Logic (advanced level, 7.5 hp)

Course code and home page

Stockholm University course code: MM7008

Home page (Fall 2013)

Overall motivation and description

Logic is the study of reasoning. In the middle of the 19th century Boole and others started to study logic with mathematical methods, e.g. Boolean algebra, which gave rise to formal logic. The treatment of logic as a mathematical subject is indispensible in computer science, and opens the possibility for automatizing many intellectual tasks, even mathematical reasoning itself.

This course is intended to be studied as first course in logic. It treats the two most important logics: propositional logic and predicate logic in depth and show how they can be used in modelling reasoning, especially mathematical reasoning. In particular, the formal language of predicate logic, substitution, semantics and natural deduction are studied. The system's soundness and completeness with respect to the semantics are proved, and is then applied to different problems.

Aim of the course

The student should become familiar using propositional and predicate logic formulas for expressing mathematical statements, and how formulas may be interpreted in different models. Another important goal is to learn how to make formal proofs in the system of natural deduction, and how to use models to conclude that a statement is not provable from certain axioms. The student should become acquainted with further logical tools and notions and important theoretical implications of mathematical logic.

Erik Palmgren, August 29, 2013