On Obligations and Abilities

In this paper, we combine deontic logic with Alternating-time Temporal Logic (ATL) into a framework that makes it possible to model and reason about obligations and abilities of agents. The way both frameworks are combined is technically straightforward: we add deontic accessibility relations to ATL models (concurrent game structures), and deontic operators to the language of ATL (an additional operator $\mathcal{UP}$ is proposed for ldquounconditionally permittedrdquo properties, similar to the ldquoall I knowrdquo operator from epistemic logic). Our presentation is rather informal: we focus on examples of how obligations (interpreted as requirements) can be confronted with ways of satisfying them by actors of the game. Though some formal results are presented, the paper should not be regarded as a definite statement on how logics of obligation and strategic ability must be combined; instead, it is intended for stimulating discussion about such kinds of reasoning, and the models that can underpin it. Keywords: deontic logic, alternating-time logic, multi-agent systems.