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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.