1. Description Logic
Rajendra Akerkar
j
Western Norway Research Institute, Norway
2. Knowledge Representation
f
facilitate inferencing
f g
Inferencing often involves making classes
o
of objects, defining a hierarchy, giving
e g e a c y, g v g
attributes to objects and specifying
constraints.
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3. Predicate Calculus
Uses (i) Predicates for describing relationships
and (ii) Rules for inferencing
A special kind of inferencing is Inheritance
where all properties of a super class are passed
onto its subclasses
For
F example, it can b inferred that men- b i
l i be i f d h being
human have 2 legs by virtue of their inheriting
human-properties.
human-properties
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4. Structured Knowledge
Representation
Components and their interrelationships have to
be expressed
Semantic Nets and Frames prove more
effective than predicate calculus
Reminiscent of calculus where using
differentiation to find the rate of change of one
q y p
quantity with respect to another is more
convenient than using the more foundational
y
Lt
L
x 0 x R. Akerkar 4
6. Frames
(example f
l from medical entities dictionary, Columbia
di l i i di i C l bi
University)
Have slots and fillers
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7. Motivation to study
Structure of the knowledge may not be
visible, and obvious inferences may be difficult
to draw
Expressive power is too high for obtaining
decidable and efficient inference
Inference power may be too low f
I f b l for
expressing interesting, but still decidable
theories
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8. Wikipedia Definition
“Description logics (DL) are a family of knowledge
representation languages which can be used to
represent the terminological knowledge of an
application domain in a structured and formally well-
understood way. The name description logic refers on the
way refers,
one hand, to concept descriptions used to describe a
domain and, on the other hand, to the logic-based
semantics which can be given by a translati n int first
hich i en b translation into first-
order predicate logic. Description logic was designed as
an extension to frames and semantic networks, which
were not equipped with formal logic-based semantics.”
t i d ith f ll i b d ti ”
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9. Constituents of DL
Individuals (such as Ralf and John)
( f J )
Concepts (such as Man and Woman)
Roles (such as isStudent)
Individuals are like constants in predicate calculus,
while Concepts are like Unary predicates
and Roles are like Binary Predicates.
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10. Constructors of DL and their
meaning
Constructor Syntax Example Semantics using PC
Atomic Concept A Human {x | human(x)}
Atomic Role R Has-child { y
{<x,y> | has-child(x,y)}
( y)}
Conjunction C∩D Human ∩ Male {x | human(x) male(x)}
Disjunction CD Doctor Lawyer {x | doctor(x) lawyer(x)}
Negation C Male {x | male(x)}
Exists Restriction R.C Has-child.Male {x | y has-child(x,y)
male(y)}
Value Restriction R.C Has-child.Doctor {x | y has-child(x,y)
doctor(y)}
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11. Examples
For example the set of all those p
p parents
having a male child who is a doctor or a
lawyer is expressed as
y p
Has-child.Male ∩( Doctor U Lawyer)
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12. Quantifiers and ‘Dots’
Dots
HasChild.Girl is interpreted as the set
◦ {x | (y)( HasChild(x,y)Girl(y))} and
isEmployedBy.Farmer is interpreted as
p y y p
◦ {x | (y)( isEmployedBy(x,y) Farmer(y))}
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13. Inference in DL
Main mechanism: Inheritance via subsumption
DL suitable for ontology engineering
A concept C subsumes a concept D iff
I(D) I(C) on every interpretation I
For example: Person subsumes Male, Parent
subsumes Father etc Every attribute of a
etc.
concept is also present in the subsumed
concepts
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