WIR FORSCHEN FÜR SIE

Reasoning in Expressive Extensionsof the RDF Semantics

Michael Schneider (FZI Karlsruhe, Germany)ESWC 2011 PhD Symposium

Heraklion (Greece), 31 May 2011

RDF Semantics and Semantic Extensions• RDF Semantics:

– Part of W3C RDF Specification (Hayes, 2004)– Defines formal meaning of RDF graphs (as a model-theory)– Includes four increasingly expressive semantics:

Simple Entailment, RDF, RDFS, and D-Entailment– Characteristics:

• all RDF graphs are valid and have a semantic meaning• Semantics is defined on the level of RDF triples and sets of triples• all nodes represent resources (aka individuals)

• Semantic Extensions of the RDF Semantics:– Semantics that builds on top of RDF(S) or D-Entailment:

• all parts of semantics of weaker language are reused and extended• Syntax is all RDF graphs

– Example: RDFS is a semantic extension of RDF– Example: OWL 2 Full is a semantic extension of RDFS (or D) 2

Semantic Web Ontology Languages:Syntactic Flexibility vs. Semantic Expressivity

• Unclear: Differences of OWL 2 Full to OWL 2 DL and OWL 2 RL/RDF?• Unclear: Implementability of OWL 2 Full (or any expressive RDF extension)?

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Semantic Expressivity

Synt

actic

Flex

ibili

ty(R

DF)

OWL 2 RL/RDF RDFS OWL 2

Full

OWL 2 DL

OWL Lite

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?

?

OWL 2 Full vs. OWL 2 DL:Enhanced Syntactic Flexibility in RDF

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OWL API 3.2 read/write roundtrip:re-declaration of both propertiesas OWL annotation properties

dcels:title rdf:type rdf:Propertydcterms:title rdf:type rdf:Propertydcterms:title rdfs:subPropertyOf dcels:title

Use of RDF(S) Entity Types

dcels:title rdf:type owl:AnnotationPropertydcterms:title rdf:type owl:AnnotationPropertydcterms:title rdfs:subPropertyOf dcels:title

Result (after read/write roundtrip)

OWL 2 DL tools typically cannot properly deal with every RDF graph:

OWL 2 Full vs. OWL 2 RL/RDF Rules:Enhanced Semantic Expressivity

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RDF entailment rule reasoning not always sufficient:

Vocabulary (GoodRelations):gr:condition rdfs:domain [ owl:unionOf ( gr:Offering gr:ProductOrService ) ] .gr:eligibleRegions rdfs:domain [ owl:unionOf ( gr:Offering gr:DeliveryChargeSpecification) ] . gr:DeliveryChargeSpecification rdfs:subClassOf gr:PriceSpecification .gr:PriceSpecification owl:disjointWith gr:ProductOrService .

Data (invented example):ex:myThingy gr:condition "old but fine"^^xsd:string .ex:myThingy gr:eligibleRegions "de"^^xsd:string .

Expected Result (OWL 2 Full/DL):ex:myThingy rdf:type gr:Offering .

Beyond the OWL 2 RL/RDF rules !

OWL 2 Full vs. OWL 2 DL & RL/RDF Rules:Enhanced Modeling & Reasoning Capabilities

• Metamodelinge.g. reasoning upon zoological hierarchies: Harry → Eagle → Species

• Cyclic relationshipse.g. detection of circular chemical molecules

• Macros, conditional semantics, etc. e.g. custom entity types

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Usage Scenarios for OWL 2 Full Reasoners

• Complementing RDF entailment-rule reasoners:– much stronger in terminological reasoning– RDF rule reasoners advantage: faster, better scalability– fully compatible with RDFS and OWL 2 RL/RDF rules:

OWL 2 Full reasoner can safely operate in parallel

• Complementing description-logic reasoners:– basically compatible due to „correspondence theorem“– robust on weakly-structured data (typical for LOD cloud)– „trans-DL“ reasoning (metamodeling, cyclic structures, …)– DL reasoners advantage: better on valid OWL 2 DL input

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Prior Art in OWL Full Reasoning

• Fikes, McGuinness, Waldinger: A First-Order Logic Semantics for Semantic Web Markup Languages. TR, Stanford, 2002.– translation of specifications of precursers of OWL and RDF into first-order

logic (FOL) theory, and application of FOL reasoners. – focus: checking for technical issues in specifications (less on inferencing)

• Hayes: Translating Semantic Web Languages into Common Logic.TR, Pensacola (Florida), 2005.– translation of OWL 1 Full into Common Logic– no report on reasoning experiments

• Hawke: Surnia. 2003. URL: http://www.w3.org/2003/08/surnia– OWL 1 Full reasoner based on FOL translation using Otter FOL reasoner– did not perform well on W3C OWL 1 test suite– ad hoc implementation: does not properly follow specification; many flaws

Research Questions

1. What are the distinctive features of OWL 2 Full compared to other approaches used forSemantic Web reasoning?

2. To which degree and how can reasoning in OWL 2 Full be implemented?

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Approach

• „Feature Analysis“ (addresses 1st research question):– Building up catalogs of distinctive pragmatic features of OWL 2 Full– „distinctive“: not supported by either OWL 2 DL or OWL 2 RL/RDF rules– will cover both syntactic (parsing) and semantic (reasoning) aspects:

• syntactic aspect example: disjoint annotation properties (SKOS)• semantic aspect example: entailments from metamodeling (vs. „punning“)

• „Implementability Analysis“ (addresses 2nd research question) :– Focus: in-deph investigation of „naive“ FOL translation approach:

• Translation of OWL 2 Full semantics into a first-order logic (FOL) theory• Translation of RDF graphs into FOL formulae• Applying FOL reasoners (theorem provers, model finders) for reasoning

• Evaluation:– Collecting evidence for all identified OWL 2 Full features (empirical)– Evaluating FOL-based reasoner prototype w.r.t. identified features

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Feature Analysis: First Results

• Created: Catalog of syntactic-aspect features for OWL /1/ Full– identified 14 feature categories and 90 features– Example feature: “Anonymous Individuals with Cyclic Relationships”– Example category: “Unrestricted Use of Blank Nodes“

• Usage: Evaluation of ontology engineering tools in EU Project SEALS– per identified feature: created one small example ontology („spot test“)– for each example ontology: analyzed read/write roundtrip for tool under test

• Results:– OWL DL tools (OWL API 3.1, Protege 4, …) had many difficulties:

• almost all test ontologies were changed during read/write roundtrips• in many cases, the changes were significant or even severe

– see SEALS deliverable D-10.3, specifically Appendix A for detailed analysis11

Implementability Analysis: First Results

• Test suite: 32 characteristic OWL 2 Full conclusions („Fullish Testsuite“)– „characteristic“: either OWL 2 DL reasoner or OWL 2 RL/RDF rule reasoner expected to fail– Example test: „{} |= owl:equivalentClass rdfs:subPropertyOf rdfs:subClassOf“

• Results:1. OWL 2 DL reasoner Pellet: 9 correct, 22 wrong, 1 system error2. OWL 2 RL/RDF rule reasoner OWLIM : 9 correct, 23 wrong3. ATP iProver-SInE, complete OWL 2 Full axiomatization: 28 correct, 4 timeouts (median: 5.31s)4. ATP iProver-SInE, small subset of sufficient axioms per test case: all correct (median: 0.08s)

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+ + + - - - - - + + - - - - + - - - - + + - - - - + - - ? - - -

+ - - + - - + + - - + + - - + - - + + - - - - - - - - - - - - -

+ + + + + + + + + + + ? ? + + + + + + ? ? + + + + + + + + + + +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Pellet 2.2.2

BigOWLIM 3.4

iProver 0.8, all axioms

iProver 0.8, sufficient

+ success (termination with correct result)

- failure (termination with wrong result)

? unknown (timeout, system error, etc.)

Conclusions and Future Work

• OWL 2 Full has many distinguishing features and potential benefits

• OWL 2 Full reasoning generally works with FOL reasonersbut there is a serious efficiency issue due to the large FOL axiomatization

Report on the results of all reasoning experiments (to appear):Michael Schneider, Geoff Sutcliffe: Reasoning in the OWL 2 Full Ontology Languageusing First-Order Automated Theorem Proving. CADE 2011.

• FOL-translation approach is very flexible:– applies to arbitrary extension of RDF semantics (including complete RDFS)– enables rule-style extensions (e.g. RIF+OWL-Full combination)

• Future work: finish feature analysis (syntactic and semantic features)

• Future work: address main efficiency issue: method to remove irrelevant axioms

• Future work: investigate query answering (towards SPARQL 1.1) 13

Thank You !

Questions ?

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Backup Slides

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Enhanced Modeling & Reasoning:Metamodeling Example

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Species

GoldenEagleBaldEagle DogTiger

NonEndangeredSpecies= ¬ EndangeredSpecies п Species

Endangered Species= { BaldEagle, Tiger }

Indi

vidu

als

Clas

ses

(mut

ually

disj

oint

)M

eta-

Clas

ses

rdf:t

ype

ex:hasMetaClass owl:propertyChainAxiom ( rdf:type rdf:type )

Harry

Enhanced Modeling & Reasoning:Cyclic Relationship Example

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ex:r owl:propertyChainAxiom ( ex:hasRelative[ owl:inverseOf ex:hasBoss ] ) .

ex:HasRelativeAsBoss owl:equivalentClass [rdf:type owl:Restriction ;owl:onProperty ex:r ;owl:hasSelf "true"^^xsd:boolean ] .

ex:alice ex:hasRelative ex:bob .ex:alice ex:hasBoss ex:bob .|=ex:alice rdf:type ex:HasRelativeAsBoss .

Complex Cycle(Coincidence with

intermediate Nodes)

Basic Cycle(Coincidence with Inverse)

Coin

cide

nces

bobalice

HasRelativeAsBoss

hasRelative

hasBoss

rdf:t

ype

Cycl

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Enhanced Modeling & Reasoning:Macros Example

Premise (Definition and Data)Definition:foaf:Person rdf:type owl:Class .ex:PersonAttribute

owl:intersectionOf (owl:DatatypePropertyowl:FunctionalProperty[ rdf:type owl:Restriction ;owl:onProperty rdfs:domain ;owl:hasValue foaf:Person ] ) .

Data:ex:name rdf:type ex:PersonAttribute .ex:alice ex:name „Alice" .

Expected Conclusionex:name rdf:type owl:DatatypeProperty .ex:name rdf:type owl:FunctionalProperty .ex:alice rdf:type foaf:Person .

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Modeling Aim: Define the „custom entity type“ PersonAttributeas the class of all functional data properties that have class foaf:Person as their domain.

Syntactic-Aspect Feature Categories

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Syntactic Aspect Feature Analysis:Evaluation of OWL API 3.1 (coarse)

• Application of concrete example OWL Full ontologies to OWL API 3.1• Observation: most test ontologies were modified („repaired“)• Note: the differences have been analysed in detail (not shown)

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HR CR TR TC NT ME DP AP DT LT BN CP LS LR

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Syntactic Aspect Feature Analysis:Evaluation of OWL API 3.1 (fine-grained)

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OWL (2) Full Perspective OWL (2) DL Perspective

FOL Translation Approach

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OW

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Reas

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ntai

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ckin

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negatedFOL-Translation of Conclusion Graph

FOL-Translations of Semantic Conditions

FOL Reasoner

(ATP)

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model-theoretic OWL 2 Full semantic condition

corresponding FOL formula (TPTP)

FOL-

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Gra

phs

RDF graph (Turtle)corresponding FOL formula (TPTP)

rdfbased-sem Test Suite:Language Coverage: (no datatypes)

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iProver-SInE 0.8 (sufficient axioms)

iProver-SInE 0.8 (all axioms)

Vampire 0.6 (all axioms)

Parliament 2.6.9 (default config)

Jena 2.6.4 (OWL_MEM_RULE_INF)

BigOWLIM 3.4 (owl2-rl)

FaCT++ 1.5.0 (OWL API 3.1)

HermiT 1.3.2 (OWL API 3.1)

Pellet 2.2.2 (OWL API 3.1)

Success Failure Unknown

rdfbased-sem Test Suite: Performance

Vampire 0.6complete axiomset

iProver-SInE 0.8complete axiomset

min 0.01 s 0.05 s

max N/A N/A

max succ 27.57 s 278.71 s

Q1 (1st quantil) 0.03 s 0.09 s

Q2 (median) 0.35 s 0.29 s

Q3 (3rd quantil) 0.56 s 5.21 s

mean succ 0.42 s 14.59 s

StD succ 2.06 s 36.45 s24

Fullish Testsuite Evaluation Results: Selected Semantic Web Reasoners

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Hermit 1.3.2

Fact++ 1.5.0

BigOWLIM 3.4 (owl2-rl)

Jena 2.6.4 (OWL)

Parliament (default)

+ success (termination with correct result)

- failure (termination with wrong result)

? unknown (timeout, system error, unsupported, etc.)

Fullish Testsuite Evaluation Results:ATPs on small sufficient Axiomsets

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Equinox 5.0

iProver 0.8

Metis 2.3

Prover9 0908

SPASS 3.5

Vampire 0.6

+ success (termination with correct result)

- failure (termination with wrong result)

? unknown (timeout, system error, unsupported, etc.)

Fullish Test Suite: Performance

iProver-SInE 0.8complete axiomset

iProver-SInE 0.8small axiomsets

iProver-SInE 0.81M bulk RDF data

min 0.08 s 0.04 s 21.73 s

max N/A 164.20 s N/A

max succ 123.01 s 164.20 s 63.10 s

Q1 (1st quantil) 0.72 s 0.05 s 21.91 s

Q2 (median) 5.31 s 0.08 s 22.07 s

Q3 (3rd quantil) 89.45 s 0.14 s 22.50 s

mean succ 30.63 s 7.82 s 24.76 s

StD succ 43.41 s 29.82 s 10.02 s 27

Model-Finding Experiments• Task: Detection of consistency of ontologies and non-entailments• Prerequisite: detection of satisfiability for whole axiomatization

Results (Summary):• OWL 2 Full:

– No FOL model-finder confirmed satisfiability of axiomatization (timeouts) – Fortunately: no theorem prover confirmed unsatisfiability! – Good: all „small-sufficient“ sub-axiomatizations of test cases satisfiable!

• ALCO Full (undecidable fragment of OWL 2 Full [Motik05]):– Consistency checking for axiomatization successful ! – Non-entailment checking often successful ! (but still some failures)– Performance: median ~18s with model-finder Paradox

• RDFS (actually: RDFS-EXT, Sec. 4.2 of RDF Semantics): – Consistency and non-entailment checking always successful ! – pretty fast: ~1/10s for most experiments with model-finder DarwinFM

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Model-Finding Experiments:Consistency / Non-Entailment Detection

Language: RDFS-EXTTestsuite: Fullish

ATP: DarwinFM 1.4.5

Language: ALCO FullTestsuite: FullishATP: Paradox 4.0

min 0.01 s 8.21 s

max 7.35 s N/A

max succ 7.35 s 89.21 s

Q1 (1st quantil) 0.05 s 13.60 s

Q2 (median) 0.07 s 17.62 s

Q3 (3rd quantil) 0.12 s N/A

mean succ 0.71 s 19.18 s

StD succ 1.86 s 18.99 s29