Mathematical logic

Mathematical Logic

Mathematical Logic is a fundamental course designed to provide students with a rigorous understanding of formal reasoning and logical thinking used in mathematics and computer science. The course introduces the principles of symbolic logic and the methods used to represent, analyze, and verify logical statements and arguments.

The course begins with an introduction to the foundations of logic, including the objectives of logical reasoning, the concepts of syntax and semantics, and the role of logic in problem solving and formal systems. Students are then introduced to propositional logic, where they study propositions, logical connectives, propositional variables, and logical formulas. Important concepts such as truth tables, semantic equivalence, tautologies, contradictions, conjunctive and disjunctive normal forms, satisfiability, and validity are explored in detail.

In addition, the course covers methods of logical resolution and proof techniques, including refutation, clause form transformation, propositional resolution rules, and resolution methods used in automated reasoning and artificial intelligence.

The second major part of the course focuses on predicate logic. Students learn about terms, predicates, quantifiers, and the construction of logical formulas involving free and bound variables. The semantic interpretation of predicate logic and the satisfaction of formulas within logical structures are also studied.

Throughout the course, students develop analytical and abstract reasoning skills that are essential in fields such as computer science, software engineering, cybersecurity, artificial intelligence, and formal verification. By the end of the course, students are expected to be able to formalize reasoning processes, analyze logical arguments, construct valid proofs, and apply logical methods to computational and mathematical problems.