Lectures related to Rule of inference

Concept of Proof in Mathematics

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

Knowledge Representation: Introduction

Covers knowledge representation in AI, logical inference, and applications in various domains.

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Proofs: Logical Equivalence and Inference Rules

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

Logic Programming: Examples and Rules

Demonstrates logic programming with examples and rules, showcasing a tool for practical application.

Propositional Logic: Inference Rules

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

Proofs: Rules and Applications

Explores rules of inference, quantified statements, and proof methods in logic and mathematics.

Proofs: Arguments in Predicate Logic

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

Theorem Proving and Vampire

Explores theorem proving in first-order logic and the saturation-based approach, highlighting the Vampire theorem prover.

Proofs: Arguments in Predicate Logic

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

Search Algorithms: Abductive Reasoning

Explores abductive reasoning, search algorithms, and heuristic search for problem-solving.

Sequent Calculus: Basics and Applications

Covers the basics and applications of Sequent Calculus in Logic and Proof Theory, including Cut Elimination and practical proof analysis.

Quantum Mechanics: Derivation and Logical Inference

Explores demystifying quantum mechanics through logical inference and robust experimental descriptions, emphasizing the separation of conditions and fundamental quantum equations.

Soundness and Completeness of a Propositional Proof System

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

Propositions and Proofs

Explores propositions, proofs, and contraposition in mathematical theory, emphasizing logical rules and proof methods.

Inference Engines: Resolution and Horn Clauses

Covers inference engines based on resolution, Horn clauses, filtering, and unification in artificial intelligence.

Valid Arguments

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

Inference Rules in Propositional Logic

Covers inference rules in propositional logic and common logical fallacies.

Mathematical Recursion: Induction and Recursion

Explains mathematical induction for proving propositions true for all positive integers.

Mathgraph Theorem Prover

Introduces the Mathgraph Theorem Prover, showcasing its unique approach to representing propositions and organizing graphs for first-order logic.