Talk given at the CENTRIA, Lisbon, Portugal.

1. Semantic Diff as the Basis for
Knowledge Base Versioning
Enrico Franconi1 Thomas Meyer2 Ivan Varzinczak2
1 Free University of Bozen/Bolzano 2 Meraka Institute, CSIR
Bolzano, Italy Pretoria, South Africa
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 1 / 24

2. Motivation
Knowledge Base
Ontology (DL, RDF)
Agents’ beliefs
Regulations or norms
...
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 2 / 24

3. Motivation
Knowledge Base
Ontology (DL, RDF)
K1
Agents’ beliefs
Regulations or norms
...
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 2 / 24

4. Motivation
Knowledge Base
Ontology (DL, RDF)
K1 K2
Agents’ beliefs
Regulations or norms
...
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 2 / 24

5. Motivation
K3
Knowledge Base
Ontology (DL, RDF)
K1 K2 K5
Agents’ beliefs
Regulations or norms
...
K4
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 2 / 24

6. Motivation
K3 ...
Knowledge Base
Ontology (DL, RDF)
K1 K2 K5 ...
Agents’ beliefs
Regulations or norms
...
K4 K6
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 2 / 24

7. Motivation
K3 ...
Knowledge Base
Ontology (DL, RDF)
K1 K2 K5 ...
Agents’ beliefs
Regulations or norms
...
K4 K6
Need for a versioning system
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 2 / 24

8. Motivation
Issues K6
Maintaining different versions
Parsimonious representation K5 K1
Reasoning with versions Kc
In which of the KBs does α hold,
K2
but not β?
K4
Difference between versions
K3
How they differ in meaning
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 3 / 24

9. Motivation
Issues K6
Maintaining different versions
Parsimonious representation K5 K1
Reasoning with versions Kc
In which of the KBs does α hold,
K2
but not β?
K4
Difference between versions
K3
How they differ in meaning
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 3 / 24

10. Motivation
Issues K6
Maintaining different versions
Parsimonious representation K5 K1
Reasoning with versions Kc
In which of the KBs does α hold,
K2
but not β?
K4
Difference between versions
K3
How they differ in meaning
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 3 / 24

11. Motivation
Issues K6
Maintaining different versions
Parsimonious representation K5 K1
Reasoning with versions Kc
In which of the KBs does α hold,
K2
but not β?
K4
Difference between versions
K3
How they differ in meaning
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 3 / 24

12. Outline
1 Logical Preliminaries
2 Knowledge Base Versioning
Semantic Diff
A General Framework
Compiled Representation
3 Conclusion
Contributions
Future Work
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 4 / 24

13. Outline
1 Logical Preliminaries
2 Knowledge Base Versioning
Semantic Diff
A General Framework
Compiled Representation
3 Conclusion
Contributions
Future Work
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 4 / 24

14. Outline
1 Logical Preliminaries
2 Knowledge Base Versioning
Semantic Diff
A General Framework
Compiled Representation
3 Conclusion
Contributions
Future Work
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 4 / 24

15. Logical Preliminaries
Knowledge bases
A knowledge base K is a (possibly infinite) set of formulas
Cn(K) = {α | K |= α}
Cn(.) is called Tarskian iff it satisfies
Inclusion: X ⊆ Cn(X )
Idempotence: Cn(Cn(X )) ⊆ Cn(X )
Monotonicity: X ⊆ Y implies Cn(X ) ⊆ Cn(Y )
[α] = {β | α ≡ β}
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 5 / 24

16. Logical Preliminaries
Knowledge bases
A knowledge base K is a (possibly infinite) set of formulas
Cn(K) = {α | K |= α}
Cn(.) is called Tarskian iff it satisfies
Inclusion: X ⊆ Cn(X )
Idempotence: Cn(Cn(X )) ⊆ Cn(X )
Monotonicity: X ⊆ Y implies Cn(X ) ⊆ Cn(Y )
[α] = {β | α ≡ β}
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 5 / 24

17. Logical Preliminaries
Knowledge bases
A knowledge base K is a (possibly infinite) set of formulas
Cn(K) = {α | K |= α}
Cn(.) is called Tarskian iff it satisfies
Inclusion: X ⊆ Cn(X )
Idempotence: Cn(Cn(X )) ⊆ Cn(X )
Monotonicity: X ⊆ Y implies Cn(X ) ⊆ Cn(Y )
[α] = {β | α ≡ β}
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 5 / 24

18. Logical Preliminaries
Knowledge bases
A knowledge base K is a (possibly infinite) set of formulas
Cn(K) = {α | K |= α}
Cn(.) is called Tarskian iff it satisfies
Inclusion: X ⊆ Cn(X )
Idempotence: Cn(Cn(X )) ⊆ Cn(X )
Monotonicity: X ⊆ Y implies Cn(X ) ⊆ Cn(Y )
[α] = {β | α ≡ β}
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 5 / 24

19. Outline
1 Logical Preliminaries
2 Knowledge Base Versioning
Semantic Diff
A General Framework
Compiled Representation
3 Conclusion
Contributions
Future Work
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 6 / 24

20. Semantic Diff
Difference in meaning between knowledge bases K and K
Analogy with the Unix diff command
diff distinguishes between syntactically different files
Semantic diff highlights the difference in (logical) meaning
Assume a logic with a Tarskian consequence relation
Example
Let the (propositional) knowledge bases:
K1 = {p, q} and K2 = {p, p → q}
K1 and K2 differ in syntax
But K1 and K2 convey the same meaning (K1 ≡ K2 )
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 7 / 24

21. Semantic Diff
Difference in meaning between knowledge bases K and K
Analogy with the Unix diff command
diff distinguishes between syntactically different files
Semantic diff highlights the difference in (logical) meaning
Assume a logic with a Tarskian consequence relation
Example
Let the (propositional) knowledge bases:
K1 = {p, q} and K2 = {p, p → q}
K1 and K2 differ in syntax
But K1 and K2 convey the same meaning (K1 ≡ K2 )
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 7 / 24

22. Semantic Diff
Difference in meaning between knowledge bases K and K
Analogy with the Unix diff command
diff distinguishes between syntactically different files
Semantic diff highlights the difference in (logical) meaning
Assume a logic with a Tarskian consequence relation
Example
Let the (propositional) knowledge bases:
K1 = {p, q} and K2 = {p, p → q}
K1 and K2 differ in syntax
But K1 and K2 convey the same meaning (K1 ≡ K2 )
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 7 / 24

23. Semantic Diff
Difference in meaning between knowledge bases K and K
Analogy with the Unix diff command
diff distinguishes between syntactically different files
Semantic diff highlights the difference in (logical) meaning
Assume a logic with a Tarskian consequence relation
Example
Let the (propositional) knowledge bases:
K1 = {p, q} and K2 = {p, p → q}
K1 and K2 differ in syntax
But K1 and K2 convey the same meaning (K1 ≡ K2 )
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 7 / 24

24. Characterizing Semantic Diff
KBs closed under logical consequence
(P1) K = Cn(K) and K = Cn(K )
Semantic diff of K and K : pair A, R
A is the add-set of (K, K )
R as the remove-set of (K, K )
(P2) K = (K ∪ A) R
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 8 / 24

25. Characterizing Semantic Diff
KBs closed under logical consequence
(P1) K = Cn(K) and K = Cn(K )
Semantic diff of K and K : pair A, R
A is the add-set of (K, K )
R as the remove-set of (K, K )
(P2) K = (K ∪ A) R
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 8 / 24

26. Characterizing Semantic Diff
KBs closed under logical consequence
(P1) K = Cn(K) and K = Cn(K )
Semantic diff of K and K : pair A, R
A is the add-set of (K, K )
R as the remove-set of (K, K )
(P2) K = (K ∪ A) R
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 8 / 24

27. Characterizing Semantic Diff
Minimal change and no redundancy
(P3) A ⊆ K
(P4) R ⊆ K
Duality of semantic diff
(P5) K = (K ∪ R) A
‘Undo’ operation when moving between versions
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 9 / 24

28. Characterizing Semantic Diff
Minimal change and no redundancy
(P3) A ⊆ K
(P4) R ⊆ K
Duality of semantic diff
(P5) K = (K ∪ R) A
‘Undo’ operation when moving between versions
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 9 / 24

29. Characterizing Semantic Diff
Minimal change and no redundancy
(P3) A ⊆ K
(P4) R ⊆ K
Duality of semantic diff
(P5) K = (K ∪ R) A
‘Undo’ operation when moving between versions
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 9 / 24

30. Characterizing Semantic Diff
Definition
K and K knowledge bases, A and R sets of sentences
A, R is semantic diff compliant w.r.t. (K, K ) iff (K, K ) and A, R
satisfy Postulates (P1)–(P5)
(P1) K = Cn(K) and K = Cn(K )
(P2) K = (K ∪ A) R
(P3) A ⊆ K
(P4) R ⊆ K
(P5) K = (K ∪ R) A
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 10 / 24

31. Characterizing Semantic Diff
Definition
K and K knowledge bases, A and R sets of sentences
A, R is semantic diff compliant w.r.t. (K, K ) iff (K, K ) and A, R
satisfy Postulates (P1)–(P5)
(P1) K = Cn(K) and K = Cn(K )
(P2) K = (K ∪ A) R
(P3) A ⊆ K
(P4) R ⊆ K
(P5) K = (K ∪ R) A
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 10 / 24

32. Characterizing Semantic Diff
Specific construction for the semantic diff operator:
Definition
The ideal semantic diff of (K, K ) is the pair A, R , where
A = K K and R = K K
Neither A nor R are logically closed:
Example
Let K = Cn(p ∧ q) and K = Cn(¬q)
A = {[¬q], [¬p ∨ ¬q]}
R = {[p ∧ q], [p], [q], [p ↔ q], [p ∨ q], [¬p ∨ q]}
p ∨ ¬q ∈ Cn(A), p ∨ ¬q ∈ Cn(R), but p ∨ ¬q ∈ A and p ∨ ¬q ∈ R
/ /
In fact, for any ideal semantic diff A, R , ∈ A and
/ ∈R
/
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 11 / 24

33. Characterizing Semantic Diff
Specific construction for the semantic diff operator:
Definition
The ideal semantic diff of (K, K ) is the pair A, R , where
A = K K and R = K K
Neither A nor R are logically closed:
Example
Let K = Cn(p ∧ q) and K = Cn(¬q)
A = {[¬q], [¬p ∨ ¬q]}
R = {[p ∧ q], [p], [q], [p ↔ q], [p ∨ q], [¬p ∨ q]}
p ∨ ¬q ∈ Cn(A), p ∨ ¬q ∈ Cn(R), but p ∨ ¬q ∈ A and p ∨ ¬q ∈ R
/ /
In fact, for any ideal semantic diff A, R , ∈ A and
/ ∈R
/
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 11 / 24

34. Characterizing Semantic Diff
Specific construction for the semantic diff operator:
Definition
The ideal semantic diff of (K, K ) is the pair A, R , where
A = K K and R = K K
Neither A nor R are logically closed:
Example
Let K = Cn(p ∧ q) and K = Cn(¬q)
A = {[¬q], [¬p ∨ ¬q]}
R = {[p ∧ q], [p], [q], [p ↔ q], [p ∨ q], [¬p ∨ q]}
p ∨ ¬q ∈ Cn(A), p ∨ ¬q ∈ Cn(R), but p ∨ ¬q ∈ A and p ∨ ¬q ∈ R
/ /
In fact, for any ideal semantic diff A, R , ∈ A and
/ ∈R
/
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 11 / 24

35. Characterizing Semantic Diff
Specific construction for the semantic diff operator:
Definition
The ideal semantic diff of (K, K ) is the pair A, R , where
A = K K and R = K K
Neither A nor R are logically closed:
Example
Let K = Cn(p ∧ q) and K = Cn(¬q)
A = {[¬q], [¬p ∨ ¬q]}
R = {[p ∧ q], [p], [q], [p ↔ q], [p ∨ q], [¬p ∨ q]}
p ∨ ¬q ∈ Cn(A), p ∨ ¬q ∈ Cn(R), but p ∨ ¬q ∈ A and p ∨ ¬q ∈ R
/ /
In fact, for any ideal semantic diff A, R , ∈ A and
/ ∈R
/
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 11 / 24

36. Characterizing Semantic Diff
Specific construction for the semantic diff operator:
Definition
The ideal semantic diff of (K, K ) is the pair A, R , where
A = K K and R = K K
Neither A nor R are logically closed:
Example
Let K = Cn(p ∧ q) and K = Cn(¬q)
A = {[¬q], [¬p ∨ ¬q]}
R = {[p ∧ q], [p], [q], [p ↔ q], [p ∨ q], [¬p ∨ q]}
p ∨ ¬q ∈ Cn(A), p ∨ ¬q ∈ Cn(R), but p ∨ ¬q ∈ A and p ∨ ¬q ∈ R
/ /
In fact, for any ideal semantic diff A, R , ∈ A and
/ ∈R
/
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 11 / 24

37. Characterizing Semantic Diff
There is a unique ideal semantic diff associated with any two KBs
Theorem
Let A, R be the ideal semantic diff of K and K . Then
A, R is semantic diff compliant with respect to (K, K )
A, R is unique w.r.t. (K, K )
Corollary
For the ideal semantic diff A, R of (K, K ), A ∩ R = ∅
Ideal semantic diff and symmetric difference: (K K) ∪ (K K )
Corollary
For the ideal semantic diff A, R of (K, K ), A, R = ∅, ∅ iff K = K
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 12 / 24

38. Characterizing Semantic Diff
There is a unique ideal semantic diff associated with any two KBs
Theorem
Let A, R be the ideal semantic diff of K and K . Then
A, R is semantic diff compliant with respect to (K, K )
A, R is unique w.r.t. (K, K )
Corollary
For the ideal semantic diff A, R of (K, K ), A ∩ R = ∅
Ideal semantic diff and symmetric difference: (K K) ∪ (K K )
Corollary
For the ideal semantic diff A, R of (K, K ), A, R = ∅, ∅ iff K = K
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 12 / 24

39. Characterizing Semantic Diff
There is a unique ideal semantic diff associated with any two KBs
Theorem
Let A, R be the ideal semantic diff of K and K . Then
A, R is semantic diff compliant with respect to (K, K )
A, R is unique w.r.t. (K, K )
Corollary
For the ideal semantic diff A, R of (K, K ), A ∩ R = ∅
Ideal semantic diff and symmetric difference: (K K) ∪ (K K )
Corollary
For the ideal semantic diff A, R of (K, K ), A, R = ∅, ∅ iff K = K
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 12 / 24

40. Characterizing Semantic Diff
There is a unique ideal semantic diff associated with any two KBs
Theorem
Let A, R be the ideal semantic diff of K and K . Then
A, R is semantic diff compliant with respect to (K, K )
A, R is unique w.r.t. (K, K )
Corollary
For the ideal semantic diff A, R of (K, K ), A ∩ R = ∅
Ideal semantic diff and symmetric difference: (K K) ∪ (K K )
Corollary
For the ideal semantic diff A, R of (K, K ), A, R = ∅, ∅ iff K = K
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 12 / 24

41. Outline
1 Logical Preliminaries
2 Knowledge Base Versioning
Semantic Diff
A General Framework
Compiled Representation
3 Conclusion
Contributions
Future Work
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 13 / 24

42. A Framework for Knowledge Base Versioning
Scenario:
n versions, K1 , . . . , Kn , of a KB that need to be stored
A core knowledge base Kc
For 1 ≤ i, j ≤ n:
Ideal semantic diff of (Ki , Kj ): Dij , Dji
Ideal semantic diff of (Kc , Ki ): Dci , Dic
From Properties
(P2) K = (K ∪ A) R
(P5) K = (K ∪ R) A
The add-set Dij of (Ki , Kj ) is also the remove-set of (Kj , Ki )
The remove-set Dji of (Ki , Kj ) is also the add-set of (Kj , Ki )
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 14 / 24

43. A Framework for Knowledge Base Versioning
Scenario:
n versions, K1 , . . . , Kn , of a KB that need to be stored
A core knowledge base Kc
For 1 ≤ i, j ≤ n:
Ideal semantic diff of (Ki , Kj ): Dij , Dji
Ideal semantic diff of (Kc , Ki ): Dci , Dic
From Properties
(P2) K = (K ∪ A) R
(P5) K = (K ∪ R) A
The add-set Dij of (Ki , Kj ) is also the remove-set of (Kj , Ki )
The remove-set Dji of (Ki , Kj ) is also the add-set of (Kj , Ki )
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 14 / 24

44. A Framework for Knowledge Base Versioning
Scenario:
n versions, K1 , . . . , Kn , of a KB that need to be stored
A core knowledge base Kc
For 1 ≤ i, j ≤ n:
Ideal semantic diff of (Ki , Kj ): Dij , Dji
Ideal semantic diff of (Kc , Ki ): Dci , Dic
From Properties
(P2) K = (K ∪ A) R
(P5) K = (K ∪ R) A
The add-set Dij of (Ki , Kj ) is also the remove-set of (Kj , Ki )
The remove-set Dji of (Ki , Kj ) is also the add-set of (Kj , Ki )
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 14 / 24

45. A Framework for Knowledge Base Versioning
In order to access any version, it is sufficient:
To store Kc , and
To store Dic and Dci for all Ki s.t. 1 ≤ i ≤ n
By Theorem 1, Ki = (Kc ∪ Dci ) Dic for every i s.t. 1 ≤ i ≤ n
Dc6 , D6c
•
Dc5 , D5c • • Dc1 , D1c
Kc
• Dc2 , D2c
Dc4 , D4c •
• Dc3 , D3c
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 15 / 24

46. A Framework for Knowledge Base Versioning
In order to access any version, it is sufficient:
To store Kc , and
To store Dic and Dci for all Ki s.t. 1 ≤ i ≤ n
By Theorem 1, Ki = (Kc ∪ Dci ) Dic for every i s.t. 1 ≤ i ≤ n
Dc6 , D6c
•
Dc5 , D5c • • Dc1 , D1c
Kc
• Dc2 , D2c
Dc4 , D4c •
• Dc3 , D3c
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 15 / 24

47. A Framework for Knowledge Base Versioning
In order to access any version, it is sufficient:
To store Kc , and
To store Dic and Dci for all Ki s.t. 1 ≤ i ≤ n
By Theorem 1, Ki = (Kc ∪ Dci ) Dic for every i s.t. 1 ≤ i ≤ n
Dc6 , D6c
•
Dc5 , D5c • • Dc1 , D1c
Kc
• Dc2 , D2c
Dc4 , D4c •
• Dc3 , D3c
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 15 / 24

48. A Framework for Knowledge Base Versioning
We can generate the ideal semantic diff of Ki and Kj
Proposition
Dij = (Dcj Dci ) ∪ (Dic Djc ) and Dji = (Dci Dcj ) ∪ (Djc Dic )
K1
Dn1 , D1n D1i , Di1
Dc1 , D1c
Kn Kc Dci , Dic Ki
Dcn , Dnc
Dcj , Djc
Dnj , Djn Dij , Dji
Kj
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 16 / 24

49. A Framework for Knowledge Base Versioning
We can generate the ideal semantic diff of Ki and Kj
Proposition
Dij = (Dcj Dci ) ∪ (Dic Djc ) and Dji = (Dci Dcj ) ∪ (Djc Dic )
K1
Dn1 , D1n D1i , Di1
Dc1 , D1c
Kn Kc Dci , Dic Ki
Dcn , Dnc
Dcj , Djc
Dnj , Djn Dij , Dji
Kj
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 16 / 24

50. Outline
1 Logical Preliminaries
2 Knowledge Base Versioning
Semantic Diff
A General Framework
Compiled Representation
3 Conclusion
Contributions
Future Work
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 17 / 24

51. Compiled Representation
Our characterization of Semantic Diff is in the knowledge level
Need for a compiled representation of KBs and the diffs
Computationally, a compiled format is required: F (K)
Given any representation of Ki and Kj , look for an intermediate
representation of the ideal semantic diff I (Dij ), I (Dji )
From Ki together with this intermediate representation of the ideal
semantic diff, generate Kj
From this intermediate representation generate the ideal semantic diff
Dij , Dji
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 18 / 24

52. Compiled Representation
Our characterization of Semantic Diff is in the knowledge level
Need for a compiled representation of KBs and the diffs
Computationally, a compiled format is required: F (K)
Given any representation of Ki and Kj , look for an intermediate
representation of the ideal semantic diff I (Dij ), I (Dji )
From Ki together with this intermediate representation of the ideal
semantic diff, generate Kj
From this intermediate representation generate the ideal semantic diff
Dij , Dji
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 18 / 24

53. Compiled Representation
Our characterization of Semantic Diff is in the knowledge level
Need for a compiled representation of KBs and the diffs
Computationally, a compiled format is required: F (K)
Given any representation of Ki and Kj , look for an intermediate
representation of the ideal semantic diff I (Dij ), I (Dji )
From Ki together with this intermediate representation of the ideal
semantic diff, generate Kj
From this intermediate representation generate the ideal semantic diff
Dij , Dji
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 18 / 24

54. Compiled Representation
Our characterization of Semantic Diff is in the knowledge level
Need for a compiled representation of KBs and the diffs
Computationally, a compiled format is required: F (K)
Given any representation of Ki and Kj , look for an intermediate
representation of the ideal semantic diff I (Dij ), I (Dji ) such that:
From Ki together with this intermediate representation of the ideal
semantic diff, generate Kj
From this intermediate representation generate the ideal semantic diff
Dij , Dji
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 18 / 24

55. Compiled Representation
Our characterization of Semantic Diff is in the knowledge level
Need for a compiled representation of KBs and the diffs
Computationally, a compiled format is required: F (K)
Given any representation of Ki and Kj , look for an intermediate
representation of the ideal semantic diff I (Dij ), I (Dji ) such that:
From Ki together with this intermediate representation of the ideal
semantic diff, generate Kj
From this intermediate representation generate the ideal semantic diff
Dij , Dji
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 18 / 24

56. Compiled Representation
With the intermediate representation
We can also generate one KB from another
Theorem
F (Ki ) = (F (Kj ) I (Dji )) ∪ I (Dij )
= (F (Kj ) ∪ I (Dij )) I (Dji )
We can generate the ideal diff (details in the NMR’10 paper)
We can get I (Dij ) and I (Dji )
Theorem
For 1 ≤ i, j ≤ n, I (Dij ) = (I (Dcj ) I (Dci )) ∪ (I (Dic ) I (Djc ))
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 19 / 24

57. Compiled Representation
With the intermediate representation
We can also generate one KB from another
Theorem
F (Ki ) = (F (Kj ) I (Dji )) ∪ I (Dij )
= (F (Kj ) ∪ I (Dij )) I (Dji )
We can generate the ideal diff (details in the NMR’10 paper)
We can get I (Dij ) and I (Dji )
Theorem
For 1 ≤ i, j ≤ n, I (Dij ) = (I (Dcj ) I (Dci )) ∪ (I (Dic ) I (Djc ))
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 19 / 24

58. Compiled Representation
With the intermediate representation
We can also generate one KB from another
Theorem
F (Ki ) = (F (Kj ) I (Dji )) ∪ I (Dij )
= (F (Kj ) ∪ I (Dij )) I (Dji )
We can generate the ideal diff (details in the NMR’10 paper)
We can get I (Dij ) and I (Dji )
Theorem
For 1 ≤ i, j ≤ n, I (Dij ) = (I (Dcj ) I (Dci )) ∪ (I (Dic ) I (Djc ))
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 19 / 24

59. Outline
1 Logical Preliminaries
2 Knowledge Base Versioning
Semantic Diff
A General Framework
Compiled Representation
3 Conclusion
Contributions
Future Work
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 20 / 24

60. Contributions
Groundwork for a semantic-driven notion of versioning
Intuitive, simple and general
Notion of semantic diff applicable to a large class of KR languages
Our results hold for any KB in a Tarskian logic
Parsimonious representation
Core KB: sufficient to reconstruct any of the versions
Diff between KBs: no direct access to any of the versions
This holds for any syntactic representation (see the NMR’10 paper)
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 21 / 24

61. Contributions
Groundwork for a semantic-driven notion of versioning
Intuitive, simple and general
Notion of semantic diff applicable to a large class of KR languages
Our results hold for any KB in a Tarskian logic
Parsimonious representation
Core KB: sufficient to reconstruct any of the versions
Diff between KBs: no direct access to any of the versions
This holds for any syntactic representation (see the NMR’10 paper)
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 21 / 24

62. Contributions
Groundwork for a semantic-driven notion of versioning
Intuitive, simple and general
Notion of semantic diff applicable to a large class of KR languages
Our results hold for any KB in a Tarskian logic
Parsimonious representation
Core KB: sufficient to reconstruct any of the versions
Diff between KBs: no direct access to any of the versions
This holds for any syntactic representation (see the NMR’10 paper)
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 21 / 24

63. Contributions
Groundwork for a semantic-driven notion of versioning
Intuitive, simple and general
Notion of semantic diff applicable to a large class of KR languages
Our results hold for any KB in a Tarskian logic
Parsimonious representation
Core KB: sufficient to reconstruct any of the versions
Diff between KBs: no direct access to any of the versions
This holds for any syntactic representation (see the NMR’10 paper)
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 21 / 24

64. Contributions
Groundwork for a semantic-driven notion of versioning
Intuitive, simple and general
Notion of semantic diff applicable to a large class of KR languages
Our results hold for any KB in a Tarskian logic
Parsimonious representation
Core KB: sufficient to reconstruct any of the versions
Diff between KBs: no direct access to any of the versions
This holds for any syntactic representation (see the NMR’10 paper)
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 21 / 24

65. Outline
1 Logical Preliminaries
2 Knowledge Base Versioning
Semantic Diff
A General Framework
Compiled Representation
3 Conclusion
Contributions
Future Work
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 22 / 24

66. Ongoing and Future Work
How to choose the core knowledge base Kc
Which normal forms are more appropriate
Experiments with realistic data for evaluation of the approach
Ontology versioning in Description Logics
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 23 / 24

67. Reference
E. Franconi, T. Meyer, I. Varzinczak. Semantic Diff as the Basis for
Knowledge Base Versioning. Workshop on Nonmonotonic Reasoning
(NMR), 2010.
Thank you!
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 24 / 24

68. Reference
E. Franconi, T. Meyer, I. Varzinczak. Semantic Diff as the Basis for
Knowledge Base Versioning. Workshop on Nonmonotonic Reasoning
(NMR), 2010.
Thank you!
Franconi, Meyer, Varzinczak (FUB/Meraka) Semantic Diff for KB Versioning 24 / 24