The first step in establishing the reliability of an expert system is to verify that its knowledge base is free from anomalies such as redundant, conflicting or missing knowledge. Such anomalies are suggestive of errors in the knowledge base; empirical evidence suggests that at errors revealed by verification may be hard to detect by conventional system testing. Verification can be performed automatically by a domain-independent anomaly checking tool because the anomalies can be formally defined in terms of logic and detected by syntactic inspection of logic-based knowledge bases. This paper provides not only a formal framework for verification in the form of a set of anomaly definitions expressed in first-order predicate logic, but also detailed descriptions and algorithms for an automatic verification program called COVER. COVER offers a number of advantages over previous anomaly detection tools: firstly, it detects a wider range of anomalies; secondly, it incorporates a number of novel features which afford its users more flexibility to make the checking task more practical for large knowledge bases. A familiarity with first-order predicate logic is assumed for the reader of this paper.