Prof. Tobias Nipkow, Sommersemester 2018


  • 09.07.: The last tutorial (on 10.07.) is cancelled. Instead, there will be office hours at the same time (10:15–11:45) in MI 00.09.039. Bring any questions related to the lecture, tutorial, or homework.
  • 29.06.: Updated Homework 12.3: a restriction was missing; F must not contain any quantifiers.
  • 22.06.: Updated Exercise 11.4: one branch of the ND tree applied conjunction and existential elimination in the wrong order.
  • 11.06.: Updated Homework 9.3: there was another, more severe error in the assignment. A fixed version has been uploaded, but we have decided to award 0 points because the problem was impossible to solve.
  • 06.06.: Updated Homework 9.3: the formulas representing instructions were wrong; this has been updated.
  • 15.05.: Updated Homework 6.2: there was a closing parenthesis missing.
  • 15.05.: Updated exercise sheet 6 again to reflect the changed deadline for homework.
  • 15.05.: The tutorial on 22.05. is cancelled because of Whitsun Vacation (Pfingstferien). The replacement tutorial is on Wednesday, 23.05., 12:00–14:00, MI 00.13.054. The change is reflected in TUMonline.
  • 14.05.: Updated Exercise 6.3 and Homework 6.2. Please download an updated version of sheet 6.
  • 27.04.: The tutorial on 08.05. is cancelled because of the student assembly. The replacement tutorial is four hours later: 14:00–16:00, MI 00.13.054. The change is reflected in TUMonline.
  • 24.04.: Homework for sheet 3 is due via email or on paper in Lars' office (MI 00.09.063) by Wednesday, 02.05.2018, 12:00.
  • 24.04.: The tutorial on 01.05. is cancelled because of public holiday. The next tutorial will be on Monday, 30.04., 12:00-14:00, MI 01.11.018. The change is reflected in TUMonline.
  • 23.04.: An error on sheet 2 has been fixed.


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 on the final exam's grade, provided the exam is passed.


Typically before the tutorial in the week after (see sheet). Submission at the start of the tutorial or to the tutor's email address.



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 first-order logic; disjunctive and conjunctive normal forms; basic equivalences of propositional and first-order 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.
  • Meta-theory of first order logic: compactness, model theoy, undecidability, incompleteness of arithmetic.
  • Decision procedures for fragments of logic and arithmetic.


Propositional logic: First-order predicate logic: