forall x: Calgary

Study overview of the reviewed opening

The preface introduces formal logic as the study of precisely defined languages and relationships between their sentences. Entailment concerns what must follow from assumptions; satisfiability concerns whether sentences can hold together without contradiction. These ideas can be studied through interpretations or through formal derivations.

The book first develops logical notions informally, then introduces truth-functional language. Its connectives combine sentences, allowing semantic methods such as truth tables and proof-theoretic methods such as natural deduction to be compared. First-order logic adds names, predicates, identity and quantifiers, making its language more expressive. The preface next identifies modal logic and advanced topics as extensions to that route.

The instructor guidance explains how selections can form a semester course and stresses the value of using one stable version. Appendices, a glossary and alternative notation discussions support reference use. The guide covers the preface and verified structure, not the individual proofs or exercise solutions. Students should match notation and rule names to this Calgary edition rather than importing conventions from another remix without checking them.

Book contents

1. 1 Arguments
2. 2 The scope of logic
3. 3 Other logical notions
4. 4 First steps to symbolization
5. 5 Connectives
6. 6 Sentences of TFL
7. 7 Ambiguity
8. 8 Use and mention
9. 9 Characteristic truth tables
10. 10 Truth-functional connectives
11. 11 Complete truth tables
12. 12 Semantic concepts
13. 13 Limitations of TFL
14. 14 Truth table shortcuts
15. 15 Partial truth tables
16. 16 The very idea of natural deduction
17. 17 Basic rules for TFL
18. 18 Constructing proofs
19. 19 Additional rules for TFL
20. 20 Proof-theoretic concepts
21. 21 Derived rules
22. 22 Soundness and completeness
23. 23 Building blocks of FOL
24. 24 Sentences with one quantifier
25. 25 Multiple generality
26. 26 Identity
27. 27 Sentences of FOL
28. 28 Definite descriptions
29. 29 Ambiguity
30. 30 Extensionality
31. 31 Truth in FOL
32. 32 Semantic concepts
33. 33 Using interpretations
34. 34 Reasoning about interpretations
35. 35 Properties of relations
36. 36 Basic rules for FOL
37. 37 Proofs with quantifiers
38. 38 Conversion of quantifiers
39. 39 Rules for identity
40. 40 Derived rules
41. 41 Proofs and semantics
42. 42 Introducing modal logic
43. 43 Natural deduction for ML
44. 44 Semantics for ML
45. 45 Normal forms
46. 46 Functional completeness
47. 47 Proving equivalences
48. 48 Soundness
49. A Symbolic notation
50. B Alternative proof systems
51. C Quick reference
52. Glossary

Questions for study

The following prompts are Academic Master’s editorial material.

• How do entailment and satisfiability ask different questions?
• What is the relationship between semantic and proof-theoretic methods?
• Why should an entire class work from the same revision?

Sources and coverage

Preface read in full (PDF pages 7–10); title, licence, revision identifier and contents checked.

Source edition · Source licence