Introduction to Logic
The aim of the course is to give an advanced introduction to logic with emphasis on topics relevant for computer science.
The first part of the course studies the syntax (`proof theory') and semantics (`model theory') of first order logic thereby deepening the understanding of topics touched upon in ModLog:
- Propositional logic (resolution, normal forms and Horn formulas).
- Predicate logic, properties of various calculi like Hilbert systems, sequent and natural deduction calculi and their completeness.
- Compactness theorem and Loewenheim-Skolem theorem, Herbrand's theorem, unification.
The second part of the course treats further topics as:
- undecidability of predicate logic, decidable fragments, Peano arithmetic and Goedel's incompleteness results.
- extensions of first order logic (e.g. second order logic),
- basic intuitionistic logic (i.e. the logic formalizing constructive reasoning) together with a discussion of the Curry-Howard isomorphism.
- basic modal logic.
Lecturers:
Ulrich Kohlenbach
Literature Will be announced
Prerequisites dModLog (very useful but not strictly necessary),some mathematical maturity.
Course Language English
Evaluation Compulsory homework assignments, oral exam.
Credits 2 points/10 ECTS credits
Semester Fall