G. E. Hughes, D. G. Londey

The Elements of Formal Logic

• Broschiertes Buch

Produktbeschreibung

Originally published in 1965. This is a textbook of modern deductive logic, designed for beginners but leading further into the heart of the subject than most other books of the kind. The fields covered are the Propositional Calculus, the more elementary parts of the Predicate Calculus, and Syllogistic Logic treated from a modern point of view. In each of the systems discussed the main emphases are on Decision Procedures and Axiomatisation, and the material is presented with as much formal rigour as is compatible with clarity of exposition. The techniques used are not only described but given a theoretical justification. Proofs of Consistency, Completeness and Independence are set out in detail. The fundamental characteristics of the various systems studies, and their relations to each other are established by meta-logical proofs, which are used freely in all sections of the book. Exercises are appended to most of the chapters, and answers are provided.

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Produktdetails

• Verlag: Routledge
• Seitenzahl: 420
• Erscheinungstermin: 31. März 2021
• Englisch
• Abmessung: 216mm x 140mm x 23mm
• Gewicht: 526g
• ISBN-13: 9780367426200
• ISBN-10: 036742620X
• Artikelnr.: 69890699

Autorenporträt

Hughes\, G. E.; Londey\, D. G.

Inhaltsangabe

Preface 1. Validity Part 1: The Propositional Calculus: Elements and
Decision Procedures 2. Some Simple Forms of Inference 3. Establishing
Validity (Theory) 4. Establishing Validity (Practice) 5. Disjunction and
Disjunctive Inference 6. Material Equivalence: 'If and Only If' 7. Valid
Inference and Proof 8. The Propositional Calculus 9. Truth-tables as a
Decision Procedure 10. Equivalence Transformations 11. Another Decision
Procedure Part 2: The Propositional Calculus: Axiomatic Systems 12.
Operations of Inference 13. Axiomatic Systems 14. Formal Axiomatic Systems
15. The System PM (I) 16. PM (II) Substitution of Equivalents 17. PM (III)
Some Further Theorems 18. PM (IV) Independence and Non-independence 19.
Consistency and Completeness of PM 20. The System TB 21. Extensions of TB:
The System W 22. Consistency and Completeness of W 23. The Elements of
Formal Logic Part 3: The Lower Predicate Calculus Some General Remarks on
Part 3 23. The Lower Predicate Calculus: Introduction 24. The System LPCl
25. LPCl: Decision Procedure I - The Truth-table Method 26. Universes of
Discourse - Justification of Decision Procedure 27. LPCI : Decision
Procedure II - Exposition 28. LPCI : Decision Procedure II - Justification
29. LPCl: Axiomatization 30. LPCl : Consistency and Completeness 31. The
System LPC2: Introductory 32. LPC2: Decision Procedure I 33. LPC2: Decision
Procedure II - Exposition 34. LPC2: Decision Procedure II - Justification
35. LPC2: Axiomatization 36. LPC2 and the Logic of an Empty Universe 37.
Multiple Quantification I 38. Equivalence Transformations of Quantifiers
39. Multiple Quantification II 40. Multiple Quantification III 41. The
Lower Predicate Calculus: Conclusion Part 4: Syllogistic Introductory Note
42. Résumé of Traditional Syllogistic Logic 43. Syllogistic and the
Predicate Calculus 44. Syllogistic Moods under Interpretation 1: The
Antilogism Theorem 45. Syllogistic and LPC1: Further Interpretations 46.
Syllogistic and LPC1: Another Approach 47. The Validity of Syllogisms
Reconsidered: An Extension of the Antilogism Theorem 48. Syllogistic: An
Axiomatic Presentation 49. On the Meta-Iogic of AS. Appendices