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