Philosophical, Computational, and Mathematical Logic

• Formal logic basics
  • [Predicate Logic]
  • [Axiomatic Set Theory]
  • [Recursion Theory and Computability]
  • [Gödel’s Incompleteness Theorems]
  • [Model Theory]
  • [Contemporary Set Theory]

• Computer algebra

• Models of Computation
  • [Turing Machines]
  • [Decidable Languages]
  • [Recursion Theorem]
  • [Undecidability]
  • [Reductions]
  • [Time Complexity]
  • [P vs. NP]
  • [Polynomial Hierarchy]
  • Boolean Circuits
  • Non-Uniform Computation
  • Boolean Formulas
  • Satisfiability
  • Randomized Computations
  • Space Complexity
  • Logarithmic and Sublogarithmic Space
  • Nonregular Languages
  • Communication Complexity

• [Is the World Deterministic?]

• [Modal Logic]
  • K, T, S4, S5, Kripke sementics, possible world, canonical model, completeness, axiom-frame correspondence
  • type theory: STLC, Curry-Howard correspondence, modal type theory
  • HoTT: identity type, path induction, univalence axiom, HITs, modalities(cohesive/spatial..)
  • Modal HoTT: epistemic, monads, index theory, belief modeling&temporal reasoning