Logic

Logical reasoning constitutes the methodological foundation of mathematics, computer science, the natural and technical sciences, as well as the social sciences and humanities. The course initially deals with elementary logic, encompassing propositional and first-order predicate logic. Topics include:

1. Traditional logic
2. Formalisation of statements in natural language
3. Truth Tables
4. Propositional logic 4.1 The notion of a formal language 4.2 The calculus of Natural Deduction (NK) for classical propositional logic 4.3 Concepts of (propositional) truth and logical inference 4.4 Soundness (Correctness) for propositional logic 4.5 Completeness for propositional logic
5. First-order predicate logic 5.1 Formal language for first-order predicate logic 5.2 The calculus of Natural Deduction (NK) for first-order predicate logic 5.3 Tarski semantics for the predicate logic language 5.4 Proof of the Adequacy Theorem (Soundness and Completeness Theorem for first-order NK with identy)

The course aims to provide students with a foundational understanding of formal logic, focusing on propositional logic and first-order predicate logic. Students will acquire: • familiarity with the formal tools and methods of logical reasoning, • the ability to formalise statements of natural language into logical expressions, • an understanding of the syntax and semantics of logical systems, • the capacity to construct formal proofs using the calculus of Natural Deduction (NK), and • insight into key metatheoretical results such as soundness and completeness. Although no prior knowledge is required, a certain familiarity with mathematical thinking is recommended.

In a written examination (120 min) the students demonstrate a foundational understanding of formal logic within all aspects described in “Intended Learning Outcomes”.

No formal prerequisites are required. A general openness to abstract and mathematical reasoning is helpful.

• A script will be provided at the beginnig of the course.

• Lectures
• Guided exercises in formalisation and proof construction