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Mathematics
Mathematical Logic
1. Introduction to Mathematical Logic
2. Propositional Logic
3. First-Order Logic
4. Model Theory
5. Computability Theory
6. Incompleteness Theorems
7. Axiomatic Set Theory
8. Proof Theory
9. Modal Logic
10. Intuitionistic Logic
11. Higher-Order Logic
9.
Modal Logic
9.1.
Basic Modal Logic
9.1.1.
Syntax and Formation Rules
9.1.2.
Necessity and Possibility Operators
9.1.3.
Modal Axioms
9.1.3.1.
Axiom K
9.1.3.2.
Axiom T
9.1.3.3.
Axiom 4
9.1.3.4.
Axiom 5
9.1.4.
Normal Modal Logics
9.2.
Kripke Semantics
9.2.1.
Possible Worlds
9.2.2.
Accessibility Relations
9.2.3.
Truth Conditions for Modal Operators
9.2.4.
Frame Conditions
9.2.5.
Correspondence Theory
9.3.
Applications of Modal Logic
9.3.1.
Alethic Modality
9.3.2.
Epistemic Logic
9.3.3.
Deontic Logic
9.3.4.
Temporal Logic
9.4.
Advanced Topics in Modal Logic
9.4.1.
Completeness Results
9.4.2.
Decidability
9.4.3.
Bisimulation
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8. Proof Theory
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10. Intuitionistic Logic