Advanced Topics
- Philosophical Logic
- Logic for Computer Science & AI
- Mathematical Logic Advanced
- Limits and Extensions of Classical Logic
You should only begin these after completing the entire Core sequence (sections I–V). Each track goes deeper in one direction (Choose according to your goals):
-
Philosophical Logic
Focuses on the connections between logic, philosophy, language, knowledge, and norms. -
Logic for Computer Science & AI
Focuses on the practical and theoretical tools used in programming, computation, verification, and artificial intelligence. -
Mathematical Logic (Advanced)
Focuses on the most abstract and foundational parts of modern logic as a branch of mathematics. -
Limits and Extensions of Classical Logic Modal logic, non-classical logics survey, and detailed Gödel incompleteness
Philosophical Logic
| Subject | Book | Online Course |
|---|---|---|
| Philosophical Logic | Philosophical Logic (Burgess, Archive.org) | — |
| Logic & Language | Logic, Language, and Meaning (Gamut) | — |
| Epistemic Logic | Reasoning About Knowledge (Fagin et al.) | — |
| Deontic Logic | Handbook of Deontic Logic (Open PDF) | — |
Logic for Computer Science & AI
| Subject | Book | Online Course |
|---|---|---|
| Automata & Formal Languages | Introduction to Automata Theory (Hopcroft et al.) | Automata (MIT OCW Automata, related) |
| Logic Programming | Foundations of Logic Programming (Lloyd) | — |
| Temporal Logic | Temporal Logic (Emerson) | — |
| Automated Theorem Proving | Handbook of Automated Reasoning (Vol. I, open sections) | — |
Mathematical Logic (Advanced)
| Subject | Book | Online Course |
|---|---|---|
| Model Theory | Marker – Model Theory (Free PDF) | — |
| Axiomatic Set Theory | Jech – Set Theory | — |
| Large Cardinals | Kanamori – The Higher Infinite | — |
| Reverse Mathematics | Simpson – Subsystems of Second-Order Arithmetic | — |
Limits and Extensions of Classical Logic
| Subject | Book | Online Course |
|---|---|---|
| Gödel’s Incompleteness Theorems | Gödel’s Proof (Nagel & Newman, Archive.org) | Theory of Computation (MIT OCW) |
| Modal Logic | An Introduction to Non-Classical Logic (Priest) | Modal Logic (MIT OCW) |
| Non-Classical Logics (Survey) | Priest | Modal Logic (MIT OCW Modal Logic) |