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In an open multi-agent system (MAS), agent autonomy and heterogeneity may possibly exploit cooperation, leading the system to an undesirable state. Since an MAS has no central control, a coordination mechanism must be developed to allow agents to fulfill their design goals. It is proposed to incorporate the dependability explicit computing (DepEx) ideas into a law-governed approach in order to build a dependable open MAS. The authors show that the law specification can explicitly incorporate dependability concerns, collect data and publish them in a metadata registry. This data can be used to realise DepEx and, for example, it can help to guide design and runtime decisions. The advantages of using a law-governed approach are (i) the explicit specification of the dependability concerns; (ii) the automatic collection of the dependability metadata reusing the infrastructure of the mediators presenting in law-governed approaches; and (iii) the ability to specify reactions to undesirable situations, thus preventing service failures.