1. Chapter 5Knowledge Representation &
Description Logic

2. Introduction
• Logic based Knowledge Representation formalisms
– Descendants of semantic networks
– KL-ONE
– Domain description in the form of concepts (classes),
roles (properties, relationships) and individuals.
– A knowledge base (KB) is a pair K = < A> where T
T, ,
is a TBox, and A is an Abox.
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3. Introduction
• Description Logic: set of concept and role
forming operators
– ALC is a type of description logics.
– Concepts constructed using u, t, :, 9 and 8
• S used for ALC with transitive roles (R+)
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4. DL Architecture
Knowledge Base
===============
Inference
Interface
Tbox (schema) System
Abox (data)
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5. Syntax & Semantics
ALC provides two special classes as shortcuts:
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6. Example 5.11
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7. ALC Description Logic
• Two kinds of concept descriptions
– elementary descriptions and
– complex descriptions
• ALC concept formulas are built up from basic
concept names and roles.
• ALC statements relate named or anonymous
concepts by means of one of the following:
– Inclusion,
– inverse inclusion, and
– Equivalence.
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8. Reasoning About Knowledge
• Description logics uses tableau algorithms
– for deciding concept satisfiability with respect to a
knowledge base.
– A tableau algorithm for a DL language contains the
following elements:
• A completion graph, known as tableau, which represents a
model of the DL language.
• A set of tableau expansion rules to construct a complete and
consistent completion graph.
• A set of blocking rules to detect infinite cyclic models and
ensure termination.
• A set of clash conditions to detect logic contradictions.
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9. CLASSIC
• Example 5.1: Express the sentences in the
CLASSIC language.
– The set of men with at most two daughters.
AND(Man, AT-MOST(2, Daughter).
– The set of men with at most two daughters who are all
professors in physics or mathematics departments.
AND(Man, AT-MOST(2, Daughter)),
ALL(Daughter, AND(Professor, FILLS(Department, Physics,
Mathematics))).
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10. CLASSIC & OWL
• CAR = AND (FOURWHEELER, ALL (hasMaker,
FACTORY)).
<owl:Class rdf:ID="Car">
<rdfs:subClassOf rdf:resource="&vehicle;FourWheeler" />
...
<rdfs:subClassOf>
<owl:Restriction>
<owl:onProperty rdf:resource="#hasMaker" />
<owl:allValuesFrom rdf:resource="#Factory" />
</owl:Restriction>
</rdfs:subClassOf>
...
</owl:Class>
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11. • CAR = AND (FOURWHEELER, AT-LEAST (1 engine))
<owl:Class rdf:ID="Car">
<rdfs:subClassOf rdf:resource="&vehicle;FourWheeler"/>
<rdfs:subClassOf>
<owl:Restriction>
<owl:onProperty rdf:resource="#hasEngine"/>
<owl:minCardinality
rdf:datatype="&xsd;nonNegativeInteger">1</owl:minCardinality>
</owl:Restriction>
</rdfs:subClassOf>
...
</owl:Class>
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12. • SCOOTYPEPPLUS = AND (TWOWHEELER, FILLS
(hasColour Pink))
<owl:Class rdf:ID="ScootyPepPlus">
<rdfs:subClassOf rdf:resource="#TwoWheeler"/>
<rdfs:subClassOf>
<owl:Restriction>
<owl:onProperty rdf:resource="#hasColour" />
<owl:hasValue rdf:resource="#Pink" />
</owl:Restriction>
</rdfs:subClassOf>
</owl:Class>
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13. Rule Languages
• RuleMarkup in XML
• WSML
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14. F-Logic
ABC[hasLegalName -> ‘ABC Travel Agency’,
hasOfficesIn ->> {Bangalore, Mumbai},
hasPhones ->> {00918023514537, 0091223885270},
hasEmployees ->> {Anita, Sunita, Punita}].
Anita[hasName -> ‘Miss Anita’,
hasAddress -> AddressAnita[hasStreet -> ‘Nariman Point’,
hasNumber -> 320,
hasCity -> Mumbai].
BookingABCAnita[bookedBy -> ABC,
bookedFor -> Anita,
issuedFor -> LH635].
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15. Company :: LegalEntity.
Company[hasLegalName => STRING,
hasOfficesIn =>> City,
hasPhones =>> NUMBER,
hasEmployees =>> Person].
Person :: LegalEntity.
Person[hasName => STRING,
hasAddress => Addresss].
Employee :: Person.
Employee[isEmployedAt => Company].
Booking[bookedBy => LegalEntity,
bookedFor => Person,
issuedFor => Flight].
ABC : Company.
Anita : Person.
LH635 : Flight.
BookingABCAnita : Booking.
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16. Tools & Reasoners
– Protégé: a free, open source ontology editor
and a knowledge acquisition system.
– OntoEdit
– KAON2
– Pellet
– FaCT+
– SESAME
– OWL Validator
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17. Suggested Readings
1. F. Baader, D. Calvanese, D. McGuinness, D. Nardi, and P.
Patel-Schneider, editors. The Description Logic Handbook:
Theory, Implementation and Applications. Cambridge
University Press, 2003.
2. R. J. Brachman and al. Living with classic: When and how to
use a kl-one-like language. In John Sowa, editor, Principles of
Semantic Networks: Exploration in the Representation of
Knowledge, pages 401--456. Morgan Kaufmann, 1991.
3. I. Horrocks, U. Sattler, Ontology reasoning in the SHOQ(D)
description logic, in: Proc. of the 17th Int. Joint Conf. on
Artificial Intelligence (IJCAI 2001), pp. 199–204, 2001.
4. I. Horrocks, P. F. Patel-Schneider, S. Bechhofer, and D.
Tsarkov. OWL Rules: A Proposal and Prototype
Implementation. Journal of Web Semantics, 3,1, 2005.
5. B. Motik, U. Sattler, and R. Studer. Query Answering for OWL-
DL with Rules. Journal of Web Semantics 3,1, 2005.
http://www.Websemanticsjournal.org/ps/pub/2005-3.
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