Uncertainty Treatment in the Rule Uncertainty Treatment in the Rule Interchange Format:

From Encoding to ExtensionJidi Zh 1 H ld B l 2Jidi Zhao1, Harold Boley2

1 Faculty of Computer Science, University of New Brunswick, F d i NB E3B 5AC C dFredericton, NB, E3B 5AC, Canada

Judy.Zhao AT unb.ca

2 Institute for Information Technology National Research 2 Institute for Information Technology, National Research Council of Canada, Fredericton, NB, E3B 9W4 Canada

Harold Boley AT nrc gc caHarold.Boley AT nrc.gc.ca

Talk OutlineTalk Outline• Introduction and Motivation• DLP and Representation in RIF • Encoding Uncertainty in RIF• Encoding Uncertainty in RIF

• Fuzzy LP• Using RIF Functionsg• Using RIF Predicates

• Uncertainty Extension of RIF• Definition of Truth Values and Truth Valuation• Proposed RIF-URD

• Fuzzy Description Logic Programs and Their Representation in RIF

• Conclusions and Future Work2

Semantic Web Layer CakeSemantic Web Layer CakeUser Interface & Applications

Trust

Unifying Logic

Proof

Rules: RIF

Unifying Logic

EncryOntology: OWL

SPA

Signa

RDF

yption

RQ

L

atureRDFS

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RDF

XML3

IRI/Unicode

RIF BackgroundRIF BackgroundLiterally hundreds of rule system i l t tiimplementationsRIF: Rule Interchange FormatRIF defines

a basic logic dialect: RIF-BLDga framework in the form of a menu of syntactic and semantic features that can be ycombined into different specializations: RIF-FLD

th i li tiother specializations

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Motivation o a oDL and LP cover different but overlapping areas of knowledge representationg p

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Motivationo a oDL and LP cover different but

l i f k l doverlapping areas of knowledge representationDL cannot represent “more than one free variable at a time”free variable at a timeLP/Horn Logic cannot represent a disjunction or an existential in thedisjunction or an existential in the head

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Motivation o a o

DL and LP cover different but overlapping f k l d t tiareas of knowledge representation

Handling uncertain knowledge is b i iti l h di ti fbecoming a critical research direction for the (Semantic) Web

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Talk OutlineTalk Outline• Introduction and Motivation• DLP and Representation in RIF • Encoding Uncertainty in RIF• Encoding Uncertainty in RIF

• Fuzzy LP• Using RIF Functionsg• Using RIF Predicates

• Uncertainty Extension of RIF• Definition of Truth Values and Truth Valuation• Proposed RIF-URD

• Fuzzy Description Logic Programs and Their Representation in RIF

• Conclusions and Future Work8

DLP Expressive Power and DLP mappings

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DLP

•Figure . Relationship between the fragments (profiles) of OWL 1.1•http://www.webont.org/owl/1.1/tractable.html

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DLP comprises basic RDFS & morep•RDFS subset of DL permits the following t t tstatements:

•Subclass, Domain, Range, Subproperty (also SameClass SameProperty)SameClass, SameProperty)•instance of class, instance of property

•more DL statements beyond RDFS:more DL statements beyond RDFS:•Intersection in class descriptions•Transitive or symmetric property, inverse

tproperty•Disjunction or Existential in a subclass expressionexpression•Universal in a superclass expression

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DLP limitations

•Does not allow using disjunction or existentialDoes not allow using disjunction or existential in a superclass expression.

E g CvD tD Cv∃P DE.g., CvD1tD2, Cv∃P.D•A universal restriction as a subclass of an i l i iinclusion axiom

E.g. ∀P.DvC•Negation (¬) and cardinality restrictions (≤,≥)

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OWL 2 RLOWL 2 RL

•Created by W3C OWL Working Group•Created by W3C OWL Working Group•Is a syntactic profile of OWL 2 DL•Based on Description Logic Programs (DLP)(DLP)•Syntactic restrictionshtt // 3 /2007/OWL/ iki/P fil #OWL 2 RL•http://www.w3.org/2007/OWL/wiki/Profiles#OWL_2_RL

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RIF BLD OverviewRIF-BLD OverviewDefinite Horn rules FunctionsEquality (in conclusion and condition)Equality (in conclusion and condition)Internationalized resource identifiers (IRIs)XML syntaxXML syntaxPresentation syntaxP bli h d “L t C ll” d ft i J lPublished “Last Call” draft in JulySlides 14-17 are adapted from Chris Welty’s talk on RIF-BLD

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RulesRulesIF diti THEN l iIF <condition> THEN <conclusion>

<condition> aka rule body, antecedantl i k l h d t<conclusion> aka rule head, consquent

BLD rule:F ll * ( l i diti )Forall var* (<conclusion> :- <condition>)Conclusions may contain conjunctionConditions may contain conjunction disjunction andConditions may contain conjunction, disjunction, and existential

Restrictions on conclusionRestrictions on conclusionNo existential, disjunction, external functions

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Document Structure (in presentation syntax)

Groups occur in DocumentsDocument(

Group(Forall ?x (Q(?x) :- P(?x))Forall ?x (Q(?x) :- R(?x)))( ( ) ( )))

Group(Forall ?y (R(?y) :- ex:op(?y))))

Rules occur in GroupsRules occur in GroupsGroup(Forall ?x (Q(?x) :- P(?x))

Forall ?x (Q(?x) : R(?x)) )Forall ?x (Q(?x) :- R(?x)) )

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DLP in RIF

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Talk OutlineTalk Outline• Introduction and Motivation• DLP and Representation in RIF • Encoding Uncertainty in RIF• Encoding Uncertainty in RIF

• Fuzzy LP• Using RIF Functionsg• Using RIF Predicates

• Uncertainty Extension of RIF• Definition of Truth Values and Truth Valuation• Proposed RIF-URD

• Fuzzy Description Logic Programs and Their Representation in RIF

• Conclusions and Future Work18

Fuzzy LPFuzzy LP•Syntax of a fuzzy ruleSyntax of a fuzzy rule

S ti•Semantics•The body: Gödel’s semanticsy

•The implication: productp p

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Fuzzy LP example: cheapFlightFuzzy LP example: cheapFlight

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Encoding Uncertainty in RIF:Using RIF FunctionsUsing RIF Functions

•Map all predicates to functionsp p•Use equality for letting the functions return uncertainty valuesy•A fuzzy rule in RIF-BLD

•The semantics of the fuzzy rules is encodedThe semantics of the fuzzy rules is encoded using built-in functions from RIF_DTB and planned extensions

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planned extensions

Example cheapFlight encoded in RIF-BLDg

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Encoding Uncertainty in RIF:U i RIF P di tUsing RIF Predicates

•Make all n ary predicates into (1+n) ary•Make all n-ary predicates into (1+n)-ary predicatesA fuzzy rule in RIF BLD•A fuzzy rule in RIF-BLD

•The semantics of the fuzzy rules is also d d i b ilt i f ti f RIF DTBencoded using built-in functions from RIF_DTB

and planned extensions

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Example cheapFlight encoded inExample cheapFlight encoded in RIF-BLD

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Talk OutlineTalk Outline• Introduction and Motivation• DLP and Representation in RIF • Encoding Uncertainty in RIF• Encoding Uncertainty in RIF

• Fuzzy LP• Using RIF Functionsg• Using RIF Predicates

• Uncertainty Extension of RIF• Definition of Truth Values and Truth Valuation• Proposed RIF-URD

• Fuzzy Description Logic Programs and Their Representation in RIF

• Conclusions and Future Work25

Uncertainty Extension of RIFU ce a y e s o o•Set of Truth Values TV from FLD:

th i t l [0 1]the interval [0,1]•Let ≤ denote the numerical truth order

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Uncertainty Extension of RIFUncertainty Extension of RIF

•Truth Valuation•Truth Valuation

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RIF Uncertainty Rule Dialect: URDy

•Proposed RIF-URDProposed RIF URD•Rule•Fact•Fact

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Talk OutlineTalk Outline• Introduction and Motivation• DLP and Representation in RIF • Encoding Uncertainty in RIF• Encoding Uncertainty in RIF

• Fuzzy LP• Using RIF Functionsg• Using RIF Predicates

• Uncertainty Extension of RIF• Definition of Truth Values and Truth Valuation• Proposed RIF-URD

• Fuzzy Description Logic Programs and Their Representation in RIF

• Conclusions and Future Work29

fhDLP•Mappings in fhDLP

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fhDLP

S

fhDLP

Semantics

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fhDLP in RIF functions,,RIF predicates and RIF-URD

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Talk OutlineTalk Outline• Introduction and Motivation• DLP and Representation in RIF • Encoding Uncertainty in RIF• Encoding Uncertainty in RIF

• Fuzzy LP• Using RIF Functionsg• Using RIF Predicates

• Uncertainty Extension of RIF• Definition of Truth Values and Truth Valuation• Proposed RIF-URD

• Fuzzy Description Logic Programs and Their Representation in RIF

• Conclusions and Future Work33

Conclusions•Presented two different principles of encoding uncertainty in RIF-BLD

•Proposed an extension of RIF l di t RIF URDleading to RIF-URD

•Presented fhDLP, a fuzzy extension to Description Logic Programsto Description Logic Programs

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Future Work

•Parameterize RIF-URD to support ppdifferent theories of uncertainty in a unified mannerunified manner

•Complement RIF URD presentation•Complement RIF-URD presentation syntax with RIF-URD XML syntax

•Explore further combination strategies p gof DL and LP

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Questions?