Elements of Logical Reasoning
Cambridge University Press, 1/23/2014
EAN 9781107036598, ISBN10: 1107036593
Hardcover, 271 pages, 24.7 x 17.4 x 1.7 cm
Language: English
Some of our earliest experiences of the conclusive force of an argument come from school mathematics: faced with a mathematical proof, we cannot deny the conclusion once the premises have been accepted. Behind such arguments lies a more general pattern of 'demonstrative arguments' that is studied in the science of logic. Logical reasoning is applied at all levels, from everyday life to advanced sciences, and a remarkable level of complexity is achieved in everyday logical reasoning, even if the principles behind it remain intuitive. Jan von Plato provides an accessible but rigorous introduction to an important aspect of contemporary logic: its deductive machinery. He shows that when the forms of logical reasoning are analysed, it turns out that a limited set of first principles can represent any logical argument. His book will be valuable for students of logic, mathematics and computer science.
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.