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Approximate Inference Techniques and Their
Applications to the Semantic Web
Perry Groot
IPA Fall days, 26 November 2004
IPA 2004 2Perry Groot
Motivation behind Approximation
Reducing complexityReasoning under time pressureReasoning with other limited resources
Reduce/increase number of solutions Reasoning that is not “perfect” but “good
enough”
IPA 2004 5Perry Groot
The purpose of this review is to remind operators of the
existence of the Operations Manual Bulletin 80-1, which provides
information regarding flight operations with low fuel quantities,
and to provide supplementary information regarding main tank
boost pump low pressure indications.747 <concept id=fuel-pump>FUEL PUMP </concept> LOW PRESSURE INDICATIONS
When operating 747 airplanes with low fuel quantities for short
Shared Hydraulics Repository (SHR)
(pump has (superclasses (mechanical-device)) (text-def (“A device for …”)) (thesaurus-term (|Pumps|)))
(every pump has (physical-parts (piston, valve, cylinder)) (device-purpose (Pumping-A-Fluid)))
Hey, I knowthis ontology, so now I know something about Fuel Pump.
What the heckis a Fuel Pump?
Semantic Markup
has(superclasses SHR: pump))
( fuel-pump
<concept id=fuel-pump>FUEL PUMP</concept>
Machine Processible Semantics
© Mike Ushold
IPA 2004 8Perry Groot
Woman Person Female
Man Person Woman
Mother Woman hasChild.Person
Mother(MARY), hasChild(MARY, PETER)
TBox + ABox
IPA 2004 9Perry Groot
Reasoning
Satisfiability Subsumption Classification Concept/Instance retrieval Instance realization
IPA 2004 10Perry Groot
Application: Individual Retrieval (I)
Retrieval Process1. Classify Query Q
2.
3.
Q
IPA 2004 11Perry Groot
Application: Individual Retrieval (II)
Retrieval Process1. Classify Query Q
2. Select Instances from subsumed classes
3. Q
IPA 2004 12Perry Groot
Application: Individual Retrieval (III)
Retrieval Process1. Classify Query Q
2. Select Instances from subsumed classes
3. Realize instancesfrom direct parents, if they belong to Q
Q
IPA 2004 13Perry Groot
KB
Architecture
TBox
ABox
ReasoningDescriptionLanguage
Query
LanguageWeakening
ApproximateDeduction
KnowledgeCompilation
IPA 2004 14Perry Groot
Approximate Entailment
Two approximate entailment operators [Schaerf & Cadoli, 1995]S-1-Entailment: Complete but unsoundS-3-Entailment: Sound but incomplete
Propositional TheoryUnderlying finite language LSubset S of L used as parameter
IPA 2004 15Perry Groot
Approximate Entailment
S-1-entailment: interpret everything outside of S as false
S-3-entailment: interpret everything outside of S as true (or normal)
SL
x ¬x
S1 S3
0/0 1/11/0
0/1
IPA 2004 16Perry Groot
Approximate Entailment
S1L S2
L S3 L Sn = L
Anytime behaviour when Si is increased Previous steps can be reused
IPA 2004 17Perry Groot
Approximate Entailment
Semantically well-founded Computationally attractive Improvable Dual Flexible
IPA 2004 18Perry Groot
Approximate Entailment
Unclear effect Parameter S is crucial for
approximate behaviour Almost no quantitative
analysis
IPA 2004 19Perry Groot
Approximation for DLs
Elements: Concept expressions Task: Satisfiability checking Approximation: “Simpler” concept expr.
Stronger (more specific) Weaker (less specific)
- Unsatisfiability of D implies unsatisfiability of C- Satisfiability of C implies satisfiability of D
IPA 2004 20Perry Groot
Approximation for DLs
Depth of subconcept D: number of universal quantifiers that have D in its scope.
Depth: 0 Depth: 1Depth: 2
IPA 2004 21Perry Groot
Approximation for DLs
Ci: Replace every existentially quantified subconcept D of depth greater or equal than i by .
C =
C0 =
C1 =
IPA 2004 22Perry Groot
Approximating Subsumption
Level := 0
Compute
Level := Level+1
Unsatisfiable?
Max Level?
t
f
f t
TRUE
FALSE