From Explicit Allowances to Defeasible Deontic Operators: A Modal View

Abstract

Preference-based deontic logics provide a foundation for normative reasoning but fail to distinguish between explicit allowances – specified by a designer – and implicit ones derived by inference. This distinction is crucial in systems where agents may act only if (explicitly or implicitly) permitted. In this paper, we formalize this inference by grounding the preference ordering over possible worlds in a permission base, i.e., a set of explicit allowances, and derive implicit permissions, as well as defeasible prohibitions and obligations. Our framework provides solutions to key deontic paradoxes and is a conservative extension of Åqvist’s dyadic deontic system F extended with cautious monotony. We illustrate the approach with a case study involving robotic agents operating under normative constraints and provide complexity results together with a QBF-based decision procedure to support automated reasoning.