Logic and Computability (SS 2023)

Course Number IND04033UF | Sommersemester 2023


In this course, you will learn to understand logic formulas, to use concise mathematical notations, to formulate and solve problems in formal languages, and to reason with logics manually and algorithmically. We will use powerful tools, so called SMT solvers, that are able to quickly solve complex problems involving constraints over integers, reals, first-order logic predicates, list, and other data types. We will teach logic proof systems, and you will gain the ability to construct logic proofs on your own and you will master common proof techniques of computer science.

The content of this lecture includes:

  • Syntax and semantics of logic formulas in propositional logic and predicate logic (first-order logic)
  • Propositional satisfiability problem – DPLL algorithm – Resolution proofs
  • Satisfiability modulo Theories – DPLL(T)
  • Basics of logical reasoning (natural deduction)
  • Binary Decision Diagrams
  • Temporal Logic
  • Introduction to the SMT Solver Z3


The students will be provided with videos, slides, lecture notes and a questionnaire. The material will be online before the corresponding lecture.

NR Date Topic Lecture Notes Slides Questionnaire
0 2023-03-03 Administrative Information Slides 0
1 2023-03-10 Introduction to Z3 Lecture 1 ( + z3 Examples) Questionnaire 1


2 2023-03-24 Propositional and Predicate Logic Lecture Notes 2 Slides 2 Questionnaire 2

Solutions 2

3 2023-03-31 SAT Procedures – DPLL Lecture Notes 3 Slides 3 Solutions Questionnaire 3

Solutions 3

4 2023-04-21 Natural Deduction for Propositional Logic Lecture Notes 4 Slides 4 Questionnaire 4

Solutions 4

5 2023-04-28 Predicate Logic Lecture Notes 5 Slides 5 Questionnaire 5

Solutions 5

6 2023-04-28 Natural Deduction for Predicate Logic – Part 1 Lecture Notes 6 Slides 6 Questionnaire 6

Solutions 6

6 2023-05-05 Natural Deduction for Predicate Logic – Part 2 Lecture notes 6 (see above) Slides 6-Part2 Questionnaire 6 (see above)
7 2023-05-05 Satisfiability Modulo Theories Lecture Notes 7 Slides 7 Questionnaire 7

Solutions 7

7 2023-05-12 Binary Decision Diagrams Lecture Notes 8 Slides 8 Questionnaire 8

Solutions 8

8 2023-05-26 Equivalence Checking Lecture Notes 9 Slides 9 Questionnaire 9

Solutions 9

9 2023-06-02 Symbolic Encoding Lecture Notes 10 Slides 10 Questionnaire 10

Solutions 10

9 2023-06-02 Temporal Logic Lecture Notes 11 Slides 11 Questionnaire 11

Solutions 11

10 2023-06-16 Probabilistic Temporal Logic and BDDs Slides 12

The  proof rules for Natural Deduction and the Tseitin’s encoding rules can also be used during the exam and the exercise classes.

Solutions for the questions from the questionnaire will be released here. We have compiled a version of the questionnaire containing all chapters here. A version with solutions can be found here.

You can watch videos explaining the topics discussed in the lecture in the TUbe.


Number Topic Kick-Off Deadline Assignment Solutions
1 Programming Assignment 1 2023-03-10 2023-03-16 Assignment 1
2 Programming Assignment 2 2023-03-17 2023-03-23 Assignment 2
3 Programming Assignment 3 2023-03-24 2023-03-30 Assignment 3
4 SAT Solving 2023-03-31 2023-04-20 Assignment 4 [DPLL Table] Solutions 4
5 Natural Deduction for Propositional Logic 2023-04-21 2023-04-27 Assignment 5 Solutions 5
6 Predicate Logic and Natural Deduction for Predicate Logic 2023-04-28 2023-05-04 Assignment 6 Solutions 6
7 Natural Deduction for Predicate Logic and Eager Encoding 2023-05-05 2023-05-11 Assignment 7 Solutions 7

Note that the exercises discussed in the practicals are also contained in the respective chapter of the questionnaire.

Administrative Information

Administrative Information – Lecture


Students will be provided with a questionnaire. These questions cover the theoretical aspects of the lecture as well as practical examples. Questions within the questionnaire will have one of the following labels:

  • [Lecture] Questions that will be solved during the lecture on Friday. Solutions will be provided by us after the lecture.
  • [Practicals] These questions form the practical assignments. Solutions will be provided by us after the corresponding practical class.
  • [Self-Assessment] These questions are for self-assessment.

The questions for a particular topic will be published on Monday before the corresponding lecture. The questions at the exam are a subset of the questions of the questionnaire.

Course Procedure

The lecture takes place every Friday at 10:15-12:00 at i13. During class, we will interactively work out the theory and solve the questions of the questionnaire labelled with [Lecture].


Dates for exams will be set via TUGrazonline, please register there. Exams will have a duration of 90 minutes and there will be at least 3 possible dates for exams each semester. The questions at the exam are a subset of the questions of the questionnaire.

Communication – Discord

Please use the Discord invitation link to simplify the communication during the semester.

Administrative Information – Practicals

Course Procedure

In total, we will have 7 practical assignments. The first three assignments will be simple programming exercises using the Python API of the SMT solver Z3. The next four assignments are pen-and-paper assignments to practice the basic decisions procedures algorithms and to perform simple proofs by hand.

The exercises will be part of the questionnaire and will be labelled with [Practicals].

The assignments will be discussed by students during live blackboard sessions in class. Please register for any of the 10 groups.

Students are required to tick the tasks they have solved via the TeachCenter. The deadline for ticking is Thursday 23:59am before the respective practical session. Students will be randomly selected during class to present their solutions.

Submitting the programming examples will be handled via git. You will receive your repository after the registration deadline for the course has ended.

The attendance of practical classes is compulsory. For justified reasons (sickness), exceptions can be made. In such cases, students have to tick and upload their solutions in time (according to the deadline of the assignment) and have to present their solutions in a replacement interview that will be held in the following week, on Thursday at 2:00pm.

If students are not able to explain their solution or their solution is completely wrong, students may lose either 50% or 100% of the points of that assignment. Minor errors or typos will not lead to any point reductions.

Grading for the Practicals

  • Assignment 1: 10 points
  • Assignment: 2-7: 15 points each
  • Assignments may include bonus points.

If Points…

  • >= 87.5%: (1) Sehr Gut / Excellent
  • >= 75.0%: (2) Gut / Good
  • >= 62.5%: (3) Befriedigend / Satisfactory
  • >= 50.0%: (4) Genügend / Sufficient
  • >= 00.0%: (5) Nicht Genügend / Insufficient

Communication – Discord

Please use the Discord invitation link to simplify the communication during the semester.

For any questions, please contact either Stefan Pranger or Bettina Könighofer.


Bettina Könighofer

Assistant Professor

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