This book is an accessible and scientifically rigorous introduction to the principles of logical reasoning, covering many topics including the deductive machinery of metalogic, otherwise known as the nature and function of proofs. It will be valuable to students of logic, mathematics and computer science.
This book is an accessible and scientifically rigorous introduction to the principles of logical reasoning, covering many topics including the deductive machinery of metalogic, otherwise known as the nature and function of proofs. It will be valuable to students of logic, mathematics and computer science.
Jan von Plato is Professor of Philosophy at the University of Helsinki. He is the author of Creating Modern Probability (Cambridge University Press, 1994) and, with Sara Negri, Structural Proof Theory (Cambridge University Press, 2001) and Proof Analysis (Cambridge University Press, 2011).
Inhaltsangabe
Part I. First Steps in Logical Reasoning: 1. Starting points; 2. Rules of proof; 3. Natural deduction; 4. Proof search; 5. Classical natural deduction; 6. Proof search in classical logic; 7. The semantics of propositional logic; Part II. Logical Reasoning with the Quantifiers: 8. The quantifiers; 9. Derivations in predicate logic; 10. The semantics of predicate logic; Part III. Beyond Pure Logic: 11. Equality and axiomatic theories; 12. Elements of the proof theory of arithmetic; Part IV. Complementary Topics: 13. Normalization and cut elimination; 14. Deductive machinery from Aristotle to Heyting.
Part I. First Steps in Logical Reasoning: 1. Starting points; 2. Rules of proof; 3. Natural deduction; 4. Proof search; 5. Classical natural deduction; 6. Proof search in classical logic; 7. The semantics of propositional logic; Part II. Logical Reasoning with the Quantifiers: 8. The quantifiers; 9. Derivations in predicate logic; 10. The semantics of predicate logic; Part III. Beyond Pure Logic: 11. Equality and axiomatic theories; 12. Elements of the proof theory of arithmetic; Part IV. Complementary Topics: 13. Normalization and cut elimination; 14. Deductive machinery from Aristotle to Heyting.
Rezensionen
'Elements of Logical Reasoning fills a gap by providing some much needed explanation and motivation to an otherwise dry literature.' Henry Towsner, The Mathematical Intelligencer
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