On obligations and normative ability: Towards a logical analysis of the social contract

We develop a logic of normative ability, as an extension to the Alternating-time Temporal Logic (atl) of Alur, Henzinger, and Kupferman. While conventional atl contains cooperation modalities of the form 《C》φ, intended to express the fact that coalition C have the capability to bring about φ, in Normative atl* (natl*), these expressions are replaced with constructs of the form 《η:C》φ, with the intended interpretation that C have the ability to achieve φ within the context of the normative system η. A normative system is a set of constraints on the actions that may be performed in any give state. We show how these normative ability constructs can be used to define obligations and permissions: φ is said to be obligatory within the context of the normative system η if φ is a necessary consequence of every agent in the system behaving according to the conventions of η. After introducing natl*, we investigate some of its axiomatic properties. To demonstrate its value as a logic for reasoning about multi-agent systems, we show how natl* can be used to formalise a version of the social contract.