The Deontic Component of Action Language $n{\mathcal{C}}+$

Abstract

The action language ${\mathcal{C}}+$ of Giunchiglia, Lee, Lifschitz, McCain, and Turner is a formalism for specifying and reasoning about the effects of actions and the persistence (‘inertia') of facts over time. An ‘action description' in ${\mathcal{C}}+$ defines a labelled transition system of a certain kind. $n{\mathcal{C}}+$ (formerly known as $({\mathcal{C}}+)^{++}$) is an extended form of ${\mathcal{C}}+$ designed for representing normative and institutional aspects of (human or computer) societies. The deontic component of $n{\mathcal{C}}+$ provides a means of specifying the permitted (acceptable, legal) states of a transition system and its permitted (acceptable, legal) transitions. We present this component of $n{\mathcal{C}}+$, motivating its details with reference to some small illustrative examples.