Chapter 5
A Semantic Web Primer
1
Chapter 5
Logic and Inference: Rules
Grigoris Antoniou
Frank van Harmelen

Chapter 5
A Semantic Web Primer
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Lecture Outline
1.
Introduction
2.
Monotonic Rules: Example
3.
Monotonic Rules: Syntax & Semantics
4.
Description Logic Programs (DLP)
5.
Semantic Web Rules Language (SWRL)
6.
Nonmonotonic Rules: Syntax
7.
Nonmonotonic Rules: Example
8.
Rule Markup Language (RuleML)

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A Semantic Web Primer
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Knowledge Representation
The subjects presented so far were related to
the representation of knowledge
Knowledge Representation was studied long
before the emergence of WWW in AI
Logic is still the foundation of KR, particularly
in the form of predicate logic (first-order
logic)

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A Semantic Web Primer
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The Importance of Logic
High-level language for expressing
knowledge
High expressive power
Well-understood formal semantics
Precise notion of logical consequence
Proof systems that can automatically derive
statements syntactically from a set of
premises

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A Semantic Web Primer
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The Importance of Logic (2)
There exist proof systems for which semantic
logical consequence coincides with syntactic
derivation within the proof system
–
Soundness & completeness
Predicate logic is unique in the sense that sound
and complete proof systems do exist.
–
Not for more expressive logics (higher-order logics)
trace the proof that leads to a logical consequence.
Logic can provide explanations for answers
–
By tracing a proof

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A Semantic Web Primer
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Specializations of Predicate Logic:
RDF and OWL
RDF/S and OWL (Lite and DL) are
specializations of predicate logic
–
correspond roughly to a description logic
They define reasonable subsets of logic
Trade-off between the expressive power and
the computational complexity:
–
The more expressive the language, the less
efficient the corresponding proof systems

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A Semantic Web Primer
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Specializations of Predicate Logic:
Horn Logic
A rule has the form:
A1, . . ., An
B
–
Ai
and
B
are atomic formulas
There are 2 ways of reading such a rule:
–
Deductive rules
:
If
A1,..., An
are known to be
true, then
B
is also true
–
Reactive rules
: If the conditions
A1,..., An
are
true, then carry out the action
B

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A Semantic Web Primer
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Description Logics vs. Horn Logic
Neither of them is a subset of the other
It is impossible to assert that a person X who is
brother of Y is uncle of Z (where Z is child of Y) in
OWL
–
This can be done easily using rules:
brother(X,Y), childOf(Z,Y)
uncle(X,Z)
Rules cannot assert the information that a person is
either a man or a woman
–
This information is easily expressed in OWL using disjoint
union

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A Semantic Web Primer
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Monotonic vs. Non-monotonic Rules
Example
: An online vendor wants to give a
special discount if it is a customer’s birthday
Solution 1
R1: If birthday, then special discount
R2: If not birthday, then not special discount
But what happens if a customer refuses to
provide his birthday due to privacy concerns?

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A Semantic Web Primer
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- Fall '16
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- Semantics, Logic Programming, Semantic Web Primer