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# # ! , intended to express the fact that coalition C have the capability to bring about ! , in Normative ATL* (NATL*), these expressions are replaced with constructs of the form " " " : C# # ! , with the intended interpretation that C have the ability to achieve ! within the context of the normative system " . 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: ! is said to be obligatory within the context of the normative system " if ! is a necessary consequence of every agent in the system behaving according to the conventions of " . 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. ! 2005 Elsevier B.V. All rights reserved.

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