Lectures related to Proofs: Rules and Applications

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Concept of Proof in Mathematics

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Propositional Logic: Inference Rules and Valid Arguments

Covers inference rules in propositional logic and common logical fallacies.

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Inference Rules in Propositional Logic

Covers inference rules in propositional logic and common logical fallacies.

Proofs: Logical Equivalence and Inference Rules

Covers the concept of logical equivalence in proofs and inference rules.

Soundness and Completeness of a Propositional Proof System

Explores the importance of soundness and completeness in a propositional proof system.

Proofs: Arguments in Predicate Logic

Covers rules of inference for quantified statements and demonstrates constructing valid arguments using predicate logic.

Propositional Logic: Inference Rules

Covers the interpretation of propositional logic and inference rules for implication, conjunction, and double negation.

Valid Arguments

Explains how to determine and build valid arguments in propositional logic.

Inductive Propositions: Reasoning and Evaluation Techniques

Discusses inductive propositions, their definitions, and applications in reasoning and evaluation techniques in Coq.

Formal Logic: Proofs and Sets

Covers the basics of formal logic, focusing on logical expressions and mathematical proofs.

Valid Arguments: Understanding Propositional Logic

Explains how premises imply conclusions using inference rules and truth tables in propositional logic.

Introduction & Propositional Logic

Covers the basics of propositional logic, logical connectives, truth tables, and compound propositions.

Introduction to Proofs

Introduces informal proofs and their practical applications in computer science and mathematics, emphasizing the importance of proving theorems through direct and indirect methods.

Proofs and Logic: Introduction

Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.

Coq: Introduction

Introduces Coq, covering defining propositions, proving theorems, and using tactics.

Introduction to Proofs

Introduces informal proofs, explores practical applications, and explains theorem proofs using direct and indirect methods.

Predicate Logic: Quantifiers, CNF, DNF

Covers Predicate Logic, focusing on Quantifiers, CNF, and DNF.

Logic: Proof Techniques

Explores proof techniques in logic, demonstrating how to prove or disprove propositions using negations and assumptions.