Home »Mathematics »IIT Madras » Mathematical Logic



Mathematical Logic

IIT Madras Course , Prof. Arindama Singh       Subscribe to feed

Lights off      

Lecture 1: Mod-01 Lec-01 Sets and Strings

Embed
Download:   MP4, FLV and 3GP 6343 views

SEE: Guide to Download NPTEL Video Lecture

Lecture Details :

Mathematical Logic by Prof.Arindama Singh, Department of Mathematics ,IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Course Description :

Contents:
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, Resoltion in FL.

Proof Systems for FL : Axiomatic system FC, Analytic tableau FT, Adequacy of FC and FT, Compactness in FL.
Axiomatic Theories : Undecidabilty of FL, Godel's incompleteness theorems.

Other Resources :

Syllabus | Citation |

IITMadras delivers the above video lessons under NPTEL program, there are more than 6000+ nptel video lectures by other IIT's as well.

Other Mathematics Courses

» check out the complete list of Mathematics Video lectures          

 

Mathematics Lecture Notes

 

Comments

Post your Comments

  1. Mod-01 Lec-01 Sets and Strings
  2. Mod-01 Lec-02 Lecture-02-Syntax of Propositional Logic
  3. Mod-01 Lec-03 Lecture-03-Unique Parsing
  4. Mod-01 Lec-04 Lecture-04-Semantics of PL
  5. Mod-01 Lec-05 Lecture-05-Consequences and Equivalences
  6. Mod-01 Lec-06 Five results about PL
  7. Mod-01 Lec-07 Lecture-07-Calculations and Informal Proofs
  8. Mod-01 Lec-08 Lecture-08-More Informal Proofs
  9. Mod-01 Lec-09 Lecture-09-Normal forms
  10. Mod-01 Lec-10 Lecture-10-SAT and 3SAT
  11. Mod-01 Lec-11 Lecyture-11-Horn-SAT and Resolution
  12. Mod-01 Lec-12 Lecture-12-Resolution
  13. Mod-01 Lec-13 Lecture-13-Adequacy of Resolution
  14. Mod-01 Lec-14 Lecture-14-Adequacy and Resolution Strategies
  15. Mod-01 Lec-15 Lecture-15-Propositional Calculus (PC)
  16. Mod-01 Lec-16 Lecture-16-Some Results about PC
  17. Mod-01 Lec-17 Lecture-17-Arguing with Proofs
  18. Mod-01 Lec-18 Lecture-18-Adequacy of PC
  19. Mod-01 Lec-19 Lecture-19-Compactness & Analytic Tableau
  20. Mod-01 Lec-20 Lecture-20-Examples of Tableau Proofs
  21. Mod-01 Lec-21 Lecture-21-Adequacy of Tableaux
  22. Mod-01 Lec-22 Lecture-22-Syntax of First order Logic (FL)
  23. Mod-01 Lec-23 Lecture-23-Symbolization & Scope of Quantifiers
  24. Mod-01 Lec-24 Lecture-24-Hurdles in giving Meaning
  25. Mod-01 Lec-25 Lecture-25-Semantics of FL
  26. Mod-01 Lec-26 Lecture-26-Relevance Lemma
  27. Mod-01 Lec-27 Lecture-27-Validity, Satisfiability & Equivalence
  28. Mod-01 Lec-28 Lecture-28-Six Results about FL
  29. Mod-01 Lec-29 Lecture-29-Laws, Calculation & Informal Proof
  30. Mod-01 Lec-30 Lecture-30-Quantifier Laws and Consequences
  31. Mod-01 Lec-31 Lecture-31-More Proofs and Prenex Form
  32. Mod-01 Lec-32 Lecture-32-Prenex Form Conversion
  33. Mod-01 Lec-33 Lecture-33-Skolem Form
  34. Mod-01 Lec-34 Lecture-34-Syntatic Interpretation
  35. Mod-01 Lec-35 Lecture-35-Herbrand's Theorem
  36. Mod-01 Lec-36 Lecture-36-Most General Unifiers
  37. Mod-01 Lec-37 Lecture-37-Resolution Rules
  38. Mod-01 Lec-38 Lecture-38-Resolution Examples
  39. Mod-01 Lec-39 Lecture-39-Ariomatic System FC
  40. Mod-01 Lec-40 Lecture-40-FC and Semidecidability of FL
  41. Mod-01 Lec-41 Lecture-41-Analytic Tableau for FL
  42. Mod-01-Lec-42 Lecture-42-Godels Incompleteness Theorems