Semantic Diff as the Basis for Knowledge Base Versioning
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The document discusses using semantic diff as the basis for knowledge base versioning. It motivates the need for a versioning system to maintain different knowledge base versions over time, reason across versions, and determine how versions differ in meaning. The authors outline an approach using semantic diff, which highlights differences in logical meaning between knowledge bases, analogous to how file diff tools work for syntax. This would allow determining what statements hold in one version but not another.
![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](https://image.slidesharecdn.com/talk-semanticdiff-100806051818-phpapp02/85/Semantic-Diff-as-the-Basis-for-Knowledge-Base-Versioning-15-320.jpg)
![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](https://image.slidesharecdn.com/talk-semanticdiff-100806051818-phpapp02/85/Semantic-Diff-as-the-Basis-for-Knowledge-Base-Versioning-16-320.jpg)
![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](https://image.slidesharecdn.com/talk-semanticdiff-100806051818-phpapp02/85/Semantic-Diff-as-the-Basis-for-Knowledge-Base-Versioning-17-320.jpg)
![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](https://image.slidesharecdn.com/talk-semanticdiff-100806051818-phpapp02/85/Semantic-Diff-as-the-Basis-for-Knowledge-Base-Versioning-18-320.jpg)
![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](https://image.slidesharecdn.com/talk-semanticdiff-100806051818-phpapp02/85/Semantic-Diff-as-the-Basis-for-Knowledge-Base-Versioning-32-320.jpg)
![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](https://image.slidesharecdn.com/talk-semanticdiff-100806051818-phpapp02/85/Semantic-Diff-as-the-Basis-for-Knowledge-Base-Versioning-33-320.jpg)
![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](https://image.slidesharecdn.com/talk-semanticdiff-100806051818-phpapp02/85/Semantic-Diff-as-the-Basis-for-Knowledge-Base-Versioning-34-320.jpg)
![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](https://image.slidesharecdn.com/talk-semanticdiff-100806051818-phpapp02/85/Semantic-Diff-as-the-Basis-for-Knowledge-Base-Versioning-35-320.jpg)
![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](https://image.slidesharecdn.com/talk-semanticdiff-100806051818-phpapp02/85/Semantic-Diff-as-the-Basis-for-Knowledge-Base-Versioning-36-320.jpg)
Semantic Diff as the Basis for Knowledge Base Versioning
- 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