Text

Course syllabus - Mathematical Logic for Computer Science

Scope

7.5 credits

Course code

MMA130

Valid from

Autumn semester 2026

Education level

First cycle

Progressive Specialisation

G1F (First cycle, has less than 60 credits in first-cycle course/s as entry requirements)

Main area(s)

Mathematics/Applied Mathematics

Organisation

Department of Business and Mathematics

Ratified

2013-02-01

Revised

2025-11-03

Literature lists

Course literature is preliminary up to 8 weeks before course start. Course literature can be valid over several semesters.

    • Ratified date: 2021-06-24
    • Latest update: 2025-05-27

    Books

    Huth, Michael; Ryan, Mark

    Logic in computer science: modelling and reasoning about systems

    ISBN: 0-521-54310-X

    LIBRIS-ID: 9359296

    2. ed., Cambridge, Cambridge Univ. Press, xiv, 427 s.

Objectives

The course presents basic concepts and methods of mathematical logic of importance for further studies in computer science. Additionally, training in logical thinking and the ability to make self-analysis and solution of logical problems are practiced.

Learning outcomes

At the end of a passed course, the student is expected to be able to

  • describe and apply the following basic concepts: formal languages, formulas, valuations and models for formal languages.
  • formalize statements made in a natural language into a formal language.
  • perform semantic proof and deduction.
  • determine and prove the consistency and inconsistency as well as dependence and independence of formulas.
  • describe and apply the Completeness Theorem for predicate logic
  • describe the axioms and set up models for the axiom systems for Peano arithmetic and for Boolean algebra.
  • describe logic systems with multiple truth values, modal logic and temporal logic as well as perform calculations for truth values in these systems.
  • describe the main elements of Gödel's Incompleteness Theorem.

Course content

Classical first-order predicate logic: Formal language. Valuation. Model. Formal derivation (semantic proof and deduction). Consistency & inconsistency, dependency & independency. Soundness, completeness. Relation, function.
Axiom system: Axiom system for arithmetic of natural numbers and for Boolean algebra.
Non-classical logic system: Logic system with multiple truth values. Logic with new connectives (modal logic) and time structure (temporal logic).
Introduction to Gödel's Incompleteness Theorem.

Specific requirements

Discrete Mathematics, 7.5 credits, of which 3 credits must be completed at the beginning of the course, or the equivalent.

Examination

Exercises (INL1), 2.5 credits, marks Pass (G)
Written and/or oral examination (TEN1), 5 credits, marks 3, 4 or 5

A student who has a certificate from MDU regarding disability study support, can request adaptions for the examination. It is the examiner who takes decisions on any adaptions, based on the certificate and other conditions.

Grade

Grading scale: 5, 4, 3