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IBM Research SHER: Scalable Highly Expressive Reasoner 03/17/22 © 2007 IBM Corporation SHER: A Scalable Highly Expressive Reasoner and its Applications. J. Dolby, A. Fokoue, A. Kalyanpur, A. Kershenbaum, L. Ma, E. Schonberg, K. Srinivas

IBM Research © 2007 IBM Corporation SHER: Scalable Highly Expressive Reasoner 6/4/2015 SHER: A Scalable Highly Expressive Reasoner and its Applications

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IBM Research

SHER: Scalable Highly Expressive Reasoner 04/18/23 © 2007 IBM Corporation

SHER: A Scalable Highly Expressive Reasoner and its Applications.

J. Dolby, A. Fokoue, A. Kalyanpur, A. Kershenbaum, L. Ma, E. Schonberg, K. Srinivas

IBM Research

© 2007 IBM Corporation2 04/18/23SHER: Scalable Highly Expressive Reasoner

Outline

Background and motivation

Core SHER technical innovations

–Scalability via Summarization

–Refinement: Resolving Inconsistencies in a Summary

–Integration with Incomplete Reasoners

–Conjunctive Query Evaluation

SHER concrete applications

–Automated Clinical trials matching using ontologies

–Anatomy Lens: Semantic search over PubMed

–Scalable Text Analytics cleanup

Conclusion

IBM Research

© 2007 IBM Corporation3 04/18/23SHER: Scalable Highly Expressive Reasoner

Project background and Motivation

Emergence of OWL as a standardized language for expressing semantic relations in ontologies.

–2004 : OWL a W3C Recommendation

Emergence of standardized ontologies encoded in OWL, especially in healthcare, life sciences:

–Biopax

–SNOMED

–About 80 ontologies at OBO (e.g. GO, FMA)

Emerging use of ontologies in search and retrieval of structured and unstructured data.

IBM Research

© 2007 IBM Corporation4 04/18/23SHER: Scalable Highly Expressive Reasoner

Vision: Semantic Information Retrieval

John Smith visited theLouvre

Show me all people who visited France?

Semantic InformationRetrieval System

John Smith!

DB2

OntologyDefinition

Louvre located in Paris….

Unstructured data

Legacy data

RDF StoreHomogeneous

view

IBM Research

© 2007 IBM Corporation5 04/18/23SHER: Scalable Highly Expressive Reasoner

Problems

Computational complexity of reasoning

– Intractable in the worst case.

– In 2005, intractable in practice on large and expressive KBs

Imprecision/inconsistencies in ontologies.

– Reasoner inability to scale consistency check

Query answering in expressive ontologies

IBM Research

© 2007 IBM Corporation6 04/18/23SHER: Scalable Highly Expressive Reasoner

Dealing with complexity challenges Reducing the expressivity of DL languages

–Why?• 80/20 rule ~ 80% of use cases covered by 20% of the language constructs• Tractability • Ease of implementation

–Result of this line of Research:• DL-Lite family (Diego Calvanese et al.)

– Covers: ER, UML– LogSpace complexity– Easy scalable implementation on top of relational DBMS

• EL++ (Franz Baader et al.)– Covers most life science ontologies– Polynomial time complexity (satisfiability, subsumption, and instance checking)– Simple rule-style implementation

• OWL 2.0 Profiles Approximate Reasoning

–Screech OWL Reasoner (Pascal Hitzler et al.)

IBM Research

© 2007 IBM Corporation7 04/18/23SHER: Scalable Highly Expressive Reasoner

SHER – A Highly Scalable SOUND and COMPLETE Reasoner for large OWL-DL KB

Reasons over highly expressive ontologies

Reasons over data in relational databases

No inferencing on load

– hence deals better with fast changing data

– the downside: reasoning is performed at query time.

Highly scalable -- reasons on 7.7M records in 7.9 s.

– State of the art cannot run on more than 1 million records on a 64 bit dual processor machine with 4G heap.

– Can scale to more than 60 million triples

– Semantically index 300 million triples from the medical literature.

Tolerate inconsistencies

Provide explanations

IBM Research

© 2007 IBM Corporation8 04/18/23SHER: Scalable Highly Expressive Reasoner

Outline

Background and motivation

Core SHER technical innovations

–Scalability via summarization

–Refinement: Resolving inconsistencies in a summary

–Integration with incomplete reasoners

–Conjunctive Query Evaluation

SHER concrete applications

–Automated Clinical trials matching using ontologies

–Anatomy Lens: Semantic search over PubMed

–Scalable Text Analytics cleanup

Conclusion and future work

IBM Research

© 2007 IBM Corporation9 04/18/23SHER: Scalable Highly Expressive Reasoner

Scalability via Summarization (ISWC 2006)

C1

M1

H1

isTaughtBy

C2

M2

H2

Original ABox

likes likes

P1

P2

Summary

M’

H’

likes

P’

C’

Legend: C – Course P - Person M - ManW – WomanH - Hobby

C’{C1, C2}

isTaughtBy

The summary mapping function f that satisfies the constraints:

– If any individual a is an explicit member of a concept C in the original Abox, and f(a) is an explicit member of C in the summary Abox.

– If a≠b is explicitly in the original Abox, then f(a) ≠f(b) is explicitly in the summary Abox.

– If a relation R(a, b) exists in the original ABox, then R(f(a), f(b)) exists in the summary.

If the summary is consistent, then the original Abox is consistent (converse is not true).

isTaughtBy isTaughtByisTaughtBy

isTaughtBy

TBox:Functional (isTaughtBy)Disjoint (Man, Woman)

IBM Research

© 2007 IBM Corporation10 04/18/23SHER: Scalable Highly Expressive Reasoner

Summarization effectiveness

Ontology Instances Role Assertions

I R A

Biopax 261,149 582,655 81 583

LUBM-1 42,585 214,177 410 16,233

LUBM-5 179,871 927,854 598 35,375

LUBM-10 351,422 1,816,153 673 49,176

LUBM-30 1,106,858 6,494,950 765 79,845

NIMD 1,278,540 1,999,787 19 55

ST 874,319 3,595,132 21 183

I – Instances after summarizationRA – Role assertions after summarization

IBM Research

© 2007 IBM Corporation11 04/18/23SHER: Scalable Highly Expressive Reasoner

Scalability via Filtering (ISWC 2006)

For expressive ontologies, query answering can be reduced to a consistency check on the Abox.

For the SHIN subset of DL (OWL-DL minus datatype reasoning and nominals), only certain types of relations are key to finding an inconsistency.

Specifically, any relation R which appears as part of an universal restriction (S.C) or a maximum cardinality (nS) are key for finding inconsistencies.

All relations that do not participate in such concept expressions can be filtered, provided we can compute all relevant concepts in the ontology…

IBM Research

© 2007 IBM Corporation12 04/18/23SHER: Scalable Highly Expressive Reasoner

Filtering effectiveness

Ontology Instances Role Assertions

I R A

Biopax 261,149 582,655 38 98

LUBM-1 42,585 214,177 280 284

LUBM-5 179,871 927,854 426 444

LUBM-10 351,422 1,816,153 474 492

LUBM-30 1,106,858 6,494,950 545 574

NIMD 1,278,540 1,999,787 2 1

ST 874,319 3,595,132 18 50

I – Instances after filteringRA – Role assertions after filtering

IBM Research

© 2007 IBM Corporation13 04/18/23SHER: Scalable Highly Expressive Reasoner

Refinement (AAAI 2007)

What if summary is inconsistent?

– Either, • Original ABox has a real inconsistencyOr,• ABox was consistent but the process of summarization introduced

fake inconsistency in the summary

Therefore, we follow a process of Refinement to check for real inconsistency

• Refinement = Selectively decompress portions of the summary• Use Justifications for the inconsistency to select portion of

summary to refine– Justification = minimal set of assertions responsible for inconsistency

• Repeat process iteratively till refined summary is consistent or justification is “precise”

IBM Research

© 2007 IBM Corporation14 04/18/23SHER: Scalable Highly Expressive Reasoner

Refinement: Resolving inconsistencies in a summary

C1

M1

H1

isTaughtBy

C2

M2

H2

C3

W1

Original ABox

likes likes

P1

P3

P2

Summary

M’

H’

likes

P’

C’

W’

isTaughtBy

Legend: C – Course P - Person M - ManW – WomanH - Hobby

M’

H’

likes

P’

Cx’

W’

isTaughtBy

Cy’

M’

likes

Px’

Cx’

W’

isTaughtBy

Cy’

Py’

H’

After 1st Refinement After 2nd Refinement – Consistent Summary

Summary is inconsistent

Summary still inconsistent!

C’{C1, C2, C3}

Cx’{C1, C2} Cy’{C3}

isTaughtBy

isTaughtBy

Py’{P3}Px’{P1, P2}

isTaughtBy isTaughtBy isTaughtByisTaughtByisTaughtBy isTaughtBy

TBox:Functional (isTaughtBy)Disjoint (Man, Woman)

isTaughtBy isTaughtBy isTaughtByisTaughtBy

IBM Research

© 2007 IBM Corporation15 04/18/23SHER: Scalable Highly Expressive Reasoner

C1

M1

H1

isTaughtBy

C2

M2

H2

C3

W1

Original ABox

likes likes

P1

P3

P2

Summary

M’

H’

likes

P’

C’

W’

isTaughtBy

Legend: C – Course P - Person M - ManW – WomanH - Hobby

M’

H’

likes

P’

Cx’

W’

isTaughtBy

Cy’

M’

likes

Px’

Cx’

W’

isTaughtBy

Cy’

Py’

H’

After 1st Refinement After 2nd Refinement – Consistent Summary

Summary is inconsistent

Summary still inconsistent!

C’{C1, C2, C3}

Cx’{C1, C2} Cy’{C3}

isTaughtBy

isTaughtBy

Py’{P3}Px’{P1, P2}

Sample Q: PeopleWithHobby?

Not(Q)

Not(Q)

Not(Q)

Solns: P1, P2

Px’

Not(Q)

Not(Q)

Refinement: Solving Membership Query (AAAI 2007)

TBox:Functional (isTaughtBy)Disjoint (Man, Woman)

isTaughtBy isTaughtBy isTaughtBy

isTaughtByisTaughtByisTaughtBy isTaughtBy

IBM Research

© 2007 IBM Corporation16 04/18/23SHER: Scalable Highly Expressive Reasoner

Results : Consistency Check

Ontology Instances Role Assertions Time for consistency check (in s)

Biopax 261,149 582,655 2.3

LUBM-1 42,585 214,177 2.9

LUBM-5 179,871 927,854 5.4

LUBM-10 351,422 1,816,153 5.1

LUBM-30 1,106,858 6,494,950 7.9

NIMD 1,278,540 1,999,787 0.8

ST 874,319 3,595,132 0.4

IBM Research

© 2007 IBM Corporation17 04/18/23SHER: Scalable Highly Expressive Reasoner

Results: Membership Query AnsweringOntology Type assertions Role Assertions

UOBM-1 25,453 214,177

UOBM-10 224,879 1,816,153

UOBM-30 709,159 6,494,950

Reasoner Dataset Avg. Time (in sec)

St. Dev (in sec)

Range

(in sec)

KAON2 UOBM-1 21 1 18 - 37

KAON2 UOBM-10 448 23 414 - 530

SHER UOBM-1 4 4 2 - 24

SHER UOBM-10 15 26 6 - 191

SHER UOBM-30 35 63 12 - 391

IBM Research

© 2007 IBM Corporation18

Improving SHER Performance through integration with a fast but incomplete reasoner Refinement

– Critical for completeness – But time consuming (joins between large tables): majority of time spent in

refinement– However, a lot of solutions “easily” detected using query expansion

• e.g. ColonNeoplasm(x) = Disease(x) ^ hasAssociatedMorphology(x, y) ^ Neoplasm(y) ^ hasFindingSite(x, z) ^ Colon(z)

Improved SHER Performance by adding Query Expansion module– General Idea:

• Quickly find solutions to query• Refine summary to isolate solution individuals• Test remaining individuals

– Advantages:• Any sound technique to find solutions quickly can be used (QE, forward-

chaining based rule system)• Much less refinement required if above technique finds many solutions

– Depending on expressivity of logic, you may not need refinement at all

IBM Research

© 2007 IBM Corporation19

SHER Hybrid Algorithm Evaluation

Avg. Query Answering time for Clinical Trials Use-Case down to 15mins

– Huge reduction in number of refinement steps

IBM Research

© 2007 IBM Corporation20

Conjunctive Query in SHER (ISWC 2008) SHER also supports Grounded Conjunctive Queries (CQ), which combine

membership/type queries and relationship queries R(x,y)– GraduateStudent(x) ^ isMemberOf(x, y) ^ Department(y) ^ subOrganizationOf(y, z)

Solving CQ much harder than MQ– Summarization/Refinement algorithm does not directly apply for RQ

• Intuitively, summarization groups individuals based on type – works well for type queries, but for relationship queries we need to consider pairs of individuals

Alternate 3-step Approach:– Use a Datalog Rule engine to estimate potential relationships– Use various heuristics to find definite relationships– Test remaining relationships in Summary and solve by splitting– Advantage:

• Graceful degradation depending on complexity of query and ontology/data (very fast on realistic queries and datasets)

IBM Research

© 2007 IBM Corporation21

Conjunctive Query Evaluation

Comparison with KAON2 on the UOBM Benchmark

IBM Research

© 2007 IBM Corporation22 04/18/23SHER: Scalable Highly Expressive Reasoner

Outline

Background and motivation

Core SHER technical innovations

–Scalability via summarization

–Refinement: Resolving inconsistencies in a summary

–Integration with incomplete reasoners

–Conjunctive Query Evaluation

SHER concrete applications

–Automated Clinical trials matching using ontologies

–Anatomy Lens: Semantic search over PubMed

–Scalable Text Analytics cleanup

Conclusion and future work

IBM Research

© 2007 IBM Corporation23 04/18/23SHER: Scalable Highly Expressive Reasoner

Matching Patient Records to Clinical Trials Using

OntologiesWith collaboration with Columbia University Medical Center : Chintan Patel and James Cimino

Work presented at ISWC 2007

IBM Research

© 2007 IBM Corporation24 04/18/23SHER: Scalable Highly Expressive Reasoner

ProblemIn complex domains such as healthcare, there is a “semantic gap” between data and queries. E.g.,

Patient data Queries

Patient on Hydrocortisone 2% Patients on drugs with steroids as ingredients

Patient tested positive for Patients with tuberculosis meningitismycobacterium tuberculosis

Can ontology analytics using ontologies such as SNOMED be used to bridge this gap?

Case study on patient recruitment for clinical trials problem

IBM Research

© 2007 IBM Corporation25 04/18/23SHER: Scalable Highly Expressive Reasoner

Clinical Trials MatchingCurrent scenario: A day in the life of Columbia’s Clinical Trials Investigator

Look at criteria in the trial protocol

Pore throughpatient charts

Call Physician to discuss consent

Result: Poor participation in clinical trials!Can ontology analytics be used to find patients that match clinical trial criteria to improve participation?

IBM Research

© 2007 IBM Corporation26 04/18/23SHER: Scalable Highly Expressive Reasoner

Clinical Trials Matching

What we want to do: A day in the life of Columbia’s Clinical Trials Investigator

QuickTime™ and aGIF decompressor

are needed to see this picture.

Look at criteria in the trial protocol

Call Physician to discuss consent

Find patientsautomatically

Patient Data

OntologOntology y

ReasoneReasonerr

Ontologies(SNOMED)

Query for criteria Find matching patients

IBM Research

© 2007 IBM Corporation27 04/18/23SHER: Scalable Highly Expressive Reasoner

Technical Challenges to using ontologies

Knowledge engineering

Clinical Data Repository

NY PresbyterianMedical Entities Dictionary (MED)

Concepts:100210ISA Relationships:148,821

Extensive Local Knowledge

Need to map local knowledge (MED) to domain knowledge (SNOMED),e.g.,

Presence of MRSA on a Lab test means lab test hasCaustiveAgent MRSA.

Coded in MED

IBM Research

© 2007 IBM Corporation28 04/18/23SHER: Scalable Highly Expressive Reasoner

Technical challenges to using ontologies

Scalability of reasoning

– ABox (patient data): 1 year data at Columbia (250K patients) 60M RDF triples

– TBox (SNOMED+MED, 461K concepts)

Expressivity of reasoning: SNOMED is EL++, but ABox contains negation, e.g.,

– Lab results ruled out the presence of an organism

Inconsistent, noisy and incomplete data

– Lab results that indicate both the presence and absence of an organism.

IBM Research

© 2007 IBM Corporation29 04/18/23SHER: Scalable Highly Expressive Reasoner

Overall Solution

MEDLocal Knowledge

SNOMEDDomain Knowledge

∃associatedObservation.MRSA

Patient Data

LabA MRSAOrganism Present

coded in

coded in

ETL

Mapping

Integrated Tbox

Patient Data

LabA:∃causativeAgent.MRSAOrganism

SHER SHER Ontology Ontology ReasonerReasoner

Abox

Query Extraction

semi-automatic

Matching patients

IBM Research

© 2007 IBM Corporation30 04/18/23SHER: Scalable Highly Expressive Reasoner

Results for ~250K patients

Query # Matches Time (in min)Optimized Time

(mins)

MRSA Disorder 1052 68.9 10.8

On Warfarin 3127 63.8 6.3

Breast neoplasm 74 26.4 7.7

Colon neoplasm 164 31.8 6.5Pneumococcal

pneumonia.. 107 56.4 10.7

On metronidazole 2 61.4 5.4

Acute amebiasis... 1357 370.8 20.2

Steroids/cyclosporine 5555 145.5 6.6

Corticosteroids 4794 78.8 6.1

Optimizations to use query expansion to quickly compute and remove “obvious” solutions.

IBM Research

© 2007 IBM Corporation31

AlphaWorks Service: Anatomy Lens

Ontology-based PubMed Search

– GOAL: Real-time Ontology Reasoning on the Web

– Overcome Keyword Search: Poor precision & recall

– Link 3 large OWL Ontologies: FMA, GO, MeSH

– Dataset Size: 16 Million MEDLINE Articles, ~300M Triples

– Support Structured queries:

• Find articles about “neuron development” (GO Process) in the “Hippocampus” region (FMA Part) of the brain

• Possible solution article may be about “dendrite morphogeneis” in the “Archicortex“

IBM Research

© 2007 IBM Corporation32

Real-time Reasoner for Service

EL+ Reasoner in SHER for Anatomy Lens

– Many HCLS Ontologies fall in this EL+ fragment of OWL

Highly optimized:

– Classification Times:

• GO (32K) – 3 s• FMA (75K concepts) – 30 s• SNOMED (350K concepts) – 8 mins

– State-of-the-art reasoner - CEL - takes >2hrs on SNOMED

Additional Features:

– Incremental reasoning

– Explanations support

IBM Research

© 2007 IBM Corporation33

Anatomy Lens Demo

Online Video: http://anatomylens.alphaworks.ibm.com/AnatomyLens/AnatomyLensVideo/AnatomyLensVideo.html

IBM Research

© 2007 IBM Corporation34 04/18/23SHER: Scalable Highly Expressive Reasoner

Scalable Cleanup of Information Extraction Data Using Ontologies

In collaboration with Christopher Welty, James Fan, and William Murdock

Presented at ISWC 2007

IBM Research

© 2007 IBM Corporation35 04/18/23SHER: Scalable Highly Expressive Reasoner

Problem Text extraction from natural language is imperfect

Relationship extraction is especially problematic, e.g.

...the decision in September 1991 to withdraw tactical nuclear bombs, missiles and torpedos from US Navy ships...

Text extraction:

–nuclear ownerOf bombs

–nuclear type Weapon, bombs type Weapon

Can ontology reasoning be used to improve relationship extraction?

IBM Research

© 2007 IBM Corporation36 04/18/23SHER: Scalable Highly Expressive Reasoner

Background SemantiClean (ISWC-2006)

Ontology

–ownerOf domain (Person Organization)⊔

–Person disjointFrom Organization

–Person disjointFrom Weapon

–Organization disjointFrom Weapon...

Add triple at a time

nuclear ownerOf bombnuclear ownerOf bombCheck with Check with

DLDLReasonerReasoner

Discard ifDiscard ifinconsistentinconsistent

Improves relationship extraction by 8-15%.

IBM Research

© 2007 IBM Corporation37 04/18/23SHER: Scalable Highly Expressive Reasoner

Evaluating the Triple at a Time Approach

Scalability

– Text extraction on a normal desktop can process a million documents/day.

– Each document extracts ~70 entities, ~40 relations.

– Consistency detection in DL reasoners does not scale to such large RDF graphs.

IBM Research

© 2007 IBM Corporation38 04/18/23SHER: Scalable Highly Expressive Reasoner

Computational ExperienceDataset

# Documents # Individuals# Role

assertions# Just. Time (mins)

100 8,628 15,521 191 10

500 32,787 62,414 625 19

1500 104,507 195,206 1,570 37

3683 286,605 513,522 2,744 67

IBM Research

© 2007 IBM Corporation39 04/18/23SHER: Scalable Highly Expressive Reasoner

Conclusions

SHER–Reasons over highly expressive ontologies–Reasons on data in relational databases

–No inferencing on load, hence deals better with fast changing data–Integrates with fast incomplete reasoners–Highly scalable -- reasons on 7.7M records in 7.9 s.

• semantically indexed 300 million triples from the medical literature. –Tolerates inconsistencies–Provides explanations

Many applications:–Semantic Matching for clinical trials–Semantic search over PubMed–Scalable text analytics cleanup

What next?– SHER Code release scheduled for the end of June 2008

IBM Research

SHER: Scalable Highly Expressive Reasoner 04/18/23 © 2007 IBM Corporation

THANKS!

QUESTIONS?

More on SHER:

http://domino.research.ibm.com/comm/research_projects.nsf/pages/iaa.index.html

IBM Research

SHER: Scalable Highly Expressive Reasoner 04/18/23 © 2007 IBM Corporation

BACKUP

IBM Research

© 2007 IBM Corporation42 04/18/23SHER: Scalable Highly Expressive Reasoner

Integrating MED and SNOMED

Mapping

UMLSNLP (MMTX)Manual

100,210 concepts 361,824 concepts

MED SNOMED

• 17,446 concepts in MED directly mapped by subclass relations to SNOMED concepts (17% of MED).• Including subclasses of 17,446 concepts, the coverage of MED is 75,514 concepts. • 88% of concepts in the Abox were covered by the integrated Tbox.

Integrated Tbox

IBM Research

© 2007 IBM Corporation43 04/18/23SHER: Scalable Highly Expressive Reasoner

Modeling patient data in SNOMED

Patient DataLabA MRSAOrganism Present

ETL

Patient Data

LabA:∃causativeAgent.MRSAOrganism

Abox

• Modeling positive and negative results, e.g.

LabEventA MRSAOrganism Absent

is modeled as:LabEventA:

∀causativeAgent.¬MRSAOrganism

• Modeling groupings of eventsRadiologyEventA findingSite ColonRadiologyEventA morphology Neoplasm

is modeled as:RadiologyEventA:

∃roleGroup.(∃hasMorphology.Neoplasm ⊓∃hasFindingSite. Colon)

IBM Research

© 2007 IBM Corporation44 04/18/23SHER: Scalable Highly Expressive Reasoner

Validation (100 patient records)Query # Matches # Misses Time (in s)

MRSA Disorder 1 54

On Warfarin 4 78

Breast neoplasm 0 1 29

Colon neoplasm 1 51

Pneumococcal pneumonia.. 0 39

On metronidazole 0 1 29

Acute amebiasis... 0 225

Steroids/cyclosporine 6 117

Corticosteroids 6 8 118

Misses primarily due to incorrect mappings. No false positives

IBM Research

© 2007 IBM Corporation45 04/18/23SHER: Scalable Highly Expressive Reasoner

Solutions to Challenges

Large Aboxes (patient data): Reason on a summarized version of the data (ISWC 2006).

Large Tboxes (SNOMED+MED): Compute closure of concepts in Abox which is 22,561 concepts.

Incomplete data. MRSA defined as •∃hasCausativeAgent.MRSAOrganism Infection⊓

Patient record will never indicate infection, hence no matches.

Convert all conjuncts to disjuncts for user specified concepts (e.g., MRSA Disorder) in the query.

•∃hasCausativeAgent.MRSAOrganism Infection⊔

IBM Research

© 2007 IBM Corporation46 04/18/23SHER: Scalable Highly Expressive Reasoner

Justification based consistent subset

Set of removed assertionsx removed because of J1y cannot be removed because of J2 BUT y can be removed due to J3.

JustificationsJ1 - x, y, mJ2 - x, y, zJ3 - y, q

Justification based consistent subset by example:

BUT for knowledge bases filled with thousands of inconsistencies, even this justification based consistent subset computation may not scale.

Approximate cleanup technique

IBM Research

© 2007 IBM Corporation47 04/18/23SHER: Scalable Highly Expressive Reasoner

Approximate cleanup

Summarization: Perform consistency detection on a summarized version of the larger RDF graph.

aa

bb

a:Nation

b:Organization

partOfcc

dd

c:Nation

d:Person

ownerOfee

ff

e:Organization

f:Nation

residentOf

Original data (Abox)

uu vv

ss

u:Nation v:Organization

s:Person

Summary Abox

Mapping function f satisfies:• If a:C ∈ A, then f(a):C ∈ A’• If R(a, b) ∈ A, then R(f(a), f(b)) ∈ A’• If a≠b ∈ A, then f(a) ≠ f(b) ∈ A’If A’ is consistent, then A is consistent. Converse does not hold.

IBM Research

© 2007 IBM Corporation48 04/18/23SHER: Scalable Highly Expressive Reasoner

Isolating an inconsistency

uu vv

ss

u:Nation v:Organization

s:Person

Summary Abox

• Check consistency• Find justification (minimal set of assertions that cause the inconsistency), e.g., u ownerOf s• Refine the summary to make the justification more precise.

ownerOf

uu

ss

a,c,f in A mapped to u

s:Person

ownerOf

uu

ss

a mapped to u

s:Person

ownerOf

To make a justification more precise, refine summary individuals in the justification by the sets of role assertions they have.

uu’’

vvc,f mapped to u’

v:Organization

Refined summary

IBM Research

© 2007 IBM Corporation49 04/18/23SHER: Scalable Highly Expressive Reasoner

Is the inconsistency real?

Stop refining when a justification is precise. A justification J is precise when:For all summary individuals s ∈ J, and for all role assertions R(s, t) ∈ J implies that for all individuals a ∈ A such that f(a)=s, there is an individual b ∈ A such that f(b)=t and R(a,b) ∈ A.

uu

ss

a mapped to u

ownerOf uu’’

vvc,f mapped to u’

Precise justification

d mapped to s

Refined summaryKey to scalable inconsistency detection:Precise justification J where each individual in J has many thousand individuals in A mapped to it

IBM Research

© 2007 IBM Corporation50 04/18/23SHER: Scalable Highly Expressive Reasoner

Cleaning up inconsistencies

Once a precise justification is found, check if it is conclusive. A precise justification is conclusive if for example:

– its acyclic

– its cyclic, but can be shown to be acyclic after the application of deterministic tableau rules

– No real use cases where justifications are not conclusive.

Remove a single assertion of a precise, conclusive justification. Iterate to find all justifications, until the knowledge base is consistent.

IBM Research

© 2007 IBM Corporation51 04/18/23SHER: Scalable Highly Expressive Reasoner

Advantages of approximate cleanup

For acyclic justifications, removal of a single assertion in J in the summary is equivalent to removing a single assertion in all the justifications in the original data that are “instances” of J

Produces a justification-based consistent subset in a scaleable way if data has only acyclic justifications.

IBM Research

© 2007 IBM Corporation52 04/18/23SHER: Scalable Highly Expressive Reasoner

Disadvantages of approximate cleanup

In the case of a cyclic justification, if the cycle maps to a large cycle in the Abox, e.g:

aa

bb

cc

dd

Original Abox

R

R

R

Ra:A⊓∀R.¬AR is transitive

ssR

b:Q

c:Q

d:Qs:A⊓∀R.¬A

Summary Abox

Removal of a single role assertion in J eliminates the whole cycle! Extra deletion of assertions.

ttt:Q

J

IBM Research

© 2007 IBM Corporation53 04/18/23SHER: Scalable Highly Expressive Reasoner

How aggressive is approximate cleanup?

# Documents # Individuals# Role

assertions# Deleted

Estimated extra

deletions

100 8,628 15,521 299 19

500 32,787 62,414 1,150 89

1500 104,507 195,206 3,910 359

3683 286,605 513,522 9,574 967

Estimated extra deletions, based on the assumption that only one assertion needed to be removed from each justification.