Towards a Temporal Account of Contrary-to-Duty Constraints over Complex Actions in the Situation Calculus

With the advent of artificial agents in everyday life, it is important that these agents are guided by social norms and moral guidelines. Notions of obligation, permission, and the like have traditionally been studied in the field of Deontic Logic, where deontic assertions generally refer to what an agent should or should not do; that is they refer to actions. In Artificial Intelligence, the Situation Calculus is (arguably) the best known and most studied formalism for reasoning about action and change. In this paper, we further investigate the integration of these two areas, particularly addressing socalled contrary-to-duty (CTD) scenarios. For this purpose, we present a new logic based on Lakemeyer and Levesque’s modal Situation Calculus variant ES that we modify to express properties about programs from the action language GOLOG, extended by new constructs for negated programs and their joint execution. We use this formalism to discuss three different approaches to CTD scenarios. First, we show it to be expressive enough to fully capture Meyer’s dynamic deontic logic PDeL, and hence corresponding solutions for CTDs. Second, we demonstrate how our previous approach to tackle CTDs in terms of defeasible conditionals over a restricted set of GOLOG programs can be represented as well. Finally, we extend the language of these conditionals to include a simple notion of intention, which allows to describe CTDs not only in terms of actions that will follow immediately, but that the agent has committed to execute at some time in the foreseeable future. All in all, the contribution of the paper is thus an approach that is substantially more general than previous approaches, and is able to handle CTDs in a flexible manner.