A platform for distributing
and reasoning with OWL-EL
knowledge bases in a Peer-to-
Peer environment
Alexander De Leon1 , Michel Dumontier1,2,3
1 School of Computer Science
2 Department of Biology
3 Instititute of Biochemistry
Carleton University, 1125 Colonel By Drive, K1S 5B6, Ottawa, Canada
adlbatti@scs.carleton.ca, michel_dumontier@carleton.ca
dumontierlab.com
Friday, October 23, 2009

Introduction
• Reasoning with expressive ontologies is inherently
intractable.
• We have highly optimized domain-independent
reasoner implementations (e.g. Pellet, Fact++).
•These do not scale well for large KBs.
dumontierlab.com
Friday, October 23, 2009

Our Approach
• Extend Pellet for distributed reasoning and integrate
it into a P2P environment.
dumontierlab.com
Friday, October 23, 2009

Distributed Hash Table
Identifier Hash
Peer 1 100
Peer 2 200
http://example.org/Person 34
http://example.org/Bob 167
dumontierlab.com
Friday, October 23, 2009

Distributed KB
• Let ϕ: string ⟶ ℤ be the hash function.
• ≋ means numerically closest.
• Each peer P is responsible for:
1. The subset of base concepts C s.t. ϕ(C) ≋ ϕ(P)
2. The subset of terminological axioms of the form
equivalentTo(C,D) and subClassOf(C,D) s.t. ϕ(C)* ≋
ϕ(P)
3. All axioms about properties
4. Individual assertions of the form C(a) and R(a,b)
s.t. ϕ(a) ≋ ϕ(P)
* GCI are not supported
dumontierlab.com
Friday, October 23, 2009

Distributed KB
dumontierlab.com
Friday, October 23, 2009

Concept Satisfiability
• Want to prove that a concept C is satisfiable/
unsatisfiable w.r.t. a TBox T :
• Unfolding Technique:
• C is satisfiable w.r.t TBox T iff Unfold(C) is
satisfiable.
• Unfolding is a recursive procedure which remove all
non-based symbols from the definition of a concept.
dumontierlab.com
Friday, October 23, 2009

Concept Satisfiability
Example:
Female ≡ ¬Male
Parent ≡ ∃hasChild.Person
Mother ≡ Female ⊓ Parent
Unfold(Mother) = ¬Male ⊓ ∃hasChild.Person
dumontierlab.com
Friday, October 23, 2009

Concept Satisfiability
• Caveat: The stack of unfold calls need to be passed to avoid falling into a cycle. The
condition in line 7 needs to be expanded with: AND {d} ∉ STACK
dumontierlab.com
Friday, October 23, 2009

ABox Consistency
• Concepts satisfiability is reduced to ABox
consistency. Unfolding is not enough if we want to
support nominals.
• Some cases where peers would need to exchange
information:
‣ Resolving the class membership of a remote
individual.
‣ Obtaining the set of edges that are connected to a
remote individual (i.e. for role transitivity).
dumontierlab.com
Friday, October 23, 2009

ABox Consistency
• Our idea to solve this:
• Assert each remote individual i as _REMOTE_(i), as a
marker.
• Apply a tableau rule at each fragment simultaneously
and sync before applying the next.
• Peer exchange information about labels of remote
individuals.
dumontierlab.com
Friday, October 23, 2009

Summary
• Goal is to make OWL reasoning more scalable by
using a P2P approach where new peers can easily be
added as more resources are needed.
• Our approach is to reuse current reasoner
implementations and apply new methodologies for
distributed DL reasoning.
• Concept satisfiability checking was implemented
without support for nominals.
dumontierlab.com
Friday, October 23, 2009