Rule-based systems are being applied to tasks of increasing responsibility. Deductive methods are being applied to their validation, to detect flaws in these systems and enable us to use them with more confidence. Each system of rules is encoded as a set of axioms that define the system theory. The operation of the rule language and information about the subject domain are also described in the system theory. Validation tasks, such as establishing termination, unreachability, or consistency, or verifying properties of the system, are all phrased as conjectures. If we succeed in establishing the validity of the conjecture in the system theory, we have carried out the corresponding validation task. A method for the gradual formulation of specifications based on the attempted proof of a series of conjectures has been found to be suitable for rule-based systems. Such a specification can serve as the basis for a reengineering of the system using conventional software technology.