Nach positiver Absolvierung der Lehrveranstaltung sind Studierende in der Lage wichtige Konzepte, Techniken und Resultate der formalen Logik und der Berechenbarkeitstheorie zu unterscheiden und anzuwenden. Außerdem sollten Absolventen in der Lage sein, Verbindung zwischen Themen wie Unvollständigkeit arithmetischer Kalküle, Unentscheidbarkeit, formaler Beweisbarkeit und Ausdruckstärke zu verstehen und zu erklären.

• advanced aspects of classical first order logic as specification tool
• proof systems for classical first order logic, including  soundness and completeness proofs 
• elements of model theory (Löwenheim-Skolem, compactness, expressibility)
• principles of automated theorem proving
• methods for handling identity  
• comparison of types of inference systems 
• elements of modal logic: Kripke semantics, temporal logics 
• elements of intuitionistic logic and constructive proofs
•  computational aspects of logic
• undecidabilty of firt order logic and its consequences
• models of computation (Turing machines, lambda calculus)
• elementary recursion theory
• Church-Turing thesis
• incompleteness of arithmetic and its consequences  

• derivations in various different logical calculi
• applying formal concepts to standard problem sets
• mastering formal (mathematical) definitions
• analysis of proofs of central results

ETCS Breakdown:

6 ETCS = 150 hours

• 38 hours:  lecture time (+ 8 hours repetitorium for students not having a firm previous knowledge in logic)
• 52 hours: 4 blocks of problems/exercises 
• 60 hours: examination (preparation time )

The course will start Friday, October 4th, 10:00.

• selbständiges Lösen von Übungsbeispielen (4 Blöcke)
• schriftliche Prüfung
• mündliche Prüfung

(see lecture slides for additional literature)

Knowledge of classical propositional logic and of basic concepts of classical first order logic (logical consequence, interpretations and model structures, satisfiability versus validity, acquaintance with various proof systems), a firm understanding of the syntax/semantic distinction, some experience with formal specification, acquaintance with a range of different programming paradigms (imperative, functional, logical), concepts of formal languages (grammars, Chomsky hierarchy) and automata theory (finite automata, pushdown automata, Turing machines)

NB: If you don't have a firm background in logic yet, you are asked to join special repetitorium classes, which are open to all participants.