Secure logs are powerful tools for building systems that must resist forgery, prove temporal relationships, and stand up to forensic scrutiny. The proofs of order and integrity encoded in these tamper-evident chronological records, typically built using hash chaining, may be used by applications to enforce operating constraints or sound alarms at suspicious activity. However, the problem of how to automatically detect violations remains open. Low-level inconsistencies, such as gaps in the hash chain, are detectable without knowledge about the application, but existing research stops short of extracting or verifying application-specific log properties. In this paper we contribute the design and implementation of a system for discovering this kind of evidence. We first propose a logical language for applications to express concisely the constraints that apply to their logs and the evidence that can be extracted from them. We offer several algorithms for efficiently and incrementally evaluating these rules. Finally, we present QUERIFIER, a log analysis package that implements our proposed techniques. It can be used offline as an analyzer for static logs, or online during the runtime of a logging application. Given validity rules and available log data, it presents evidence of correctness and offers counterexamples if desired. We describe QUERIFIER's implementation and offer early performance results: for a rule set developed for a distributed voting application, we observed that our system could incrementally verify a realistic election-day log at 50 events per second.