Approximate Inference Techniques and Their Applications to the Semantic Web Perry Groot IPA Fall days, 26 November 2004

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”


Anytime Reasoning

Computation time

Qualityoutput


Types of Approximation

Numerical Logical

Soundness Completeness


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


KB

Architecture

TBox

ABox

ReasoningDescriptionLanguage

Query


C A A C D R.C R.

C A A C D R.C R.C

C A A C C D C D R.C R.C

Description Logics


Woman Person Female

Man Person Woman

Mother Woman hasChild.Person

Mother(MARY), hasChild(MARY, PETER)

TBox + ABox


Reasoning

Satisfiability Subsumption Classification Concept/Instance retrieval Instance realization


Application: Individual Retrieval (I)

Retrieval Process1. Classify Query Q

2.

3.

Q


Application: Individual Retrieval (II)


2. Select Instances from subsumed classes

3. Q


Application: Individual Retrieval (III)


2. Select Instances from subsumed classes

3. Realize instancesfrom direct parents, if they belong to Q

Q


KB

Architecture

TBox

ABox

ReasoningDescriptionLanguage

Query

LanguageWeakening

ApproximateDeduction

KnowledgeCompilation


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



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



S1L S2

L S3 L Sn = L

Anytime behaviour when Si is increased Previous steps can be reused



Semantically well-founded Computationally attractive Improvable Dual Flexible



Unclear effect Parameter S is crucial for

approximate behaviour Almost no quantitative

analysis


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



Depth of subconcept D: number of universal quantifiers that have D in its scope.

Depth: 0 Depth: 1Depth: 2



Ci: Replace every existentially quantified subconcept D of depth greater or equal than i by .

C =

C0 =

C1 =


Approximating Subsumption

Level := 0

Compute

Level := Level+1

Unsatisfiable?

Max Level?

t

f

f t

TRUE

FALSE

Thank you for your attention

Documents

Approximate Inference Techniques and Their Applications to the Semantic Web Perry Groot IPA Fall days, 26 November 2004