The computer itself was born from logic, and logic plays indispensable roles in diverse fields of science today, including computer science, mathematics, linguistics, philosophy and beyond. This course covers advanced issues in classical logic and elements of non-classical logic with emphasis on completeness proof methodologies for various logical systems; (in)completeness is the most fundamental issue in logic, elucidating the relationships between the syntax (proof theory) and semantics (model theory) of logical systems, or the correspondence between symbolic language and reality/worlds. Familiarity with elementary logic is assumed as well as general mathematical knowledge (such as sets, relations, quotients under equivalence relations).

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Understand classical and non-classical logical systems and their significance
2. Evaluate differences (advantages/disadvantages) of logical systems
3. Analyse the syntax and semantics of logics and their meta-theoretical properties
4. Formalise semantic properties and interpret syntactic properties
5. Apply translation principles for comparing different logical systems
6. Create mathematical proofs in the area of formal logic
7. Reflect on common logical systems and evaluate their limitations