Logic and Applications
Course infoSchedule
Course moduleNWI-IPI004
Credits (ECTS)6
CategoryPB (Propaedeutic)
Language of instructionEnglish
Offered byRadboud University; Faculty of Science; Informatica en Informatiekunde;
PreviousNext 1
prof. dr. J.H. Geuvers
Other course modules lecturer
dr. E.G.M. Hubbers
Other course modules lecturer
dr. E.G.M. Hubbers
Other course modules lecturer
Contactperson for the course
dr. E.G.M. Hubbers
Other course modules lecturer
dr. E.G.M. Hubbers
Other course modules lecturer
Academic year2018
KW3-KW4  (28/01/2019 to 01/09/2019)
Starting block
Course mode
RemarksFormerly "Beweren en Bewijzen"; as of 2017, taught in English. First access for students for whom course is compulsory
Registration using OSIRISYes
Course open to students from other facultiesYes
Waiting listNo
Placement procedureIn order of Study programme
ExplanationIn order of Study programme
After completing this course participants are able to:
  1. General competencies:
    • detect inconsistencies and mistakes in wrongly formulated statements
    • formulate clear, consistent and correct assertions
    • provide argumentation about the correctness of your own assertions
    • systematically derive solutions
    • take part actively and constructively in making unclear assertions clear
    • structurize text using definitions
    • indicate the distinctions between natural languages and formal languages
    • deal in a professional way with different notations for intrinsically the same language
  2. Specific competencies with respect to logic:
    • recognize which problems can be solved and which problems cannot be solved using propositional logic
    • translate natural language assertions into logic in a systematic way
    • present the semantics of formulas in propositional or predicate logic in a clear way in natural language
    • explain the semantics of the rules for natural deduction
    • prove assertions using natural deduction
    • present proofs in a comprehensible way
    • derive truth tables for assertions in propositional logic
    • derive semantic tableaux for assertions in propositional logic
    • use the terminology of tautology, logical consequences and logical equivalences
    • recognize and indicate mistakes within proofs
    • use the proof assistant Coq to prove theorems without reasonable doubt
  3. Specific competencies with respect to system modelling:
    • create a rationality square for a given artifact
    • specify important properties of simple real-time systems and their components within predicate logic
    • prove correctness of specifications in predicate logic
    • divide systems hierarchically into their components
    • prove that a system complies to certain properties using specifications in predicate logic of its components
    • clearly present an analysis, a design and a correctness proof of a system
This is a course in applied logic. On the one hand, you will learn how to specify systems both informally in natural language and formally using propositional or predicate logic. Our goal is to describe these systems in such a way that these specifications can be used as a contract. On the other hand, you will learn how to prove these assertions, or in other words, to prove that these systems operate exactly as they should according to their contracts. This process of argumentation will also be done using natural language and using formal mathematical methods. Eventually, you will use a proof assistant to check your proof.
These techniques will be practised in relatively small weekly obligatory exercises. They will be tested in written intermediate exams and a group project in which you will show that you can apply these techniques of assertion and argumentation on a complex system.
Additional comments
This course was previously known as 'Beweren en Bewijzen' and 'Assertion and Argumentation'.

- The rationality square.
- The focus of a model.
- Natural languages and formal languages.
- Propositional logic and predicate logic: syntax and semantics.
- Systematic translation of assertions in natural language to assertions in predicate logic.
- Proofs in natural language.
- Proofs in formal language using truth tables, semantic tableaux and natural deduction.
- Using a proof assistant.
- Correctness theorem of an artifact.

Test information
The obligatory parts of this course are:
- Two interim exams which give the scores IE1 and IE2; the average score of IE1 and IE2 must be at least 5.0.
- A group project; the score P for this project must be at least 5.5.
- A Coq-practicum: the average score C of the weekly Coq assignments must be at least 5.5.

In addition there are non-mandatory weekly assignments; these assignments are not graded, but act as an entrance ticket for the response lectures: only students who handed in a serious attempt for these learning tasks are admitted to the response lectures. Participation in these response lectures may lead to a small bonus B for the final grade.

Under the assumption that all requirements for the obligatory parts are met, the final grade F is MIN(10, ((IE1+IE2)/2 + P)/2 + B).

In all other situations, the final grade F is MIN(5, ((IE1+IE2)/2 + P)/2).

Final grades will be rounded in the normal way.

You need to have basic knowledge of proposition and predicate logic on the level of the courses Formal Reasoning (IPK001) or Mathematical Structures (IPC020). In addition, some experience with programming and modeling will be practical.

Recommended materials
Logic in Computer Science, by Huth and Ryan. This book is useful for background information, but there is no obligation to use this book within the course.
Title:Logic in Computer Science
Author:Huth and Ryan

Instructional modes
Attendance MandatoryYes

168 hours.


28 hours.

Attendance MandatoryYes

A mandatory part of this course is a large group assignment.

20 hours.

Response lecture

At the beginning of the course the response lectures are 45 minutes. However, near the end of the course, usually groups are combined to give lectures of 90 minutes.

Preparation of meetings
It is obligatory to hand in the learning task to be admitted to the response lecture.

14 hours.

Self study

78 hours.


28 hours.

Intermediate Test 1
Test weight0
Test typeTest
OpportunitiesBlock KW3, Block KW4

Intermediate Test 2
Test weight0
Test typeTest
OpportunitiesBlock KW4, Block KW4

Test weight0
Test typeProject
OpportunitiesBlock KW4, Block KW4

Coq Assignments
Test weight0
Test typeAssignment
OpportunitiesBlock KW4, Block KW4

Final Grade
Test weight1
Test typeExam
OpportunitiesBlock KW4, Block KW4