updating tboxes in dl-lite
DESCRIPTION
Updating TBoxes in DL-Lite. D. Zheleznyakov. Outline. I. Introduction II. Requirements A nd P rinciples of TBox U pdates III. Review of Model-Based Semantics IV. Review of Formula-Based Semantics V. Bold semantics VI. Conclusion. Description Logics (DLs). - PowerPoint PPT PresentationTRANSCRIPT
Updating TBoxes in DL-Lite
D. Zheleznyakov
Outline
I. Introduction
II. Requirements And Principles ofTBox Updates
III. Review of Model-Based Semantics
IV. Review of Formula-Based Semantics
V. Bold semantics
VI. Conclusion
Description Logics (DLs)
Formalism to represent structered knowledge
Traditinal inference tasks for static DL KBs:– concept satisfiability– concept, role hierarchies
More recently – query answering
Web services are getting more important
Web Services (?)
There are many things that might be called Web Services
We use the following meaning:software system designed to support interoperable machine-to-machine interaction over a network
DLs for Web Services
Services access data through ontologies
Services can be specified using ontologies There are needs:• to enable services do data modification
ABox changes
• to modify web services
TBox changes
Ontology Changes
There are several types of ontology changes:– Revision– Update– Smth.– and such
Updating DL-Lite Ontologies
We study updates for DL-Lite KBs:it is the most tractable family of OWL 2
ABox updates:– Prelim./limited studied in [De Giacomo&al:2006] (?)– We revised and extended it [Calvanese&al:2010]
TBox updates:– Only TBox revision studied in [Qi,Du:2009]
– Topic of this talk is TBox updates
Ontologies
PermStaff
Manager
AreaManager TopManager
Concepts: PermStaffManagerAreaManagerTopManager
TBox: Manager ⊑ PermStaffAreaManager ⊑ Manager
ABox: ∅
We considered TBox updates only for KBs with empty ABoxes
Updating Ontologies
PermStaff
Manager
AreaManager TopManager
O:
U:
✓✓ ✓ ✓
Mod(O):
Outline
I. Introduction
II. Requirements And Principles ofTBox Updates
III. Review of Model-Based Semantics
IV. Review of Formula-Based Semantics
V. Bold semantics
VI. Conclusion
Tractable Closure under Updates
We want an update operator such that: Results are expressible in DL-Lite:
we require updated KBs to be expressible in DL-Lite
Results computation is tractable:we require PTIME complexity
Principles of TBox Updates
PermStaff
Manager
AreaManager TopManager
⊨ AreaManager PermStaff⊑TBox:
U: AreaManager ¬ PermStaff⊑
IF new TBox ⊨
AreaManager PermStaff⊑AreaManager ¬ PermStaff⊑
THEN AreaManagerM=∅ ∀M – model of the new TBox
Satisfiability Preservation:IF AM≠∅ before update,THEN AM≠∅ after update
(A is a atomic concept or role)
⊨
Principles of TBox Updates
PermStaff
Manager
AreaManager TopManager
TBox: Manager PermSatff⊑AreaManager Manager⊑
Assume it is forbidden to changesome parts of TBox. There is a protected fragmentTpr ⊆ TBox E.g., Tpr = {Manager PermSatff⊑ }.
U: AreaManager ¬ PermStaff⊑
Protection:We accept update iffTpr and U togetherare fully satisfiable
Principles of TBox Updates
Satisfiability Preservation:IF AM≠ ∅ before update,THEN AM≠ ∅ after update
Protection:We accept update iff protected part and U together are fully satisfiable
Moreover, we reject any update that enforces us to drop protected part
Outline
I. Introduction
II. Requirements And Principles ofTBox Updates
III. Review of Model-Based Semantics
IV. Review of Formula-Based Semantics
V. Bold semantics
VI. Conclusion
Model-Based Semantics (MBS)PermStaff
Manager
AreaManager TopManager
O:Mod(O):
Mod(U):U:
Minimaldistance
✓ ✓ ✓ ✓
Model-Based Semantics (MBS)PermStaff
Manager
AreaManager TopManager
Employee
Manager
AreaManager TopManager
Project?
O:
O’:
✓✓ ✓ ✓
Mod(O):
Mod(O’):
Winslett's Semantics
What does minimal distance mean?This depends on semantics.
Winslett’s semantics:• Well known
• There are works on ABox update under Winslett’s semantics
• Representative of MBS
Winslett's SemanticsI:
J: K:
distance(I, J) distance(I, K)
When distance(I, J) < distance(I, K) ?AI={ John, Frank }BI={ Mary }
AJ={ John }BJ={ Mary }
AK={ John }BK=∅
Winslett's SemanticsI:
J: K:
distance(I, J) distance(I, K)
When distance(I, J) < distance(I, K) ?AI={ John, Frank }BI={ Mary }
AJ={ John }BJ={ Mary }
AK={ John }BK=∅
diff(I, J) = { {Frank}, ∅ }
Winslett's SemanticsI:
J: K:
distance(I, J) distance(I, K)
When distance(I, J) < distance(I, K) ?AI={ John, Frank }BI={ Mary }
AJ={ John }BJ={ Mary }
AK={ John }BK=∅
diff(I, J) = { {Frank}, ∅ }diff(I, K) = { {Frank}, {Mary} }
diff(I, J) ⊂ diff(I, K)
So, distance(I, J) < distance(I, K) iff diff(I, J) ⊂ diff(I, K)
Winslett's Semantics. Example
PermStaff
Manager
AreaManager TopManager
U: TopManager Manager⊑
What should the updated result be?
The expectation: like in the picture
Is it so under Winslett’s semantics?
Winslett's Semantics. Example
PermStaff
Manager
AreaManager TopManager
U: TopManager Manager⊑
John
Frank
Frank
Winslett’s semantics:• new TBox ⊨ U• Mimimal change in models
John
What is a new TBox here?
new TBox: ⊨ TopManager Manager⊑ ⊨ Manager PermStuff⊑ ⊨ AreaManager Manager⊑ ⊨ AreaManager PermStaff⊑
Anything else?
✓✗??✓?✓
Winslett's Semantics. Example
PermStaff
Manager
AreaManager TopManager
This TBox has irrelevant modelsthat cannot be obtainedfrom any model of the old TBox.
We cannot add any otherDL-Lite assertion into the new TBox,otherwise, we cut offsome relevant models
We should add something into the new TBoxto cut off them
Winslett's Semantics
Result of update under Winslett’s semantics is inexpressible in DL-Lite.
We have to drop important assertions(Manager PermStuff)⊑
Every MBS has such a problem
Consider Formula-Based semantics
Outline
I. Introduction
II. Requirements And Principles ofTBox Updates
III. Review of Model-Based Semantics
IV. Review of Formula-Based Semantics
V. Bold semantics
VI. Conclusion
Formula-Based Semantics (FBS)
PermStaff
Manager
AreaManager TopManager
O:
U:
PermStaff
Manager
AreaManager TopManager
Manager
AreaManager TopManager
O1:
O2:
O3:
Satisfiable
✓
Unsatisfiable
Satisfiable
✗
✓
FBS: closeness is measuredbtw set of formulas
How?
We take such a subset Omax ⊆ O, which is maximal by:• cardinality, or• set inclusion, or• some preferences
Omax is not unique!There are: O1
max, O2max, …
The result is: Omax ∪ U
What to do with all of them?Depends on an approach
WIDTIO Approach. Example
We take only those formulas that appear in every Omax:
The result is: U ∪ ∩ Ojmax
PermStaff
Manager
AreaManager TopManager
AreaManager ¬ PermStaff⊑U:TBox: AreaManager PermStaff⊑
Manager PermStaff⊑ ⊈ O1max
AreaManager Manager⊑ ⊈ O2max
j
Cross-Product Approach. Example
OR
The output is a disjunction of KBs,one KB for each Omax:
The result is: U ∪ {∨ Ojmax}
j
AreaManager ¬ PermStaff⊑U:TBox: AreaManager PermStaff⊑
PermStaff
Manager
AreaManager TopManager
Manager PermStaff⊑ ⊈ O1max
AreaManager Manager⊑ ⊈ O2max
Cross-Product Approach. Example
OR
The output is a disjunction of KBs,one KB for each Omax:
The result is: U ∪ {∨ Ojmax}
PermStaff
Manager
AreaManager TopManager
j
AreaManager ¬ PermStaff⊑U:TBox: AreaManager PermStaff⊑
PermStaff
Manager
AreaManager TopManager
Manager PermStaff⊑ ⊈ O1max
AreaManager Manager⊑ ⊈ O2max
Formula-Based Semantics
WIDTIO approach:– Loses too much information
Cross-product approach:– “Keeps” too much information– Inexpressible in DL-Lite
Outline
I. Introduction
II. Requirements And Principles ofTBox Updates
III. Review of Model-Based Semantics
IV. Review of Formula-Based Semantics
V. Bold semantics
VI. Conclusion
Bold Semantics
Which Omax to take?• A maximal one by cardinality.
NP-Hard• A maximal one by set inclusion.
Polynomial• A maximal one by some preferences
Bold approach:– Takes on board only one Omax
Bold Semantics. Example
PermStaff
Manager
AreaManager TopManager
• Start with empty TBox
• Add assertions from U• Add assertions from TBox
one by one,if no unsatisfiability appears
AreaManager ¬ PermStaff⊑U:TBox: AreaManager Manager⊑
The result is not unique
✓✓?
Manager PermStaff⊑ ✗?AreaManager PermStaff⊑ ?✗
Bold Semantics. Example
PermStaff
Manager
AreaManager TopManager
• Start with empty TBox
• Add assertions from U• Add assertions from TBox
one by one,if no unsatisfiability appears
AreaManager ¬ PermStaff⊑U:TBox: AreaManager Manager⊑
✓✓
Manager PermStaff⊑ ✗AreaManager PermStaff⊑ ✗
AreaManager ¬ PermStaff⊑U:TBox: AreaManager Manager⊑
✓✗
Manager PermStaff⊑ ✓AreaManager PermStaff⊑ ✗
??
?
The result is not unique
Checking Full Satisfiability
Outline
I. Introduction
II. Requirements And Principles ofTBox Updates
III. Review of Model-Based Semantics
IV. Review of Formula-Based Semantics
V. Bold semantics
VI. Conclusion
Conclusion
We proposed two principles for DL KB updates
Model-based approaches:not good for TBox updates
Formula-based approaches:WIDTIO and CP are not applicableto DL-Lite KBs
Conclusion
We proposed new semantics:Bold Semantics
We proposed polynomial time algorithmto compute update under Bold semantics
Thank you!
References
[De Giacomo&al:2006] [Calvanese&al:2010] [Qi,Du:2009]