🔑 Logic
Based on Craig DeLancey, "A Concise Introduction to Logic", licensed CC BY-SA 4.0.
Propositions, proofs, and predicates. Translated into runnable code with diagrams. See also 🔬 Boole 1854 for the historical roots.
| Chapter | |||
|---|---|---|---|
| 1. | Arguments and Validity | What makes an argument valid, and why validity is not the same as truth | 🔑 |
| 2. | Propositional Logic Syntax | Propositions, connectives, and how to parse a well-formed formula | 🔑 |
| 3. | Truth Tables | Evaluating compound propositions to find tautologies, contradictions, and contingencies | 🔑 |
| 4. | Logical Equivalence | De Morgan, distribution, contrapositive, and simplification laws | 🔑 |
| 5. | Natural Deduction | Proof rules that build valid arguments step by step | 🔑 |
| 6. | Predicate Logic | Quantifiers, predicates, and translating English into formal logic | 🔑 |
| 7. | Predicate Logic Proofs | Instantiation and generalization rules for quantified statements | 🔑 |
| 8. | Identity and Functions | Equality, uniqueness, definite descriptions, and functions in logic | 🔑 |
| 9. | Mathematical Induction | Base case plus inductive step proves all cases | 🔑 |
| 10. | Soundness and Completeness | What proof systems can and cannot reach, ending with Godel | 🔑 |
📺 Video lectures: MIT 6.042J Mathematics for Computer Science
Neighbors
- ✎ Proofs — logic is the language proofs are written in
- 🔢 Discrete Math — symbolic logic and graph theory together
- 🔀 Theory of Computation — decidability is logic made computational
- ✏️ Lean Proofs — type theory as a foundation for logic
- 🔬 Boole 1854 — the historical source of Boolean algebra