Ten Philosophical Problems in Deontic Logic J¨orgHansen1, Gabriella Pigozzi2 and Leendert van der Torre2 1 University of Leipzig, Institut f¨urPhilosophie 04107, Leipzig, Beethovenstraße 15, Germany
[email protected] 2 University of Luxembourg, Computer Science and Communications (CSC) 1359, Luxembourg, 6 rue Richard Coudenhove Kalergi, Luxembourg {gabriella.pigozzi,leon.vandertorre}@uni.lu Abstract. The paper discusses ten philosophical problems in deontic logic: how to formally represent norms, when a set of norms may be termed ‘coherent’, how to deal with normative conflicts, how contrary- to-duty obligations can be appropriately modeled, how dyadic deontic operators may be redefined to relate to sets of norms instead of pref- erence relations between possible worlds, how various concepts of per- mission can be accommodated, how meaning postulates and counts-as conditionals can be taken into account, and how sets of norms may be revised and merged. The problems are discussed from the viewpoint of input/output logic as developed by van der Torre & Makinson. We ar- gue that norms, not ideality, should take the central position in deontic semantics, and that a semantics that represents norms, as input/output logic does, provides helpful tools for analyzing, clarifying and solving the problems of deontic logic. Keywords. Deontic logic, normative systems, input/output logic Introduction Deontic logic is the field of logic that is concerned with normative concepts such as obligation, permission, and prohibition. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. Typically, a deontic logic uses Ox to mean that it is obligatory that x, (or it ought to be the case that x), and P x to mean that it is permitted, or permissible, that x.