Determining the Environment

Abstract

In the last decades logics for describing coalitional power in Multi Agent Systems have flourished. Alur’s Alternating-Time Temporal Logic (ATL) [1], Pauly’s Coalition Logic (CL) [5], Belnap’s STIT Logic [2], are only a few influential examples of them. Roughly speaking they are all multimodal logics equipped with an operator [C] to express the fact that a certain coalition of agents C can cooperate to achieve, where can be a property of a reachable outcome - like in Coalition Logic - or a temporal formula holding at certain paths - like in ATL and STIT. This work has shed light on the logical properties of interaction, giving a formal semantics to notions like “coordination” and “strategy” and allowing to reason on how agents can work together to achieve a desirable property. Nevertheless, as it happens in many real and artificial cases, things can go wrong and a desirable property may not be reached. One issue is then to find out which agent or group is responsible for such failure, in order to identify or punish it, or even remove it from the system. In CL, ATL and STIT, the environment is explicitly represented as the coalition made by the empty set of agents and, being a coalition, it can also be responsible. This is reflected in many applications, in which the environment has some interference in the course of events that will take place. In some of these situations it is impossible to understand just observing the final outcome whether the environment or the agents made or ruled out a certain choice. For this reason an issue is to identify those situations in which it is possible to safely formulate a regulation system such that a violation occurs if and only if some agent made it occur. To address this issue we provide a language to reason about Closed Interactions, i.e. all those situations in which the outcomes of an interaction can be determined by the agents themselves and in which the environment cannot interfere with what they are able to determine. Our viewpoint is that if we want to design Multi Agent Systems were responsibility can be assured, we need to focus on those interactions in which the power of the empty coalition is limited.