Author | Beth, Evert W. author |
---|---|
Title | Formal Methods [electronic resource] : An Introduction to Symbolic Logic and to the Study of Effective Operations in Arithmetic and Logi / by Evert W. Beth |
Imprint | Dordrecht : Springer Netherlands, 1962 |
Connect to | http://dx.doi.org/10.1007/978-94-010-3269-8 |
Descript | XIV, 170 p. online resource |
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. Padoaโs Method -- 24. Definition-Theoretic Incompleteness -- VII. On Machines Which Prove Theorems -- 25. Introduction โ 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