parameters that must be taken into account in a mathematical model of normative reasoning. For example, linguistic studies have uncovered various ways of arranging degrees and weights of goodness, in the sense of what is expressed or implicitly assumed to be generally desirable. This project attempts to incorporate such results into the formulation of corresponding logics and is accordingly interdisciplinary: the intended formal models of reasoning are not only based on logical and mathematical research, but also take into account philosophical and linguistic aspects of reasoning with normative statements. Possible applications of these models and corresponding graduated deontic logics are the analysis and automatic (computer-aided) reasoning with normative systems, which are increasingly needed for the specification of complex systems, such as autonomous vehicles. The project team will create a broad formal- logical framework that can serve as a flexible basis for providing appropriate formal tools for this task.