Ontology-based data management (OBDM) is a powerful knowledge-oriented paradigm for managing data spread over multiple heterogeneous sources. In OBDM, the data sources of an information system are handled through the reconciled view provided by an ontology, i.e., the conceptualization of the underlying domain of interest expressed in some formal language. In any information systems where the basic knowledge resides in data sources, it is of paramount importance to specify the acceptable states of such information. Usually, this is done via integrity constraints, i.e., requirements that the data must satisfy formally expressed in some specific language. However, while the semantics of integrity constraints are clear in the context of databases, the presence of inferred information, typical of OBDM systems, considerably complicates the matter. In this paper, we establish a novel framework for integrity constraints in the OBDM scenarios, based on the notion of knowledge state of the information system. For integrity constraints in this framework, we define a language based on epistemic logic, and study decidability and complexity of both checking satisfaction and performing different forms of static analysis on them.