Mathematical Logic (Prof. Arindama Singh, IIT Madras) | Mathematics

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.