Transcript Semantic Web

The Semantic Web –
WEEK 10: Introduction to
Description Logics
We are back down to
here!
The “Layer Cake” Model –
[From Rector & Horrocks
Semantic Web cuurse]
Recap
• First order logic is an
•expressive
•precise
•well-researched
representation language family, and has systematic semidecidable proof procedures like resolution refutation for
automated reasoning.
•BUT FOL has drawbacks – it is too perhaps too expressive and
unstructured
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Description Logic
is a FAMILY of languages which have been used to
give a semantics to
- OO modelling languages such as E-R diagrams
and UML class diagrams
- Diagrammatic representations such as ‘Semantic
Nets’
- Ontology languages such as OWL
DL relates to

formal methods in software engineering,

database

AI
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Description Logic
is centred around CLASSES
F O Logic allows the user to make assertions about
sets of individuals ..
Eg
Ax (P(x) => …)
Ex (P(x) & …)
DL allows the user to NAME SETS OF INVIDUALS for
which some property is true and COMBINE these
with other.
P = { x | P(x) }
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Description Logics from F.O.Logic
F.O.Logic
Universe
Constant name
One-place predicate
Two-place predicate
> 2 place predicate
Variables
Functions
Connectives
Quantifiers
Description Logic
Domain
Individual
Concept (or Class)
Role (or Property)
no equivalent!!
no equivalent!!
no equivalent!!
Restricted use
Restricted use
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Description Logics from F.O.Logic: Concepts
F.O.Logic
One place predicate C
Ax P(x) => Q(x)
Ax P(x) => ¬ Q(x)
Ax P(x)  Q(x)
Ax C(x)  P(x) & Q(x)
Ax C(x)  P(x) V Q(x)
Description Logic
A concept C  {x | wff}
PQ
Q subsumes P
P¬Q
Q and P are disjoint
PQ
P is equivalent to Q
CPQ
CPUQ
Examples
1.
Postgrads are (defined as) students who have a first degree
2.
Professors are also Doctors
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Description Logics from F.O.Logic: Roles
F.O.Logic
Two place predicate
AxAy R(x,y)  S(y,x)
AxAy R(x,y)  S(x,y)
AxAy R(x,y) => S(x,y)
AxAyAz R(x,y) & R(y,z)
=> R(x,z)
Description Logic
A role R = {(x.y) | R(x,y) }
R  S- inverse role
S- = {(x,y) | R(y,x)}
RS
RS
R is transitive
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Concept Expressions
Wffs are expressions whose value is true or false
In DL, concept expressions denote a set of individuals for which the value
of a wffs is TRUE
C = {x | C(x) }
P  Q = {x | P(x) & Q(x)}
P U Q = {x | P(x) V Q(x)}
P U ¬Q = {x | P(x) V ¬Q(x)}
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Concept Expressions with Roles
some values from:
E R.P = {x | Ey R(x,y) & P(x)}
General form “E Role.Class”
Examples:
E Father.Male =
“the set of fathers who have sons”
Student  E Married.Student =
“the set of students who also are married to students”
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Concept Expressions with Roles
All values from:
A R.P = {x | Ay R(x,y) => P(y)}
General form “A Role.Class”
Examples:
Parents  A Parentof.Doctor
“the set of parents whose children are (all) doctors”
Students  A Examinedby.Easy
“the set of students who had easy exams“
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Summary
DL is built around classes –
It is a logic with no variables or functions, and
a restricted number of expressions compared to
FOL
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