1. Local Closed World Reasoning in the Semantic Web
Yuan Ren, Jeff Z. Pan
University of Aberdeen, UK
NJU Departmental Seminar, June 2012
Local Closed World Reasoning in the Semantic Web

2. Agenda Intelligent Systems and Semantic Technologies (5m)
Open World Assumption v.s. Closed World Assumption (10m)
Description Logics and Ontologies (10m)
Local Closed World Reasoning in the Semantic Web (20m)
Outlook (5m)

3. Approaches to AI
AI: science and engineering of making intelligent machines, especially intelligent computer systems
John McCarthy
“Smart applications”
Large scale raw data
Pattern, relation, knowledge
Complex inductive transformation & manipulation
Magic number?
Explanation?
Complex structure?

4. Approaches to AI “Smart Data”: knowledge makes data smarter
Data reusing: explanation
Data enrichment:
Hidden knowledge
Deductive inference
Structural ontological data
Large scale raw data
Pattern, relation, knowledge
Complex inductive transformation & manipulation
Annotation
“Smart Data”: knowledge makes data smarter

5. The Semantic Web Web contains enormous amount of data
Difficult for human or software to digest
The Semantic Web: improve the description, sharing, discovery and exploitation of knowledge and data
Inter-lined datasets
Structured data models
Standard languages
Knowledge representation & reasoning
Web data
The Semantic Web
Data exchange Languages

6. Domain(supervisedBy) isA post-graduate
The Semantic Web
Identify data objects with URIs
Connect data objects with relations
Describe connections with knowledge bases
foaf#j_z_pan
Lubm#supervisedBy
LUBM:
Domain(supervisedBy) isA post-graduate
dblp#yuan_ren

7. Domain(supervisedBy) isA post-graduate
The Semantic Web
Query with the SPAQL language:
Who is supervised by Jeff?
foaf#j_z_pan
LUBM#supervisedBy
LUBM:
Domain(supervisedBy) isA post-graduate
dblp#yuan_ren
How are the knowledge bases interpreted?

8. Agenda Intelligent Systems and Semantic Technologies (5m)
Open World Assumption v.s. Closed World Assumption (10m)
Description Logics and Ontologies (10m)
Local Closed World Reasoning in the Semantic Web (20m)
Outlook (5m)

9. Possible Interpretations of Knowledge Base
A knowledge base can have multiple interpretations.
curryChicken: not VegetarianFood
pepperSalad: not SpicyFood
curryChicken: not VegetarianFood
pepperSalad: SpicyFood
curryChicken: SpicyFood
pepperSalad: VegetarianFood
curryChicken: VegetarianFood
pepperSalad: not SpicyFood
curryChicken: VegetarianFood
pepperSalad: SpicyFood

10. The Two World Assumptions
Open world assumption
Closed world assumption
Given an knowledge base KB, a statement st can be true, or false, or unknown
true: if st can always be derived by KB
false: if st can never be derived by KB
unknown: if st can be derived by some interpretations of KB
Assuming KBs only cover key aspects of the world
Compatible with the open nature of the web
Given a knowledge base KB, a statement st can be either true or false.
true: if st can always be derived by KB
false: otherwise
Assuming one has complete knowledge about the part of the world

11. Example: OWA v.s. CWA Menu Under OWA Under CWA
Is Pepper Salad SpicyFood?
UNKNOWN
Under CWA
No, because
"SpicyFood={Curry Chicken, Spicy Grilled Shrimp}"
Menu
Food
Note
Curry Chicken
Spicy
Salmon Fillet
Spicy Grilled Shrimp
Pepper Salad

12. Example: OWA v.s. CWA Who leads a Tenure that leads a non-Tenure?
CWA: no one
OWA: Full Prof.
Tenure
Full Prof.
lead
lead
Associate Prof.
lead
not
Assistant Prof.
lead
Post-Doc
Full Prof. is the answer in ALL possible interpretations!

13. Example: Explicit vs. Implicit CWA
Is Spicy Grilled Shrimp the only SpicyFood?
SpicyFood={Spicy Grilled Shrimp}?
No, because background knowledge:
"MinorSpicyFood" is SpicyFood
CWA should support necessary inference
Menu
Food
Note
Curry Chicken
Minor Spicy
Salmon Fillet
Spicy Grilled Shrimp
Spicy
Pepper Salad
Vege

14. Example: Open vs. Closed World Assumptions
Can we close concept Vegetarian?
Vegetarian={Yuting}?
Maybe not…
Whether close a concept or not depends on applications
Guests
Name
Vegetarian
Jeff No
Yuting
Yes
Jek
Yuan

15. Local Closed World Assumption
In general, it uses an OWA setting
Assuming knowledge bases only cover key aspects of the world
For certain parts, it allows CWA
Assuming one has complete knowledge about the part of the world
Implicit CWA should be allowed

16. Agenda Intelligent Systems and Semantic Technologies (5m)
Open World Assumption v.s. Closed World Assumption (10m)
Description Logics and Ontologies (10m)
Local Closed World Reasoning in the Semantic Web (20m)
Outlook (5m)

17. What is an Ontology A model of (some aspect of) the world
Introduces vocabulary relevant to domain, e.g.:
Anatomy
Koala
Specifies meaning (semantics) of terms
Koala eat only some part of Eucalypt
Eucalypt is Plant
only
eat
some
Plant
Eucalypt
partof

18. Components of Ontology
Modelling elements:
concepts (classes)
roles (properties/relations)
individuals (objects)
A TBox (Terminonagy Box) is a set of “schema” axioms (sentences), e.g.:
i.e., a background theory for the vocabulary
An ABox (Assertion Box) is a set of “data” axioms (ground facts), e.g.:
gummy: Koala

19. Ontology Reasoning
Infer implicit knowledge from explicit knowledge

20. Ontology Landscape
Related DL-based standards (OWL, OWL2) are established
Many DL reasoners available
FaCT++, Pellet, HermiT, RacerPro, TrOWL
The user community is growing fast
Swoogle searches over 10,000 online ontologies
Larger and larger ontologies
SNOMED has 379,691 concepts
More and more references to ontologies:
731 papers with “SNOMED” in title, 12,400 papers with “SNOMED” in text. (Google Scholar)
more and more complicated ontologies
FMA (Foundational Model of Anatomy, OWL DL) has 41,647 concepts and 123,564 axioms,

21. Agenda Intelligent Systems and Semantic Technologies (5m)
Open World Assumption v.s. Closed World Assumption (10m)
Description Logics and Ontologies (10m)
Local Closed World Reasoning in the Semantic Web (20m)
Outlook (5m)

22. SPARQL SPARQL 1.o supports “!bound” SPARQL 1.1 supports “NOT Exist”
A person who is not known as a post-graduate
Realised by testing for the absence of a pattern in a graph

23. Integrity Constraints
Widely used in RDBs to check data integrity
Assuming the RDB contains COMPLETE information
Based on model checking
IC in DL-based ontologies
ICs are syntactically same as TBox axioms
Checking whether facts derivable with KB+ICs can be derived with KB only.
Can be realised by SPARQL query answering. KB ?
madcow is either a Herbivore or a Carnivore
Q1: ?x <- ?x:Animal
Q2: ?x <- ?x:Herbivore
Q3: ?x <- ?x:Carnivore

24. Why Is SPARQL Not Enough?
Queries do not change the semantics of the ontology
i.e. does not really CLOSE anything
SPARQL: Who is not known as a post-graduate?
Jeff
CWA: Who is not a post-graduate?
No one
It’s unknown whether Jeff is a post-graduate
foaf#j_z_pan
LUBM#supervisedBy
LUBM:
Domain(supervisedBy) isA post-graduate
dblp#yuan_ren

25. DBox [Seylan et al., 2009] Accommodate a DB component in an ontology
DBox is syntactically same as an ABox
Consists of assertion axioms
DBox fixes the extensions of DBox predicates
Faithful encoding of database
usually with unique name assumption (UNA)
Does not allow implicit CWA

26. Grounded Circumscription
Minimising the extensions of closed predicates.
Using minimal models w.r.t. the closed predicates
A minimal model interprets a closed predicates with only named individuals in the knowledge base
Knowledge base K
Closed predicates M = {Carnivore, Herbivore}
Minimal Models
Why can we close concepts without complete knowledge?
We still don’t know the exact type of madcow

27. Epistemic Operator
Used in e.g. MKNF (Minimal Knowledge and Negation as Failure) [Motik and Rosati, 2010]
The K operator: things we know
K Koala: the concept of all known Koala in the knowledge base
The not operator: Negation as Failure
not A is equivalent to (K A)
madcow: not(Carnivore) meaning madcow is not evidently (not
known to be) a Carnivore
MKNF increases the complexity of reasoning

28. Negation as failure Box (NBox) [Ren et. al, 2010]
Closing a set of predicates with their inferable instances
To allow inference w.r.t. the closed predicates
To provide restricted forms of the K and not operators without increasing complexity drastically

29. Reasoning with NBox
Using classical reasoning to retrieve instance of predicates
E.g., Pepper is VegeFood
Using nominals to close predicates
E.g., VegeFood = {Pepper Salad}
Adding axioms back to ontology for incremental reasoning
Yuting orders Pepper!
Guest
some
some
Vegetarian
order
Food
Jeff
Yuan
SpicyFood
VegeFood
Jek
Minor
Spicy
Food
Pepper
Yuting
Shrimp
Salmon
Chicken
order

30. Agenda Intelligent Systems and Semantic Technologies (5m)
Open World Assumption v.s. Closed World Assumption (5m)
Description Logics and Ontologies (10m)
Local Closed World Reasoning in the Semantic Web (20m)
Outlook (5m)

31. LCWR and Other Themes in Ontology Reasoning
Reasoning optimisation
Many LCWR solutions increase the complexity of ontology reasoning
E.g. NBox requires nominal support
Developing optimised algorithms for LCWR, e.g. approximations
Non-standard reasoning services
Incremental reasoning (with increasing ontology)
E.g. NBox adds definitions of closed predicates
Justification (that explains the entailment)
The closure of certain part of the knowledge base should be regarded as part of the explanation
Combined reasoning with other formalisms
Ontology + rules
Ontology + RDB + datalog

32. LCWR and Other Themes in Knowledge Representation
A unified framework for different LCWR solutions
No actual semantic closure:
Integrity constraints <-> SPARQL query level CWA
Actual semantic closure:
DBox <-> Grounded Circumscription <-> Epistemic Operator <-> NBox
Relation with other non-monotonic approaches
LCWR and abduction
LCWR and induction

33. LCWR and Other AI Approaches
The separation of complete knowledge and open knowledge leads to interesting insights
Generalisation v.s. overfitting
Closing does not mean overfitting
Closing a concept does not preventing adding new instances to this concept
Static knowledge v.s. dynamic knowledge
Closed knowledge can also be dynamic!
Explicit knowledge v.s. implicit knowledge
Explicit closure -> implicit closure
Reasoning is needed!

34. Question?
Thank you!