Alexander Leitsch

The Resolution Calculus (eBook, PDF)

• Format: PDF

Produktbeschreibung

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. Building on this foundation, 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, 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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 300
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783642606052
• Artikelnr.: 53318341

Inhaltsangabe

The Basis of the Resolution Calculus.- First-Order Logic.- Transformation to Clause Form.- Term Models and Herbrand's Theorem.- Decision Methods for Sets of Ground Clauses.- The Propositional Resolution Principle.- Substitution and Unification.- The General Resolution Principle.- A Comparison of Different Resolution Concepts.- 3. Refinements of Resolution.- A Formal Concept of Refinement.- Normalization of Clauses.- Refinements Based on Atom Orderings.- Lock Resolution.- Linear Refinements.- Hyperresolution.- Refinements: A Short Overview.- 4. Redundancy and Deletion.- The Problem of Proof Search.- The Subsumption Principle.- Subsumption Algorithms.- The Elimination of Tautologies.- Clause Implication.- 5. Resolution as Decision Procedure.- The Decision Problem.- A-Ordering Refinements as Decision Procedures.- Hyperresolution as Decision Procedure.- Hyperresolution and Automated Model Building.- 6. On the Complexity of Resolution.- Herbrand Complexity and Proof Length.- Extension and the Use of Lemmas.- Structural Normalization.- Functional Extension.