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Formal Methods : an Introduction to Symbolic Logic and to the Study of Effective Operations in Arithmetic and Logi

Author: Evert W Beth
Publisher: Dordrecht : Springer Netherlands, 1970.
Series: Synthese Library, A Series of Monographs on the Recent Development of Symbolic Logic, Significs, Sociology of Language, Sociology of Science and of Knowledge, Statistics of Language and Related Fields, 4.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Evert W Beth
ISBN: 9789401032698 9401032696
OCLC Number: 851368302
Description: 1 online resource (188 pages).
Contents: 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.
Series Title: Synthese Library, A Series of Monographs on the Recent Development of Symbolic Logic, Significs, Sociology of Language, Sociology of Science and of Knowledge, Statistics of Language and Related Fields, 4.
Responsibility: by Evert W. Beth.
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