The Resolution Calculus

This is a completely new presentation of resolution as a logical calculus and as a basis for computational algorithms and decision procedures. The first part deals with the traditional topics (Herbrand's theorem, completeness of resolution, refinements and deletion) but with many new features and concepts like normalization of clauses, resolution operators and search complexity. The second part gives a systematic treatment of recent research topics. It is shown how resolution decision procedures can be applied to solve the decision problem for some important first-order classes. The complexity of resolution is analyzed in terms of Herbrand complexity, new concepts are used to classify the complexity of refinements, and functional extension is introduced with resolution to give a strong calculus.