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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)

Lecture 42 - Godel's Incompleteness Theorems

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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