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Abstract We present an abstract declarative semantics for multi-agent systems based on the idea of stable set, and argue that it can be suitably employed to describe, and to some extent verify, the dynamics of complex systems of autonomous and heterogeneous interacting agents. We view agents as black-boxes, whose semantics is abstractly understood as an input-output transformation from the agents' observations about their environment, to the actions they perform. Stable sets (of actions) characterise multi-agent systems able to reach an equilibrium point. Our semantics via stable sets takes into account the possibility that agents may fail.We illustrate how stability can characterise multi-agent systems by means of examples.We also draw considerations about how stable sets can be effectively approximated.