Resolving conflicts based on ambiguities in the public vocabulary is one of the challenges in semantic integration. Though different suggestions for resolving (ambiguity) conflicts with semantic integration operators exist, there is still a need for clear formalizations of adequacy criteria for the operators. In this article, adequacy criteria for semantic integration similar to rationality postulates of classical belief revision but adjusted to the semantic integration scenario are formalized. The criteria are intended to capture integration settings in which the integration candidates are well developed ontologies with a shared public vocabulary. In such cases, both ontologies have to be preserved in some form in the integration result and have to be recoverable from the integration result. Additionally, the integration result has to be consistent and provide connections between the integrated ontologies. The criteria are applied by evaluating a small collection of integration operators that solve conflicts deriving from ambiguities in the public vocabulary.