The Resolution Calculus
Alexander Leitsch
Springer
<p>This is a completely new presentation of resolution as a logical calculus and as a basis for computational algorithms and decision procedures.<BR>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.<BR>Building on this foundation, the second part gives a systematic treatment of recent research topics. It is shown how <I>resolution decision procedures</I> can be applied to solve the decision problem for some important first-order classes. The <I>complexity of resolution</I> is analyzed in terms of Herbrand complexity, and new concepts like ground projection are used to classify the complexity of refinements. Finally, the method of functional extension is introduced; combined with resolution it gives a computational calculus which is stronger than most others.</p>