 (IC0) ensures that the resulting merged base satisfies the integrity constraints. This is an obvious condition to impose since these are postulates for merging under integrity constraints, where the idea is to ensure that the result of the merging satisfies the integrity constraints. By employing a merging operator, the chairman knows that the group will agree on the increase of the expenses, if they decide to build at least two of the three facilities. (IC1) states that, when IC is consistent, then the result of the fusion operator will also be consistent. Again, given that the interpretations of the merged bases are selected among the interpretations of the integrity constraints, if IC is consistent, the result will also be consistent. (IC2) states that the result of the merging operator is simply the conjunction of the belief profile and the IC, whenever such conjunction is consistent. In our running example, if each person wishing to build two or more facilities endorses the rise of the expenses and the opinions given by the co-owners are consistent, then the merging will just return the conjunction of the IC and the individual opinions. (IC3) states that if two belief profiles \(E_1\) and \(E_{2}\) are logically equivalent and \(\IC_1\) and \(\IC_{2}\) are also equivalent, then merging the first belief profile with \(\IC_1\) will be equivalent as merging the second belief profile with \(\IC_{2}\). This postulate expresses a principle already imposed on belief revision operators (of which, as we shall see, merging operators are extensions), that is, the principle of irrelevance of syntax, which says that the result of a merging operator depends only on the semantical content of the merged bases and not on their syntactical expression. (IC4) is known as the fairness postulate because it states that when merging two belief bases \(K_1\) and \(K_{2}\), no priority should be given to one of them. The merging is consistent with one of them if and only if it is consistent with the other. This postulate expresses a symmetric condition that operators that give priority to one of the two bases will not satisfy. (IC5) and (IC6) were first introduced in (Revesz 1997) and together they mean that if two groups agree on at least one item, then the result of the fusion will coincide with those items on which the two groups agreed on. So, if the group of co-owners can be split in two parties, such that one wants to build the tennis court and the swimming pool and the other wants the swimming pool and the parking, the building of the swimming pool will be selected as the final group decision. Finally, (IC7) and (IC8) guarantee that if the conjunction between the merging on \(E\) under \(\IC_1\) and \(\IC_{2}\) is consistent, then \(\IC_1\) will remain satisfied if \(E\) is merged under a more restrictive condition, that is, the conjunction of \(\IC_1\) and \(\IC_{2}\). This is a natural requirement to impose as, less formally, (IC7) and (IC8) together state that if the swimming pool is chosen among the set of three alternatives, it will still be selected if we reduce the set of alternatives to the tennis court and swimming pool. The last two postulates are a generalization of two postulates for revision (R5 and R6) in (Katsuno and Mendelzon 1991), who analyzed the revision operator from a model-theoretic point of view and gave a characterization of revision operators satisfying the AGM rationality postulates (Alchourrón et al. 1985) in terms of minimal change with respect to an ordering over interpretations. Like Katsuno and Mendelzon’s postulates, (IC7) and (IC8) ensure that the notion of closeness is well behaved, in the sense that if an outcome is selected by the merging operator under \(\IC_1\), then that outcome will also be the closest (i.e., it will be selected) to \(\IC_{2}\) within the more restrictive constraint \(\IC_1 \land \IC_{2}\) (assuming \(\Delta_{\IC_1}(E) \land \IC_{2}\) to be consistent). In Katsuno and Mendelzon model-theoretic approach, revision operators change the initial belief base by choosing the closest interpretation in the new information. Similarly, IC merging operators select the closest interpretation in the integrity constraints to the set of belief bases. Hence, belief merging can be interpreted as a generalization of belief revision to multiple belief bases (Grégoire and Konieczny 2006). 