Multiagent Bayesian networks (MABNs) are a powerful new framework for uncertainty management in a distributed environment. In a MABN, a collective joint probability distribution is defined by the conditional probability tables (CPTs) supplied by the individual agents. It is assumed, however, that CPTs supplied by individual agents agree on the variable domains, an assumption that does not necessarily hold in practice.

In this paper, we suggest modelling MABNs with inclusion dependencies. Our approach is more flexible, and perhaps realistic, by allowing CPTs supplied by different agents to disagree on variable domains. Our main result is that the input CPTs define a joint probability distribution if and only if certain inclusion dependencies are satisfied. Other advantages, both practical and theoretical, of modelling MABNs with inclusion dependencies are discussed.