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Description
This second edition improves upon the first by offering a more detailed treatment of key topics and by expanding the set of problems and exercises. In particular, four new features deserve mention. First, the book now includes a more thorough exposition of natural deduction, explaining how derivations can be represented as trees of formulas. Second, it provides a detailed explanation of the main proof methods, illustrated with examples. Third, it offers a separate exposition of the logic of identity. Fourth, it presents a fuller treatment of modal logic, including results on consistency, soundness, and completeness. Additional changes include new examples drawn from elementary mathematics, a refined notation, and a more functional subdivision of the material, which simplifies some proofs and enhances clarity and readability. Overall, the text preserves the style of the first edition, aiming to present core ideas clearly, concisely, and with minimal distractions.
Table of Contents
Preface.- Chapter 1. Elementary set-theoretical notions.- Chapter 2. What logic is about.- Chapter 3. Validity.- Chapter 4. Formality.- Chapter 5. The symbols of propositional logic.- Chapter 6. The language L: syntax.- Chapter 7. The language L: semantics.- Chapter 8. The system G.- Chapter 9. Derivability in G.- Chapter 10. The system S.- Chapter 11. Consistency, soundness, completeness.- Chapter 12. Computability.- Chapter 13. The symbols of predicate logic.- Chapter 14. The language Lq: syntax.- Chapter 15. The language Lq: semantics.- Chapter 16. The system Sq.- Chapter 17. Consistency, soundness, completeness.- Chapter 18. Identity.- Chapter 19. First-order theories.- Chapter 20. Theories and models.- Chapter 21. Gödel’s incompleteness theorems.- Chapter 22. Undecidability and related results.- Chapter 23. Modal propositional logic.- Chapter 24. Quantified modal logic.- Index.
