d. calvanese, e. kharlamov, w. nutt, and d. zheleznyakov krdb research centre free university of...
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D. Calvanese, E. Kharlamov,W. Nutt, and D. Zheleznyakov
KRDB Research CentreFree University of Bozen-Bolzano
FBK, January 2011
Understanding Evolution of Semantically Annotated Data
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World Wide Web and Evolution Web content is ubiquitously dynamic (Textual) Web content has two flavors:
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Plain (HTML) data~ semantics understandable by people
Semantically annotated data (knowledge) ~ semantics understandable by machines
We focus on the second kind of data which is believed to be the Web of tomorrow [TBL99]
Our goal:To understand how to incorporate the new knowledge into the old one~ to study evolution of knowledge
date namelang.
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Semantic Annotations
Ontologies are a prime mechanism to bring semantics to the Web, they provideannotations (e.g., date, name)meta annotations (e.g., class, property)classifications of annotations (e.g., subclass-of)properties of annotations (e.g., domain, range)…
Technologies behind ontologiesResource description Framework (RDF)Ontology Web Language (OWL)Rule Languages (e.g. OWL 2 RL)
We focus on OWL 2, its one profile: OWL 2 QLwhich is based on a Description Logics family: DL-Lite
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Description Logics (DLs)
Cleric
Priest
Husband
Concepts are classes of objects
Roles are relations between objects
ABox isfor instances of concepts and roles
TBox is for structure of the knowledge
Carl
JohnAdam
Bob
DL Ontology (Knowledge Base):
TBox:
ABox:
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Example of a Knowledge Base
Single Husband
Priest
Wife
hasHb
Concepts:
Roles:
TBox:
ABox:
Wife, Husband, Single, Woman, Priest
HasHb
Wife Woman ⊑Wife ≡ HasHb∃Husband ≡ HasHb∃ –
Husband ¬ Single⊑
Priest Single⊑Husband ¬ Priest⊑
Wife(Mary), hasHb(Mary,John)Priest(Adam), Priest(Bob)
Woman
Mary
John
Adam Bob
(Mary, John)
1..n
1..n
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DL-Lite Language
TBox assertions: Formulas of the form:inclusion: disjointness:functionality:
ABox assertions: instanciations: concept:role:
No disjunction and no negation on the left of inclusions
DL-Lite ~ a bit extended Horn Logic with existential variables in head
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A R, A R⊑ ∃ ⊑ ∃ − , A B, ...⊑
(func R), ...A ¬ R, A ¬B, ...⊑ ∃ ⊑
B(a), R(a), ...∃
R(a,b), ...
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What if There Is New Information?
Single Husband
Priest
Wife
hasHb
New Inormation N:
Single(John)
How should the KB evolve?
Woman
Mary
John
Adam Bob
(Mary, John)
1..n
1..n
John
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Is Evolution Solved for DLs?
Traditional inference tasks for DL KBs are static: concept satisfiabilityKB satisfiabilityconcept and role hierarchiesquery answering
Research on ontology evolution is quite youngABoxes in expressive DLs:
Liu, Lutz, Milicic, and Wolter ABoxes in DL-Lite:
De Giacomo, Lenzerini, Poggi, RosatiTBoxes in DLs and DL-Lite: Qi, Du…
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[Qi,Du’09]
[Giacomo&al’06]
[Liu&al‘06]
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Outline
I. The problem of evolution
II. Formalizing evolution
III. Attempt to apply classical approachesa) Model-Based approachesb) Formula-Based approaches
IV. Our proposala) Bold Semanticsb) Careful Semantics
V. Conclusion
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Conceptual Requirements
Single Husband
John
RentSub
Wife
Mary
hasHb
1..n
Cleric
Minister
Carl
PriestAdam Bob
Single Husband
John
Cleric
Minister
Carl
RentSub
PriestAdam Bob
Wife
Mary
hasHb
1..n
Old Knowledge: New Knowledge: Evolved Knowledge:
DL-Lite KB Evolution Operator DL-Lite KB
Evolved knowledge should
be consistent – no logical contradictions
be coherent – no empty concepts
entail New Knowledge
minimally different from the old KB – principle of minimal change
Priest(Bob)∧¬Priest(Bob)
Priest Single⊑Priest ¬Single⊑
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Technical Requirements
Closure under evolution:Evolution result should be expressible in DL-Lite
Efficiency:Evolution result should be computable in PTime
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Can Previous Work Help?
Knowledge evolution was studied by the AI community
Primarily for Propositional Logic (PL)
Two main types of approaches to evolution in PL:1. Model-Based Approaches (MBAs)
operate with set of models2. Formula-Based Approaches (FBAs)
operate with set of formulas
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Are these approaches applicable to DL-Lite evolution?
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Outline
I. The problem of evolution
II. Formalizing evolution
III. Attempt to apply classical approachesa) Model-Based approachesb) Formula-Based approaches
IV. Our proposala) Bold Semanticsb) Careful Semantics
V. Conclusion
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Model-Based Approaches
Single Husband
John
RentSub
Wife
Mary
hasHb
1..n
Old Knowledge K:
Cleric
Minister
Carl
PriestAdam Bob
New Knowledge N:
Mod(K)
Mod(N)
Take some models of Mod(N) (since new knowledge should be preserved)
Keep those that are “closest” to Mod(K)
Two flavours of Model-Based Approaches: •Local•Global
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Local Model-Based Approaches
Single Husband
John
RentSub
Wife
Mary
hasHb
1..n
Old Knowledge K:
Cleric
Minister
Carl
PriestAdam Bob
New Knowledge N:
Mod(K)
Mod(N)
The result of evolution:
Minimaldistance
Minimaldistance
Minimaldistance
Minimaldistance
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Local Model-Based Approaches
Single Husband
John
RentSub
Wife
Mary
hasHb
1..n
Mod(K)
Mod(K’)
The result of evolution:Single Husba
nd
John
Cleric
MinisterCarl
RentSub
PriestAdam Bob
WifeMary
hasHb
1..n
Is there a representation?
Old Knowledge K:
Evolved KB K’:
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Global Model-Based ApproachesOld Knowledge K:
Cleric
Minister
Carl
PriestAdam Bob
New Knowledge N:
Mod(K)
Mod(N)
The result of evolution:
Single Husband
John
RentSub
Wife
Mary
hasHb
1..n
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Global Model-Based Approaches
Single Husband
John
RentSub
Wife
Mary
hasHb
1..n
Mod(K)
Mod(K’)
The result of evolution:Single Husba
nd
John
Cleric
MinisterCarl
RentSub
PriestAdam Bob
WifeMary
hasHb
1..n
Is there a representation?
Old Knowledge K:
Evolved KB K’:
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How to Measure Distance btw Models?
All MBAs are based ondistances between interpretations
Distance in Propositional Logic:as a setas a number
Example:
I = {p, q, r}
J = {p, s}
dist⊖(I,J) = I ⊖ J
dist|⊖| (I,J) = |I ⊖ J|
dist⊖(I,J) = {q, r, s}
dist|⊖| (I,J) = 3
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Dimensions of MBAsApproach
What is distance
Distance is built upon
set: ⊖ number: |⊖|
global: G
local: L
symbols: S
atoms: A
Propositional Logic: two dimensions. Description Logics: one more dimension!
Distance is built upon• symbols• atoms
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Dimensions of MBAsApproach
What is distance
Distance is built upon
set: ⊖ number: |⊖|
global: G
local: L
symbols: S
atoms: A
Example:
I = {Priest(Bob), Wife(Mary)}, J = {Priest(Adam), Wife(Mary)}
• Atoms: dist⊖(I,J) = {Priest(Bob), Priest(Adam)}
• Symbols: dist⊖(I,J) = {Priest}
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Dimensions of MBAsApproach
What is distance
Distance is built upon
set: ⊖ number: |⊖|
global: G
local: L
symbols: S
atoms: A
Two possibilities for each of three dimensions
⇒ eight possible semantics
Theorem (Inexpressibility):
For all of eight semantics the result of the evolutioncannot be expressed in DL-Lite
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What May Go Wrong?Single Husband
Priest
Wife
hasHb
1..n
MBAs give more cases:3. Mary is married to either Adam or Bob (but not to both)
John
Adam Bob
a guyNew Knowledge: Single(John)
What happened with Mary?
Our intuition: 2 cases
1. Mary is single
2. Mary is married to another guy
Drawback I: Mary married to one of the priest is counterintuitive
K’ Priest(Bob)⊭K’ Priest(Adam)⊭K’ Priest(Adam) ⊨ ∨ Priest(Bob)
Drawback II: Inexpressible in DL-Lite
Woman
Mary
1..n
(Mary, John )?
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Observation: In [Giacomo&al’06]
• evolution of ABoxes in DL-Lite • fixed TBoxes• under global semantics on atoms • algorithm to compute semantics is provided
⇒ Their results are wrong
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What Else May Go Wrong?Single Husband
Priest
Wife
hasHb
1..n
MBAs give a strange models M:M = { Bishop(Carl), Priest(Carl), ¬Single(Carl), … }Thus, KB’ Priest Single⊭ ⊑
John
Adam Bob
New Knowledge: Bishop Priest⊑
How does it affect the old KB?
Our intuition:
Just add the new assertion to the old KB
Woman
Mary
1..n
(Mary, John )
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Bishop
Carl
Drawback 1: it is counterintuitiveDrawback 2: inexpressible in DL-Lite
Observation: In [Qi,Du’09]
• evolution of TBoxes • in KBs with empty ABoxes • under global semantics on atoms
⇒ Their operator does not work
for general KBs in DL-Lite
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MBAs Do Not Work
… becausethey ignore structure of the KBthe allow too many casesresult of evolution cannot be expressed in DL-Lite
MBAs cannot be adopted for KB evolution in DL-Lite
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Outline
I. The problem of evolution
II. Formalizing evolution
III. Attempt to apply classical approachesa) Model-Based approachesb) Formula-Based approaches
IV. Our proposala) Bold Semanticsb) Careful Semantics
V. Conclusion
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Formula-Based Approaches
Idea:To take union K ∪ N
What if K ∪ N is unsatisfiable?
Cleric
Minister
Carl
PriestAdam Bob
Old Knowledge K:
New Knowledge N:
Cleric
Minister
Carl
PriestAdam Bob
Single Husband
John
Cleric
RentSub
Wife
Mary
hasHb
1..n
Unsatisfiable
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Formula-Based Approaches
Approach:
Choose a subset Kmax ⊆ K Consistent with N Coherent with N Maximal wrt set inclusion
Result:
Kmax ∪ N
Problem:
In general Kmax is not unique
Cleric
Minister
Carl
PriestAdam Bob
Old Knowledge K:
New Knowledge N:
Cleric
Minister
Carl
PriestAdam Bob
Single Husband
John
Cleric
RentSub
Wife
Mary
hasHb
1..n
Single
Cleric
RentSub
Husband
John
Wife
Mary
hasHb
1..n
Satisfiable
Satisfiable
Unsatisfiable
Cleric
RentSub
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What To Do?
What to do with several Kmax?
Classical approaches:When In Doubt Throw It Out:
take intersection of Kmax
Cross-Product: take disjunction of Kmax
• Loses too much data• coNP-complete
Not expressible in DL-Lite
TempStaff Teaching
PhD
K ∪ NTempStaff Teaching
PhD
(Kmax2 ∩ Kmax1) ∪ N
TempStaf Teaching
PhD
TempStaf Teaching
PhD
Kmax1 ∪ N Kmax2 ∪ NOR
∨
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Outline
I. The problem of evolution
II. Formalizing evolution
III. Attempt to apply classical approachesa) Model-Based approachesb) Formula-Based approaches
IV. Our proposala) Bold Semanticsb) Careful Semantics
V. Conclusion
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Our Proposal – Bold Semantics
Take an arbitrary Kmax
Evolution(K, N) = Kmax ∪ N The result is non-deterministic
TempStaff Teaching
PhD
K ∪ NTempStaff Teaching
PhD
Kmax ∪ N
Can be computed in PTime
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How To Avoid Non-Determinism?
Preferences “reduce” non-determinism:Order over assertionsMinimality wrt cardinalityetc.
Evolution in specific cases may be deterministic:ABox evolution
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ABox Evolution Is Deterministic
1. Add assertions from N
2. Find conflicting assertions
3. Resolve conflicts
Drawback: Mary cannot get divorced
Single Husband
Priest
Wife
John
Mary
Adam Bob
a guyJohn
Assumptions:
• N is a set of ABox assertions
• Evolution does not change TBox
Theorem: For a DL-Lite KB the result of ABox evolution is unique and computable in PTime.
New knowledge N: Single(John)
Woman
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hasHb
1..n
1..n
(Mary, John )?
Recall:
Our intuition: 2 cases1. Mary is single 2. Mary is married to another guy
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Outline
I. The problem of evolution
II. Formalizing evolution
III. Attempt to apply classical approachesa) Model-Based approachesb) Formula-Based approaches
IV. Our proposala) Bold Semanticsb) Careful Semantics
V. Conclusion
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Careful Semantics for ABox Evolution
Formula φ is unexpected for Kmax and N
if Kmax ∪ N ⊨ φ and Kmax ⊭ φ nor N ⊭ φ
In our example an unexpected formula is:φ = ∃a guy.hasHb(Mary, a guy)∧(a guy≠John)
Role-constraining formula (RCF): φ = x.R(a,x)∃ ∧(x≠c1)∧...∧(x≠cn)
Preference: We want Kmax to be careful:no unexpected RCF are allowedKmax ∪ N ⊨ φ then Kmax ⊨ φ or N ⊨ φ
Theorem: For every DL-Lite KB K and new data N, careful Kmax exists, is unique, and is computable in PTime
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Careful Semantics for ABox Evolution
New knowledge N: Single(John)
1. Run bold semantics algorithm for ABox evolution
2. Find unexpected formulas φ
3. Delete assertions entailing φ
Single Husband
Wife
John
Mary
a guyJohn
Unexpected formulas:φ = ∃a guy.hasHb(Mary, a guy)∧(a guy≠John)
Priest
Adam Bob
Woman
Mary
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hasHb
1..n
1..n
(Mary, John )? Recall:
Our intuition: 2 cases1. Mary is single 2. Mary is married to another guy
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Outline
I. The problem of evolution
II. Formalizing evolution
III. Attempt to apply classical approachesa) Model-Based approachesb) Formula-Based approaches
IV. Our proposala) Bold Semanticsb) Careful Semantics
V. Conclusion
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Conclusion We reviewed Model-Based Approaches to evolution
Found MBAs are inapplicable for DL-Lite evolution We reviewed classical Formula-Based Approaches
Showed hardness or inapplicability of them We proposed two novel Formula-Based Approaches
- Bold Semantics- Careful Semantics
We developed polynomial time algorithms for new semantics
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Thank you
ONTORULE ProjectONTOlogies Meets Business RULesFP 7 grant, ICT-231875http://ontorule-project.eu/
Webdam Project Foundations of Web Data Management ERC FP7 grant, agreement n. 226513http://webdam.inria.fr/
ACSI ProjectArtifact-Centric Service InteroperationFP 7 grant, agreement n. 257593http://www.acsi-project.eu/
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[Giacomo&al’06] - G. De Giacomo, M. Lenzerini, A. Poggi, R. Rosati: On the Update of Description Logic Ontologies at the Instance Level. AAAI 2006
[Qi,Du’09] - G. Qi, J. Du: Model-based Revision Operators for Terminologies in Description Logics. IJCAI 2009