NPTEL : Mathematical Logic (Mathematics)

Co-ordinators : Prof. Arindama Singh


Lecture 1 - Sets and Strings

Lecture 2 - Syntax of Propositional Logic

Lecture 3 - Unique Parsing

Lecture 4 - Semantics of PL

Lecture 5 - Consequences and Equivalences

Lecture 6 - Five results about PL

Lecture 7 - Calculations and Informal Proofs

Lecture 8 - More Informal Proofs

Lecture 9 - 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 PC

Lecture 17 - Arguing with Proofs

Lecture 18 - Adequacy of PC

Lecture 19 - Compactness & Analytic Tableau

Lecture 20 - Examples of Tableau Proofs

Lecture 21 - Adequacy of Tableaux

Lecture 22 - Syntax of First order Logic (FL)

Lecture 23 - Symbolization & Scope of Quantifiers

Lecture 24 - Hurdles in giving Meaning

Lecture 25 - Semantics of FL

Lecture 26 - Relevance Lemma

Lecture 27 - Validity, Satisfiability & Equivalence

Lecture 28 - Six Results about FL

Lecture 29 - Laws, Calculation & Informal Proof

Lecture 30 - Quantifier Laws and Consequences

Lecture 31 - More Proofs and Prenex Form

Lecture 32 - Prenex Form Conversion

Lecture 33 - Skolem Form

Lecture 34 - Syntatic Interpretation

Lecture 35 - Herbrand's Theorem

Lecture 36 - Most General Unifiers

Lecture 37 - Resolution Rules

Lecture 38 - Resolution Examples

Lecture 39 - Ariomatic System FC

Lecture 40 - FC and Semidecidability of FL

Lecture 41 - Analytic Tableau for FL

Lecture 42 - Godels Incompleteness Theorems