1. Temporal Database
Chap 3: The Interval-extended Relational Model and Its Applications to Valid-time Databases

2. 3.2 Underlying Formalization

3. 3.2 Underlying Formalization

4. 3.2 Underlying Formalization
The empty set is not an interval.
Boundaries of interval: start(:di, dj)) stop(:di, dj))
I(D): The set of all the intervals over 1-d space D

5. 3.2 Underlying Formalization

6. 3.2 Underlying Formalization

7. 3.2.3 N-Dimensional Intervals

8. 3.2.3 N-Dimensional Intervals
du =:2,6) × :1,6)

9. The Duality Principle

10. 3.3 The IXRM Model
b??

11. 3.3 The IXRM Model

12. 3.3 The IXRM Model

13. 3.3 The IXRM Model

14. Operations
Union, Difference, Projection, Cartesian Product

15. Operations
S = Fold: Ai ! ( R )

16. Operations

17. Operations
IF S = Fold: Ai ! ( R ) , the following properties are satisfied.

18. Operations

19. 3.3.2 Operations R = Unfold: Time ! (SALARY) SALARY = Fold: Time! (R)

20. Operations

21. Operations

22. Operations

23. Operations

24. 3.3.3 Geometric Interpretation of the New Operations

25. 3.3.3 Geometric Interpretation of the New Operations

26. 3.3.3 Geometric Interpretation of the New Operations

27. 3.3.3 Geometric Interpretation of the New Operations

28. 3.3.3 Geometric Interpretation of the New Operations

29. 3.4 Application to Valid-time Database

31. Deletion of Data

32. Retrieval of Data

33. SALARY

35. Retrieval of Data

36. Retrieval of Data

37. Retrieval of Data

38. 3.5 Implementation

39. 3.5 Implementation