Category archives: Mathematical Logic

What is Mathematical Logic? Exploring its Fundamentals Summary: In this class, you will discover the basic concepts of mathematical logic, including its relationship with languages and why the use of formal languages is preferred over natural ones. Additionally, you will learn about some of the most famous paradoxes that have…

The Language of Propositional Logic Summary This note reviews the language of propositional logic as a metalanguage used to obtain valid expressions from the base language formed by two symbols. It explains the syntax rules, the concepts of propositional variables and connectors, and also introduces joint negation, the use of…

Formal Deductive Systems in Propositional Logic Summary:In this class, we review formal deductive systems. We explain how these systems are used to decipher the relationships that may exist between different logical expressions, and the basic elements with which these proofs are built: the language, the axioms, and the inference rules….

Learn 4 Essential Deduction Techniques Summary:In this class, 4 deduction techniques of propositional logic are described to enrich the rudimentary propositional calculus presented so far. The presumption rule and its combination with the monotonicity rule are presented, as well as hypothetical syllogism and two ways to obtain this deduction rule….

5 Symmetries of Propositional Logic Summary:Throughout this class, we will explore how double negation, hypothetical syllogism, the contrapositive of implication, deduction theorems, and the definitions of connectors combine to form the symmetries of propositional logic. With clear and simple demonstrations, you will learn to master the equivalences and apply them…

Demonstration of Classical Logic Techniques SUMMARYIn this class, several techniques of classical logic for introducing and eliminating conjunctions and disjunctions are presented, along with the law of the excluded middle and the law of contradiction, also known as the principle of explosion. Additionally, the technique of proof by cases and…

Laws of DeMorgan, Distribution, and Their Proofs SUMMARYIn this class, we review the proofs of DeMorgan’s laws of Distribution for conjunction and disjunction, which are frequently used in propositional logic and areas such as set theory, probability, topology, electronics, and programming. The equivalences that formalize the distribution of negations with…

Semantics of Propositional Logic SUMMARYThis class studies the semantics of propositional logic, specifically the assignment of truth values to an expression and how they propagate from one expression to another through logical connectors. The notion of truth tables is introduced, and the truth tables of derived connectors such as negation,…

Semantic Consequence and Equivalence SUMMARYIn this class, we will study Semantic Consequence and Equivalence in propositional logic, which is a natural continuation of what we have previously covered. We will learn how to derive the notion of semantic consequence from truth value assignments and how this idea relates to the…

Completeness and Soundness in Propositional Logic SUMMARYThis class addresses the relationship between completeness and soundness in propositional logic. Although deduction techniques and semantics in propositional logic have been widely discussed, little attention has been paid to the relationship between these two facets. Soundness refers to the property of a logical…