Course Objective

The course objective is to obtain a good knowledge and understanding of
the most important logical systems: propositional logic, predicate logic
and modal logic. The students learn to use these systems to model data,
knowledge and actions. An important aspect of the course is the ability
to reason using these logics and reason about these logics: what can and
what can not be expressed with a logic system, and what are the
differences between the systems with respect to expressive power or the
existence of decision procedures.

Course Content

The focus of the lecture is on propositional logic and first-order
predicate logic. We work with natural deduction as proof system. The
relation between semantic and syntactic methods is important; the
central keywords are correctness, consistency and completeness.
Moreover, we pay attention to expressive power, for example when
formulating queries. A fundamental tool, for this purpose, is the
compactness theorem.

Algorithmically there the contrast between the decidability of
propositional logic and the undecidability of predicate logic (for
example, seen by a coding of the Post Correspondence Problem).

As a variation of the mentioned logics, we consider modal logic with
Kripke models as semantics.

Teaching Methods

Lecture (3 hours per week)
Exercise classes (3 hours per week)
Computer practicum using the Lean proof assistant, done during exercise
classes

Method of Assessment

Final exam (100%) and computer assignments using the Lean proof
assistant (required to qualify for the exam, and .5 bonus points for
doing extra problems.)

Literature

Mandatory:

Jeremy Avigad, Robert Y. Lewis, Floris van Doorn, Logic and Proof
https://avigad.github.io/logic_and_proof/

Michael Huth, Mark Ryan, Logic in Computer Science (2nd edition)
Cambridge University Press, 2004 ISBN 0 521 54310 X

Target Audience

2CS

Recommended background knowledge

Logic and Sets