Logic and Modelling

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, exercise classes and computer practicum.

TYPE OF ASSESSMENT
Exam, and computer assignments.

RECOMMENDED BACKGROUND KNOWLEDGE
Logic and Sets