Logics for computer scientists 1000-217bLOG

1. Propositional logic.
2. First-order logic: definitions, logic in use, limitations of expressive power.
3. Proof theory: proof systems for propositional logic, proof systems for first-order logic, completeness theorem for first-order logic.
4. Model theory: compactness theorem, Skolem-Loewenheim theorem about cardinalities of models.
5. Arithmetic and G?del's incompleteness theorem.
6. Logics in computer science: three-valued logics, Codd's theorem about equivalence of first-order logic and relational algebra, decidability of logical theories
7. At least one of the following topics:
a. Logic of programs: PDL,
b. Propositional temporal logic LTL,
c. Intuitionistic logic,
d. Second order logic.