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September 23, 2023

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Description

Mathematical Logic. Instructor: Prof. Arindama Singh, Department of Mathematics, IIT Madras. Propositional Logic: Syntax, Unique parsing, Semantics, Equivalences, Consequences, Calculations, Informal proofs.

Normal Forms and Resolution: Clauses, CNF and DNF representations, Adequacy of calculations, SAT, Resolution refutation, Adequacy of resolution. Proof Systems: Axiomatic system PC, Adequacy of PC, Analytic tableau PT, Adequacy of PT, Compactness of PL. First Order Logic: Syntax of FL, Scope and binding, Substitutions, Semantics of FL, Quantifier laws, Equivalences, Consequences. Normal Forms in FL: Calculations, Informal proofs, Prenex forms, Skolem forms, Herbrand's Theorem, Skolem-Lowenheim theorem, Resolution in FL. Proof Systems for FL: Axiomatic system FC, Analytic tableau FT, Adequacy of FC and FT, Compactness in FL. Axiomatic Theories: Undecidability of FL, Godel's incompleteness theorems. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Sets and Strings Unlimited
  • Lecture 02 – Syntax of Propositional Logic Unlimited
  • Lecture 03 – Unique Parsing Unlimited
  • Lecture 04 – Semantics of Propositional Logic Unlimited
  • Lecture 05 – Consequences and Equivalences Unlimited
  • Lecture 06 – Five Results about Propositional Logic Unlimited
  • Lecture 07 – Calculations and Informal Proofs Unlimited
  • Lecture 08 – More Informal Proofs Unlimited
  • Lecture 09 – Normal Forms Unlimited
  • Lecture 10 – SAT and 3SAT Unlimited
  • Lecture 11 – Horn-SAT and Resolution Unlimited
  • Lecture 12 – Resolution Unlimited
  • Lecture 13 – Adequacy of Resolution Unlimited
  • Lecture 14 – Adequacy and Resolution Strategies Unlimited
  • Lecture 15 – Propositional Calculus (PC) Unlimited
  • Lecture 16 – Some Results about Propositional Calculus (PC) Unlimited
  • Lecture 17 – Arguing with Proofs Unlimited
  • Lecture 18 – Adequacy of Propositional Calculus Unlimited
  • Lecture 19 – Compactness and Analytic Tableau Unlimited
  • Lecture 20 – Examples of Tableau Proofs Unlimited
  • Lecture 21 – Adequacy of Tableaux Unlimited
  • Lecture 22 – Syntax of First Order Logic Unlimited
  • Lecture 23 – Symbolization and Scope of Quantifiers Unlimited
  • Lecture 24 – Hurdles in Giving Meaning Unlimited
  • Lecture 25 – Semantics of First Order Logic Unlimited
  • Lecture 26 – Relevance Lemma Unlimited
  • Lecture 27 – Validity, Satisfiability and Equivalence Unlimited
  • Lecture 28 – Six Results about First Order Logic Unlimited
  • Lecture 29 – Laws in First Order Logic Unlimited
  • Lecture 30 – Quantifier Laws and Consequences Unlimited
  • Lecture 31 – Examples of Informal Proofs and Calculation Unlimited
  • Lecture 32 – Prenex Form Conversion Unlimited
  • Lecture 33 – Skolem Form Unlimited
  • Lecture 34 – Syntactic Interpretation Unlimited
  • Lecture 35 – Herbrand’s Theorem Unlimited
  • Lecture 36 – Most General Unifiers Unlimited
  • Lecture 37 – Resolution Rules Unlimited
  • Lecture 38 – Resolution Examples Unlimited
  • Lecture 39 – Axiomatic System First Order Calculus Unlimited
  • Lecture 40 – First Order Calculus, Semidecidability of First Order Logic, and Tableau Unlimited
  • Lecture 41 – Analytic Tableau for First Order Logic Unlimited
  • Lecture 42 – Godel’s Incompleteness Theorems Unlimited

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