Deduction Systems

1 Introduction. - 2 Mathematical Preliminaries. - 2. 1 Sets and Relations. - 2. 2 Functions and Countability. - 2. 3 Posets and Zorn's Lemma. - 2. 4 Trees. - 2. 5 Mathematical Induction. - 3 Syntax of First-order Languages. - 3. 1 First-order Languages. - 3. 2 Induction over Terms and Formulae. - 3. 3 Free and Bound Variables. - 3. 4 Substitutions. - 4 Semantics of First-order Languages. - 4. 1 Structures and Interpretations. - 4. 2 The Substitution Lemma. - 5 The Gentzen Calculus G. - 5. 1 The Calculus G. - 5. 2 Completeness of G. - 6 Normal Forms and Herbrand's Theorem. - 6. 1 Normal Forms. - 6. 2 Gentzen's Sharpened Hauptsatz. - 6. 3 Skolemization and Herbrand's Theorem. - 7 Resolution and Unification. - 7. 1 Ground Resolution. - 7. 2 Unification. - 7. 3 Improving Unification Algorithms. - 7. 4 Resolution and Subsumption. - 7. 5 Fair Derivation Strategies. - 8 Improving Deduction Efficiency. - 8. 1 Delaying Unification. - 8. 2 Unit Resolution. - 8. 3 Input Resolution. - 8. 4 Linear Resolution. - 8. 5 Hyperresolution. - 8. 6 Semantic Resolution and the Set-of-Support Strategy. - 8. 7 Selection and Ordering Concepts. - 8. 8 A Notion of Redundancy. - 9 Resolution in Sorted Logic. - 9. 1 Introduction. - 9. 2 Syntax and Semantics of Elementary Sorted Logic. - 9. 3 Relativization. - 9. 4 Sorted Logic with Term Declarations. - 9. 5 Unification and Resolution in Sorted Signatures. - 9. 6 Complexity of Sorted Unification. - References. Language: English