Logic
Prof. Tobias Nipkow, Sommersemester 2017
 TUMonline: Logic (IN2049)
 Lectures: Monday, 08:30–10:00 in HS3 00.06.011, and Wednesday, 08:3010:00 in HS3 00.06.011

Exercises: Tuesday, 10:15–11:45 in MI 00.08.038
 Start: 24.04. First exercise: 26.04.
 Tutors: Lars Hupel
News
 27.06.: Two mistakes in the solution for sheets 7 (Exercise 7.1) and 8 (Exercise 8.3) have been fixed.
 21.05.: Next tutorial on Tuesday, 23.05.2017, had to be moved to 14:00 because of SVV. Apologies for this inconvenience. Check your email inbox for information about the room.
 15.05.: Next tutorial is Tuesday, 16.05.2017.
 11.05.: Clarified bonus.
 08.05.: The next tutorial is Wednesday, 10.05.2017, starting 14:30.
 18.04.: Note the changed tutorial details. Due to the high number of class enrollments, we will reschedule the first four tutorials to Wednesday, 14:30–16:00, in Intermishörsaal 1. First tutorial: Wednesday, 26.04.
 Website created
Excercises
Homework Bonus
There will be graded homework assignments. Anyone who achieves more than 50% of the homework score gets awarded a bonus of 0.3/0.4 on the final exam's grade, provided the exam is passed.Submission
Typically before the tutorial in the week after (see sheet). Submission at the start of the tutorial or to the tutor's email address.Material
 Sheet 1 (Solution)
 Sheet 2 (Solution)
 Sheet 3 (Solution)
 Sheet 4 (Solution)
 Sheet 5 (Solution)
 Sheet 6 (Solution)
 Sheet 7 (Solution)
 Sheet 8 (Solution)
 Sheet 9
Contents
The course assumes that you have had a basic introduction to logic already
and are familiar with the following topics: syntax and semantics of both propositional and firstorder logic; disjunctive and conjunctive normal forms; basic equivalences of propositional and firstorder logic. These topics will only be refreshed briefly at the beginning of the course.
The main topics of the course:
 Proof theory: sequent calculus, natural deduction, resolution; their soundness and completeness; translations between proof systems.
 Metatheory of first order logic: compactness, model theoy, undecidability, incompleteness of arithmetic.
 Decision procedures for fragments of logic and arithmetic.
Slides
Propositional logic:
 Basics (Esparza/Schöning)
 Equivalences (Esparza/Schöning)
 Normal forms (Esparza/Schöning)
 Definitional CNF (Harrison)
 Horn formulas (Esparza/Schöning)
 Compactness (Harrison)
 Resolution (Esparza/Schöning)
 Basic proof theory (Troelstra&Schwichtenberg)
 Basics (Esparza/Schöning)
 Normal forms (Esparza/Schöning)
 Herbrand theory (Esparza/Schöning)
 Resolution (Esparza/Schöning)
 Equality (Esparza)
 Undecidability (Cutland)
 Compactness (Harrison)
 The Classical Decision Problem (Harrison)
 Basic proof theory (Troelstra&Schwichtenberg)
 Theories (Harrison)
Literature
 Ebbinghaus, Flum, Thomas. Einführung in die mathematische Logik (English: Mathematical Logic).
 Herbert Enderton. A Mathematical Introduction to Logic.
 Melvin Fitting. FirstOrder Logic and Automated Theorem Proving.
 Jean Gallier. Logic for Computer Science.
 John Harrison. Handbook of Practical Logic and Automated Reasoning.
 Uwe Schöning. Logik für Informatiker (English: Logic for Computer Scientists).
 A. Troelstra and H. Schwichtenberg. Basic Proof Theory.