In (KI1V13001), I explored the foundational concepts of modern logic, focusing on valid reasoning and its formalization. This course introduced me to propositional and first-order logic, blending theoretical principles with practical exercises, assessed via two exams. Below is a breakdown of the topics covered:
I learned to verify the validity of inferences using mathematical methods and developed skills to create reasoning systems, essential for AI.
Introduction to Logic: Understood valid inferences and classical logic principles.
Mathematical Foundations: Covered sets, relations, functions, and proof by induction.
Propositional Logic: Studied syntax, semantics, truth tables, and tableaux proofs.
First-Order Logic: Explored syntax, semantics, models, and tableaux with identity functions.
Soundness and Completeness: Analyzed proofs ensuring logical systems are reliable and exhaustive.
Syntax Analysis: Defined propositional and first-order formulas.
Semantics: Evaluated truth using valuations and models.
Tableaux Proofs: Built analytic tableaux to test satisfiability and consequence.
Mathematical Reasoning: Applied set theory and induction to logical problems.
Problem Solving: Tackled exercises from lecture notes to reinforce concepts.