Mathematical logic course and tutorial materials
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Date
2026
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Publisher
University of Oum El Bouaghi
Abstract
This course in Mathematical Logic introduces the fundamental principles of formal reasoning and logical analysis used in mathematics and computer science. It explores the concepts of syntax and semantics, focusing on the representation and evaluation of logical statements. The course covers propositional logic, including propositions, logical connectives, truth tables, tautologies, satisfiability, normal forms (CNF and DNF), and proof systems such as resolution and refutation methods. It also introduces predicate logic as an extension of propositional logic, emphasizing predicates, quantifiers, free and bound variables, structures, interpretations, and semantic validity. Through theoretical explanations, solved exercises, and practical applications, the course aims to develop students’ ability to formalize reasoning, analyze logical structures, and apply logical methods to problem-solving in computer science and mathematics.
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Keywords
Mathematical Logic; Formal Reasoning; Propositional Logic; Predicate Logic; Syntax; Semantics; Truth Tables; Logical Connectives; Tautology; Satisfiability; Conjunctive Normal Form (CNF); Disjunctive Normal Form (DNF); Resolution Method; Quantifiers; Predicate Calculus; Logical Validity; Formalization; Boolean Logic; Model Theory