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September 26, 2023

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Description

Introduction to Logic. Instructor: Prof. A. V. Ravishankar Sarma, Department of Humanities and Social Sciences, IIT Kanpur.

This course introduces the basic concepts of logic and explores various principles, techniques concerning valid reasoning. Since Reasoning is involved in most intellectual activities, logic is relevant to broad range of pursuits. The study of logic is essential for students of computer science, philosophy (used as a tool for their arguments) and students of Mathematics who attempts to understand the foundations of mathematics in a better way. Mathematicians might be interested in what goes on in a lengthy proof or what constitutes a mathematical proof. Introduction to Logic presents the basic techniques used to derive a valid conclusion from the premises of an argument and also techniques for determining whether or not a argument (deductive or inductive) is valid/strong. The goal of this course is to introduce students to the essential ideas and techniques from logic that are widely used in Philosophy, Computer Science, Natural sciences, and the argumentation used in the daily discourse. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Identification of Arguments Unlimited
  • Lecture 02 – Non-arguments Unlimited
  • Lecture 03 – Types of Arguments: Deductive vs Inductive Unlimited
  • Lecture 04 – Nature and Scope of Deductive and Inductive Arguments Unlimited
  • Lecture 05 – Truth, Validity and Soundness Unlimited
  • Lecture 06 – Strength of Inductive Arguments, Counterexample Method Unlimited
  • Lecture 07 – Toulmin’s Model of Argumentation Unlimited
  • Lecture 08 – Identification of Formal and Informal Fallacies Unlimited
  • Lecture 09 – Informal Fallacies: Fallacies of Relevance and Fallacies of Weak Induction Unlimited
  • Lecture 10 – Fallacies of Weak Induction and Fallacies Arising Out of Ambiguity in Language Unlimited
  • Lecture 11 – Introduction and Motivation for Syllogistic Logic Unlimited
  • Lecture 12 – Aristotle Theory of Syllogisms Unlimited
  • Lecture 13 – Syllogistic Poem, Reduction of Syllogisms Unlimited
  • Lecture 14 – Syllogistic Poem, Reduction of Syllogisms (cont.) Unlimited
  • Lecture 15 – Nature and Scope of Propositional Logic Unlimited
  • Lecture 16 – Syntax of Propositional Logic Unlimited
  • Lecture 17 – Logical Connectives: Truth Tables Unlimited
  • Lecture 18 – Truth Table Method: Validity, Consistency, Logical Equivalence Unlimited
  • Lecture 19 – Semantic Tableaux for Propositional Logic Unlimited
  • Lecture 20 – Knights and Knaves Puzzles Unlimited
  • Lecture 21 – Semantic Tableaux Method: Further Examples Unlimited
  • Lecture 22 – Natural Deduction Method Unlimited
  • Lecture 23 – Natural Deduction: Examples Unlimited
  • Lecture 24 – Conjunctive and Disjunctive Normal Forms Unlimited
  • Lecture 25 – CNF, DNF and Satisfiability and Validity Unlimited
  • Lecture 26 – Resolution and Refutation Method Unlimited
  • Lecture 27 – Resolution and Refutation Method: Examples Unlimited
  • Lecture 28 – Axiomatic Propositional Logic Unlimited
  • Lecture 29 – Hilbert-Ackermann Axiomatic System Unlimited
  • Lecture 30 – Proofs in the PM System Unlimited
  • Lecture 31 – Hilbert and Ackermann System Unlimited
  • Lecture 32 – Outlines of Predicate Logic Unlimited
  • Lecture 33 – Outlines of Predicate Logic (cont.) Unlimited
  • Lecture 34 – Building Blocks of Predicate Logic Unlimited
  • Lecture 35 – Quantifiers, Freedom, Bondage Unlimited
  • Lecture 36 – Translation into Predicate Logic Unlimited
  • Lecture 37 – Semantics of Predicate Logic Unlimited
  • Lecture 38 – Truth, Satisfiability, Validity in Predicate Logic Unlimited
  • Lecture 39 – Formation Trees for WFF in Predicate Logic Unlimited
  • Lecture 40 – Semantic Tableaux Method for Predicate Logic Unlimited
  • Lecture 41 – Semantic Tableaux Method: Satisfiability, Validity Unlimited
  • Lecture 42 – Natural Deduction in Predicate Logic Unlimited
  • Lecture 43 – Important Theorems in First Order Logic Unlimited
  • Lecture 44 – Limitations of First Order Logic Unlimited

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