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
10 - Quantification
Published online by Cambridge University Press: 08 February 2024
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
Summary
The model theory for quantified relevant logic developed by Robert Goldblatt and Mares is adapted to the present semantical framework. A universally quantified statement ‘For all x A(x)’ is taken to mean that there is some proposition in the present theory that entails every instance of A(x). An axiomatization of the logic is given, and completeness is proven in the Appendix to the book. Identity, the nature of domains, and higher-order quantification are also discussed.
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- The Logic of Entailment and its History , pp. 192 - 214Publisher: Cambridge University PressPrint publication year: 2024