An integrity specification language (ISL) based upon a form of interval temporal logic is defined and the framework for a logic of knowledge and beliefs about data integrity is developed. The intended purpose of ISL is for the design of integrity kernels in an office information system in which the dynamic evaluation of data integrity based upon partial knowledge and informed judgement relative to update request by clients, is required. ISL itself is described in an earlier paper and summarized in this paper. Beliefs in ISL are specified with a form of interval temporal logic and provide an extension of the Moser technique for formulating beliefs. The Clark and Wilson model designed to prevent fraudulent and erroneous data modification is subsumed. An integrity Characteristic Tuple (ICT) incorporates the notions of correctness, completeness, quality, timeliness and confidence is associated with each Constrained Data Item (CDI). An integrity system which includes extensions of the concept and function of the server architecture as defined in the Multimedia Office Server (MULTOS) project, is given. An integrity kernel is defined which incorporates an algorithm for the detection of faults in presumptions about data integrity based upon knowledge and beliefs. A simplified integrity kernel is specified formally and a corresponding sample server-client session is provided.