Formal Methods

I. Purely Implicational Logic.- 1. Introduction.- 2. Deduction-Theoretic Approach.- 3. Semantic Approach.- 4. Axiomatic Approach.- 5. Completeness.- II. Full Sentential Logic.- 6. Introduction.- 7. Introduction of Further Sentential Connectives.- III. Theory of Quantification, Equality, and Functionality.- 8. Notation.- 9. Reduction Schemata.- 10. Axiomatic Method.- 11. Weak Completeness Theorems.- 12. Equality.- 13. Functionality.- IV. Completeness of Elementary Logic.- 14. Introduction.- 15. Quantification Theory.- 16. Theory of Equality and Functionality.- V. The Formalization of Arithmetic and its Limitations.- 17. An Axiom System for Arithmetic.- 18. Syntactic Incompleteness.- 19. Semantic Incompleteness.- 20. Logic of Higher Order.- VI. The Theory of Definition.- 21. Introduction.- 22. Definability of Primitive Notions.- 23. Padoa's Method.- 24. Definition-Theoretic Incompleteness.- VII. On Machines Which Prove Theorems.- 25. Introduction - Computation and Formal Deduction.- 26. Formal Deduction and Computing Machines.- 27. The Subformula Principle.- 28. Semantic Tableaux and Natural Deduction.- 29. Complications.- 30. Introduction of New Individual Parameters.- 31. Types of Logical Problems.- 32. Concluding Remarks.- Appendix: Supplementary Explanations.- 33. Formal Description of Deduction by Closed Semantic Tableaux.- 34. Independence.- 35. Intuitionistic Logic and Minimal Calculus.- 37. Elementary Logic with Equality and Terms.- 39. Semantic Rules for Quantification Theory.- 40. Deduction-Theoretic Treatment of the Theory of Quantification.- 41. Numerical Computation.- 42. The Interpolation Theorem of Craig-Lyndon.- List of Schemata and Axioms.- (A) Sources.- (B) Recommended Reading.- (C) Periodicals.- Index of Authors and Subjects.