Logic in Computer Science (LICS)

Course content

The aim of this course is to provide a firm theoretical foundation of formal logic, with an emphasis on logics, properties, techniques and algorithms relevant in computer science. Building on the students' existing knowledge of Boolean logic and mathematical reasoning, the course includes both fundamental logic formalisms and more specialized logics used in modelling, specification, and verification of programs and hardware systems.

The course covers introductions to

  • propositional logic,
  • predicate logic,
  • the temporal logics LTL and CTL,
  • model checking,
  • binary decision diagrams, and
  • formalised proving using a proof assistant.



BSc Programme in Computer Science

Learning outcome

At course completion, the successful student will have

Knowledge of:

  • Defining logics in terms of syntax, semantics and natural deduction systems, and formal reasoning about logical formulas.
  • A selection of specific logics, including propositional logic, predicate logic and temporal logic (e.g. LTL and CTL).
  • Fundamental properties of these logics, such as soundness, completeness and decidability.
  • Algorithms for transforming logical formulas to normal forms; for deciding fundamental properties of logical formulas such as satisfiability, validity, and entailment; and (symbolic) model checking by binary decision diagrams (BDDs).

Skills in:

  • Deciding and proving formal properties of logical formulas (e.g. satisfiability, validity, implication and equivalence) both by semantics and natural deduction arguments.
  • Proving properties relating logical inference systems and semantics, specifically soundness or completeness.
  • Applying specific algorithms for deciding properties of logical formulas: SAT solvers for propositional calculus; model checking LTL/CTL; using BDDs to represent Boolean functions and perform symbolic model checking.
  • Performing any of the above in the context of variants of the presented logics.

Competences to:

  • Use formal logic to describe real-world situations and express properties of programs, and reason about them formally.


2 lectures of 2 hours each and 1 exercise/discussion session of 4 hours per week;
obligatory written exercises.

  • Expected to be "Logic in Computer Science", 2nd Edition; by Michael Huth and Mark Ryan, Cambridge University Press, 2004, ISBN 0-521-54310X.
  • Supplementary notes.

Discrete mathematical structures (DiMS) or Discrete mathematics and algorithms (DMA) or Discrete mathematics (DIS) or Discrete mathematics for first-year students (DisRus) or other course(s) covering basic arithmetic, sets, relations, functions, big-O-notation, graphs and basic, proofs by induction, mathematical reasoning by deductive arguments.

Problem solving and programming (PoP) or equivalent: Functions, recursion, lists, user-defined data types.

7,5 ECTS
Type of assessment
Written examination, 4 hours under invigilation
Written 4-hour exam with invigilation.

The course has been selected for ITX exam at Peter Bangs Vej.
Written aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Multiple internal examiners.
Criteria for exam assessment

See "Learning Outcome."

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 28
  • Exam
  • 17
  • Theory exercises
  • 14
  • Preparation
  • 147
  • English
  • 206