Abstract
This article provides a systematic analysis of the well-known notions of weak and strong permission in input/output (I/O) logic. We extend the account of permission initially put forward by Makinson and Van der Torre to the whole family of I/O systems developed during the last two decades. The main contribution is a series of characterization results for strong permission, based on establishing the so-called non-repetition property. We also study an input/output logic not yet covered in the literature. It supports reasoning by cases—a natural feature of human reasoning. The output is not closed under logical entailment. At the same time, it avoids excess output using a consistency check—a technique familiar from non-monotonic logic. This makes it well suited for contrary-to-duty reasoning. The axiomatic characterization is in terms of a generalized OR rule. We discuss the implications of all this for our understanding of the notion of the coherence of a normative system. Topics for future research are identified.
Xavier Parent
Senior Postdoc Researcher
Xavier works mainly on logic and semantics, with a special focus on normative reasoning. He is currently funded with a research grant from FWF (Austrian Science Fund) working as Principal Investigator in a project titled “Axiomatizing conditional normative reasoning” (ANCoR), hosted at the Institute of Logic and Computation of the Faculty of Informatics at TU Wien, within A. Ciabattoni’s Theory and Logic research group.
Leon van der Torre
Professor of Artificial Intelligence and Computer Science
Leon van der Torre is a full professor of artificial intelligence and computer science at the University of Luxembourg. He has been working on deontic logic and its applications for nearly three decades. He is one of the founding fathers of input-output logic, the BOID architecture, the game-theoretic approach to normative multiagent systems, and the LogiKEy methodology.