17. Complete Systems and Answers to Questions. Classes of Questions and Algebraic Systems

Chapters in this book

1. Frontmatter 1
2. Contents 5
3. Introduction 7
4. Part One
5. 1. Introductory Remarks 11
6. 2. Symbols, Language J , Metalanguage of J 14
7. 3. Simple Numerical Operators 16
8. 4. Compound Numerical Operators 19
9. 5. Compound Numerical Operators (continuation) 21
10. 6. Operators of the Type C 23
11. 7. Numerical Operators of the Second Category 26
12. 8. Operators [δⁿ] 27
13. 9. Operators [βⁿ] and [α] 29
14. 10. Operators [e] and [η]. Conditional Questions of two Types 31
15. 11. Questions about Forbearance 34
16. 12. Remarks on Some New Types of Questions 35
17. 13. Supplementary Remarks on New Formalized Languages Useful in Logical Theory of Questions 39
18. 14. Some Remarks on Questions of the Type "Why?" 42
19. 15. Some Remarks on Classifications of Questions 44
20. 16. Some Problems of Effectiveness. Evocation of Questions 46
21. 17. Direct Answers and Some Types of Definitions. Occasional Question "What is it?" 49
22. Part Two
23. 1. Introductory Remarks 51
24. 2. Notions of Satisfaction, Model, and Truth in a Model 52
25. 3. Notions of Logical Consequence and Regular Consequence. Independent Formulas 54
26. 4. System S of the Logic of Questions 57
27. 5. Theses of the System S. Laws of Elimination of Questions 61
28. 6. Theses of the System S. Laws of Equivalence, Permutation, Reduction and Cancelling of Negation 65
29. 7. Theses of the System S. Laws of Index Alteration, Laws of Commutativity, Further Laws of Elimination of Questions 66
30. 8. Extension S* of the System S. Bases of Questions in Questions. Definability of Interrogative Operators by Interrogative Operators 69
31. 9. The Problem of Dilutions of the Regular Consequence 71
32. 10. Kinds of Answers to Questions 73
33. 11. Remarks on Some Notions of Direct Answer 74
34. 12. Logics of Answers OR and OR_* 76
35. 13. General Remarks on the Logic of Answers OR 79
36. 14. System E of the Logic of Questions 80
37. 15. Problem of Negation of Questions. Negationless Questions 83
38. 16. The Problem of Extensionality of Some Constants in the Alphabet of the Systems S, E, and OR 86
39. 17. Complete Systems and Answers to Questions. Classes of Questions and Algebraic Systems 89
40. Part Three
41. 1. Preliminary Remarks. Pragmatic Presuppositions of Questions 93
42. 2. Syntactic Presuppositions of Questions. Some Necessary Conditions 95
43. 3. Syntactic Presuppositions of Questions Containing the Symbols of the Form k<, k <, k, and (k) 96
44. 4. Syntactic Presuppositions of Questions Containing the Symbols of the Form (k<L) and (k <) 97
45. 5. Syntactic Presuppositions of Questions Containing the Constant C 100
46. 6. Syntactic Presuppositions of Questions Containing Connective Variables. Syntactic Presuppositions in the Broader Sense 101
47. 7. Systems of the Type Z of the Logic of Questions. Preliminary Remarks. Systems T¹ and T² 104
48. 8. The Systems T³ and ^T4 105
49. 9. Connections between the Systems of the Type Z. Notions of Formal Equivalence and Formal Overlapping of Systems 107
50. 10. Further Theorems on Connections between Systems of the Type Z and on Various Notions of Equivalence and Equipollence of Questions 109
51. 11. Syntactic Presuppositions of the Second Class 111
52. 12. Logical Value of Questions. Well and Wrongly put Questions 114
53. Part Four
54. 1. Introduction 117
55. 2. Metalinguistic Logics of Questions. Quotation Mark Counterparts. Questions in Stahl's Sense 119
56. 3. Questions in Harrah's Sense 121
57. 4. Terminology of Belnap. Belnap's Logical Square 123
58. 5. Terminology of Belnap (continuation). Extension of the Logic of Answers BOB 125
59. 6. Aqvist's Theory of Questions 128
60. Bibliography 132
61. Index of Subjects 137
62. Index of Authors 141
63. Index of Symbols 142