Chapter 13 Basic implication

Chapters in this book

1. Frontmatter i
2. Contents v
3. Part A Preliminaries
4. Chapter 1 Introduction for teachers 3
5. Chapter 2 Introduction for students 20
6. Chapter 3 Informal set theory 65
7. Chapter 4 Topologies and interiors (postponable) 126
8. Chapter 5 English and informal classical logic 146
9. Chapter 6 Definition of a formal language 206
10. Part B Semantics
11. Chapter 7 Definitions for semantics 235
12. Chapter 8 Numerically valued interpretations 245
13. Chapter 9 Set-valued interpretations 269
14. Chapter 10 Topological semantics (postponable) 281
15. Chapter 11 More advanced topics in semantics 295
16. Part C Basic syntactics
17. Chapter 12 Inference systems 313
18. Chapter 13 Basic implication 318
19. Chapter 14 Basic logic 336
20. Part D One-formula extensions
21. Chapter 15 Contraction 351
22. Chapter 16 Expansion and positive paradox 357
23. Chapter 17 Explosion 365
24. Chapter 18 Fusion 369
25. Chapter 19 Not-elimination 372
26. Chapter 20 Relativity 377
27. Part E Soundness and major logics
28. Chapter 21 Soundness 383
29. Chapter 22 Constructive axioms: avoiding not-elimination 385
30. Chapter 23 Relevant axioms: avoiding expansion 405
31. Chapter 24 Fuzzy axioms: avoiding contraction 417
32. Chapter 25 Classical logic 430
33. Chapter 26 Abelian logic 437
34. Part F Advanced results
35. Chapter 27 Harrop's principle for constructive logic 443
36. Chapter 28 Multiple worlds for implications 454
37. Chapter 29 Completeness via maximality 466
38. References 487
39. Symbol list 493
40. Index 495