Logic in Computer Science (LICS)
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,
- temporal logics LTL and CTL,
- model checking,
- binary decision diagrams, and
- formalised proving using a proof assistant.
Note that while some applications of logic will be covered in some detail during the course, the focus of the course is primarily on the theoretical foundations of logic in computer science rather than its concrete applications.
At course completion, the successful student will have
- 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).
- 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.
- Use formal logic to describe real-world situations, 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.
The syllabus will be posted in Absalon.
In previous years the syllabus has included:
- "Logic in Computer Science"; by Michael Huth and Mark Ryan. Latest edition.
- Supplementary notes.
Discrete mathematics and algorithms (DMA) or Discrete
mathematics (DIS) or Discrete mathematics for first-year students
(DisRus) or similar courses covering basic arithmetic, sets,
relations, functions, big-O-notation, graphs, 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 invigilationWritten exam
The course has been selected for ITX exam
- 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)
- Theory exercises
- Course number
- 7,5 ECTS
- Programme level
- Block 2
- No limit.
- Study Board of Mathematics and Computer Science
- Department of Computer Science
- Faculty of Science
- Robert Glück (6-6f747d6d6b73486c7136737d366c73)
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