# InfoCoBuild

## Mathematical Logic

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)

 Sets and Strings

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

 References Mathematical Logic Instructor: Prof. Arindama Singh, Department of Mathematics, IIT Madras. Propositional logic, normal forms and resolution, proof systems, first order logic, normal forms in first order logic, proof systems for first order logic, axiomatic theories.