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.

Technology Education

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

Objects can be said to be structured when their representation also contains their parts. While OWL in general can describe structured objects, description graphs are a recent, decidable extension to OWL which support the description of classes of structured objects whose parts are related in complex ways. Classes of chemical entities such as molecules, ions and groups (parts of molecules) are often characterized by the way in which the constituent atoms of their instances are connected via chemical bonds. For chemoinformatics tools and applications, this internal structure is represented using chemical graphs. We here present a chemical knowledge base based on the standard chemical graph model using description graphs, OWL and rules. We include in our ontology chemical classes, groups, and molecules, together with their structures encoded as description graphs. We show how role-safe rules can be used to determine parthood between groups and molecules based on the graph structures and to determine basic chemical properties. Finally, we investigate the scalability of the technology used through the development of an automatic utility to convert standard chemical graphs into description graphs, and converting a large number of diverse graphs obtained from a publicly available chemical database

The present work, “Relationships between Scientific Literacy, Attitudes towards Science, Religiosity and Superstitious Beliefs in Romanian Context” is based on the first major research conducted in Romania concerning the public understanding of science paradigm. The research took place in the summer of 2009 and is representative for the Romanian, adult population. The information gathered concerns scientific literacy, attitudes towards science, medical knowledge, superstitious beliefs and religiosity. The coexistence of apparently opposed dimensions can be often seen in the Romanian public space. An example is the last presidential elections when the candidate that lost the elections explained his failure through pseudoscientific phenomenon. In this context the authors of this presentation will try to see the relationship between scientific knowledge, attitudes concerning science, superstitious beliefs and religiosity in contemporary Romanian society. One of our hypothesis is that religiosity will not be positively associated with superstitious beliefs. We’d expect that people who explain the events around them through Divinity would not believe that number 13 will bring bad luck or that if your left hand itches you will receive money (examples of common superstitions). Another hypothesis regards religiosity and its relation with scientific knowledge. We suppose that people who are more religious would have lower score of scientific literacy and, perhaps, a negative attitude towards science. Finally we will take into consideration the relationship between scientific knowledge and superstitious beliefs. We presume that those who have a high score in the scientific knowledge scale will be less superstitious.

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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

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