Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Table of Symbols
- 1 Why Entailment?
- Part I Entailment in the Twentieth Century
- 2 C. I. Lewis and His School
- 3 Entailment and Possible Worlds
- 4 Entailment and Relevance
- 5 Reflexivity
- Part II Theories and Entailment
- 6 Theories and Closure
- 7 Theories of Entailment
- Part III The Logic E of Relevant Entailment
- 8 The Logic of Entailment
- 9 Negation and Disjunction
- 10 Quantification
- 11 Entailment and Reasoning
- Appendix Systems, Semantics, and Technical Results
- References
- Index
6 - Theories and Closure
Published online by Cambridge University Press: 08 February 2024
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Table of Symbols
- 1 Why Entailment?
- Part I Entailment in the Twentieth Century
- 2 C. I. Lewis and His School
- 3 Entailment and Possible Worlds
- 4 Entailment and Relevance
- 5 Reflexivity
- Part II Theories and Entailment
- 6 Theories and Closure
- 7 Theories of Entailment
- Part III The Logic E of Relevant Entailment
- 8 The Logic of Entailment
- 9 Negation and Disjunction
- 10 Quantification
- 11 Entailment and Reasoning
- Appendix Systems, Semantics, and Technical Results
- References
- Index
Summary
The semantical framework for the positive view of this book is one in which entailment is understood primarily in terms of theory closure. This chapter outlines both the history of the notion, beginning with Alfred Tarski’s theory of closure operators, and the relationship between closure operators and the entailment connective. At the end of the chapter, it is shown how closure operators can be used to model a simple logic, Graham Priest’s logic N4.
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- Information
- The Logic of Entailment and its History , pp. 119 - 135Publisher: Cambridge University PressPrint publication year: 2024