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

5. Semantic Net
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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 CD 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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