Data integration is difficult, due to variable data format, variable data quality, paucity of meta-data, and various social factors. If all documents had schemas and if fully automatic schema integration were feasible, then much could be done syntactically; but these assumptions are far from true. Ontologies can help, but only represent logical relations among predicates. Moreover, a given domain may have several ontologies, each potentially incomplete and/or ambiguous, written in different languages, which may be based on different logics. Thus integrating data may require integrating not just schemas and ontologies, but also ontology languages, and even ontology logics. We argue that institutions can help master this “integration chain.” Also, recent work is described on abstract schemas and their morphisms, for m-to-n matches with semantic functions and conditions; on the SCIA tool, which partially implements this theory; and perhaps on connections with work of Barwise & Seligman, of Ganter & Wille, and of Sowa.