Anytime Approximations of Classical Logic from Above

In this article we present s1, a family of logics that is useful to disprove propositional formulas by means of an anytime approximation process. The systems follows the paradigm of a parameterized family of logics established by Schaerf’s and Cadoli’s system S1. We show that s1 inherits several of the nice properties of S1, while presenting several attractive new properties. The family s1 deals with the full propositional language, has a complete tableau proof system which provides for incremental approximations; furthermore, it constitutes a full approximation of classical logic from above, with an approximation process with better relevance and locality properties than S1. When applied to clausal inference, s1 provides a strong simplification method. An application of s1 to model-based diagnosis is presented, demonstrating how the solution to this problem can benefit from the use of s1 approximations.