Foundations of Logic and Model Theory

The course is divided into two modules: - Module 1. Theory 4.5 hp - Module 2. Proficiency training 3.0 hp The course covers predicate logic, first order logic, temporal logic, and model theory. Central concepts are syntax, semantics, proof systems, soundness, completeness, satisfiability, unification and resolution. Knowledge of formal logical systems is necessary to understand the basic principles of many areas of Computer Science, e.g., databases, scientific computing, and machine learning. Module 1 creates this familiarity by teaching logical concepts and methods from a computer-science perspective. Particular emphasis is placed on (i) the difference between logically true statements and and formal proofs, i.e., the definition of logical truth on the one hand, and the development of formal systems for deriving the truth value of  a statement on the other; (ii) algorithmic aspects of proof system, focusing on resolution; and (iii) logical models for logical systems and their usefulness for verification.  Module 2 provides logical proficiency training through mandatory assignments. The module illustrates theory taught in model 1, e.g., through assignments in logical programming, and gives the student the opportunity to apply definitions, notations, and formal systems in a practical setting.