Logic of defeasible permission and its dynamics

Abstract

Abstract This paper develops a deontic logic for defeasible permission and studies norm change in various updated semantics. When one grants that $\varphi $ or $\psi $ is permitted, normally, it goes together with the conjunction of a permission of $\varphi $ and that of $\psi $. In the monotonic reasoning on this permission, a permission of $\varphi $ leads to a permission of $\varphi $ and $\psi $; however, if a prohibition of $\psi $ is introduced, we get into trouble. We face a paradox of free choice permission. Many solutions have been proposed, but a systematic account of handling norm change is still needed. This paper first introduces the notion of normality to develop a sound and complete deontic logic for defeasible permission, which can be used to analyse several notions in natural language and in game theory. Further, following Lewis’ idea of norm change, a systematic way to capture various dynamics for updating permission and obligation is proposed.