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This course covers lessons on propositional logic syntax and its semantics,tautology checking,analytic tableaux,formal theories,skalemization,resolution in FOL,verification of white,imperative programs and references.

   

S.No

Topic

1

 Introduction                             

2

 Propositional Logic Syntax              

3

 Semantics of Propositional Logic        

4

 Logical and Algebraic Concepts          

5

 Identities and Normal forms             

6

 Tautology Checking                       

7

 Propositional Unsatisfiability          

8

 Analytic Tableaux                       

9

 Consistency and Completeness            

10

 The Completeness Theorem                

11

 Maximally Consistent Sets                

12

 Formal Theories                         

13

 Proof Theory : Hilbert-style            

14

 Derived Rules                           

15

 The Hilbert System : Soundness          

16

 The Hilbert System :Completeness         

17

 Introduction to Predicate Logic         

18

 The Semantic of Predicate Logic         

19

 Subsitutions                            

20

 Models                                  

21

 Structures and Substructures            

22

 First - Order Theories                  

23

 Predicate Logic: Proof Theory (Contd..) 

24

 Existential Quantification              

25

 Normal Forms                            

26

 Skalemization                           

27

 Substitutions and Instantiations        

28

 Unification                             

29

 Resolution in FOL                       

30

 More on Resolution in FOL               

31

 Resolution : Soundness and Completeness 

32

 Resolution and Tableaux                 

33

 Completeness of Tableaux Method         

34

 Completeness of the Hilbert System      

35

 First -Order Theories                   

36

 Towards Logic Programming               

37

 Verification of Imperative Programs     

38

 Verification of WHILE Programs          

39

 References          

   
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