OWLED2009: A platform for distributing and reasoning with OWL-EL knowledge bases in a Peer-to- Peer environment
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This document proposes a peer-to-peer platform for distributed reasoning with OWL-EL knowledge bases. It describes distributing the knowledge base across peers using a hash table, with each peer responsible for concepts, axioms, and individuals mapped to it. It discusses how concept satisfiability can be checked in a distributed manner by unfolding concepts and checking satisfiability locally. It notes challenges in fully supporting nominals and the need for peers to exchange information.
OWLED2009: A platform for distributing and reasoning with OWL-EL knowledge bases in a Peer-to- Peer environment
- 1. 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
- 2. 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
- 3. Our Approach • Extend Pellet for distributed reasoning and integrate it into a P2P environment. dumontierlab.com Friday, October 23, 2009
- 4. 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
- 5. 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
- 6. Distributed KB dumontierlab.com Friday, October 23, 2009
- 7. 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
- 8. Concept Satisfiability Example: Female ≡ ¬Male Parent ≡ ∃hasChild.Person Mother ≡ Female ⊓ Parent Unfold(Mother) = ¬Male ⊓ ∃hasChild.Person dumontierlab.com Friday, October 23, 2009
- 9. 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
- 10. 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
- 11. 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
- 12. 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