Uncertainty Treatment in the Rule Interchange Format: From Encoding to Extension Jidi Zhao1, HHldarold BlBoley2 1 Faculty of Computer Science, University of New Brunswick, FdiFredericton, NB, E3B 5AC, Cana da Judy.Zhao AT unb.ca 2 Institute for Information Technology, National Research Council of Canada, Fredericton, NB, E3B 9W4 Canada Harold.Boley AT nrc.gc .ca Talk Outline • Introduction and Motivation • DLP and Representation in RIF • Encoding Uncertainty in RIF • Fuzzy LP • Using RIF Functions • 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 Work 2 Semantic Web Layer Cake User Interface & Applications Trust Proof Unifying Logic Encr Sign SPA Ontology: OWL Rules: RIF y a RQL ption ture RDFS RDF XML 3 IRI/Unicode RIF Background z Literally hundreds of rule system ilimplemen ttitations z RIF: Rule Interchange Format z RIF defines z a basic logic dialect: RIF-BLD z a framework in the form of a menu of syntactic and semantic features that can be combined into different specializations: RIF- FLD z other spec ia liza tions 4 Mooaotivation z DL and LP cover different but overlapping areas of knowledggpe representation 5 Mooaotivation z DL and LP cover different but overlilapping areas o fkldf knowledge representation z DL cannot represent “more than one free variable at a time” z LP/Horn Logic cannot represent a disjunction or an existential in the head 6 Mooaotivation z DL and LP cover different but overlapping areas ofkf knowl e dge represen ta tion z Handling uncertain knowledge is bibecoming a cr itilhditifitical research direction for the (Semantic) Web 7 Talk Outline • Introduction and Motivation • DLP and Representation in RIF • Encoding Uncertainty in RIF • Fuzzy LP • Using RIF Functions • 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 Work 8 DLP Expressive Power and DLP mappings 9 DLP •Figure . Relationship between the fragments (profiles) of OWL 1.1 •http://www.webont.org/owl/1.1/tractable.html 10 DLP comprises basic RDFS & more •RDFS subset of DL permits the following stttatement s: •Subclass, Domain, Range, Subproperty (also SameClass, SameProperty) •instance of class, instance of property •more DL statements beyond RDFS: •Intersection in class descriptions •Transitive or symmetric property, inverse property •Disjunction or Existential in a subclass expression •Universal in a superclass expression 11 DLP limitations •Does not allow using disjunction or existential in a superclass expression. EgE.g., CvD1tD2, Cv∃PDP.D •A universal restriction as a subclass of an iliinclusion ax iom E.g. ∀P.DvC •Negation (¬) and cardinality restrictions (≤,≥) 12 OWL 2 RL •Created by W3C OWL Working Group •Is a syntactic profile of OWL 2 DL •Based on Description Logic Programs (DLP) •Syntactic restrictions •http:// www.w3 .org/2007/OWL/ wiki/P rofil es#OWL _2 _RL 13 RIF-BLD Overview z Definite Horn rules z Functions z Equality (in conclusion and condition) z Internationalized resource identifiers (IRIs) z XML syntax z Presentation syntax z Pu blis he d “Las t Ca ll” dra ft in Ju ly z Slides 14-17 are adapted from Chris Welty’s talk on RIF-BLD 14 Rules z IF <con dition> THEN <conc lus ion> z <condition> aka rule body, antecedant z <conclilusion> a ka ru lhdle head, consquen t z BLD rule: z FllForall var*(* (<conc lus ion> :- <condition> ) z Conclusions may contain conjunction z Conditions may contain conjunction , disjunction, and existential z Restrictions on conclusion z No existential, disjunction, external functions 15 Document Structure (in presentation syntax) z Groups occur in Documents z Document( z Group(Forall ?x (Q(?x) :- P(?x)) z Forall ?x (((Q(?x) :- R(?x))) z Group(Forall ?y (R(?y) :- ex:op(?y)))) z Rules occur in Groups z Group(Forall ?x (Q(?x) :- P(?x)) z Forall ?x (Q(?x) :- R(?x)) ) 16 DLP in RIF 17 Talk Outline • Introduction and Motivation • DLP and Representation in RIF • Encoding Uncertainty in RIF • Fuzzy LP • Using RIF Functions • 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 Work 18 Fuzzy LP •Syntax of a fuzzy rule •StiSemantics •The body: Gödel’s semantics •The imppplication: product 19 Fuzzy LP example: cheapFlight 20 Encoding Uncertainty in RIF: Using RIF Functions •Mappp all predicates to functions •Use equality for letting the functions return uncertainty values •A fuzzy rule in RIF-BLD •The semantics of the fuzzy rules is encoded using built-in functions from RIF_DTB and planned extensions 21 Example cheapFlight encoded in RIF-BLD 22 Encoding Uncertainty in RIF: UiUsing RIFPRIF Pre ditdicates •Make all n-ary predicates into (1+n)-ary predicates •A fuzzy rule in RIF-BLD •The semantics of the fuzzy rules is also encode d us ing bu ilt-in func tions f rom RIF _DTB and planned extensions 23 Example cheapFlight encoded in RIF-BLD 24 Talk Outline • Introduction and Motivation • DLP and Representation in RIF • Encoding Uncertainty in RIF • Fuzzy LP • Using RIF Functions • 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 Work 25 UUceancertaint y Ext esooension of RIF •Set of Truth Values TV from FLD: the in terva l[01]l [0,1] •Let ≤ denote the numerical truth order 26 Uncertainty Extension of RIF •Truth Valuation 27 RIF Uncertainty Rule Dialect: URD •Proposed RIF-URD •Rule •Fact 28 Talk Outline • Introduction and Motivation • DLP and Representation in RIF • Encoding Uncertainty in RIF • Fuzzy LP • Using RIF Functions • 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 Work 29 fhDLP •Mappings in fhDLP 30 fhDLP Semantics 31 fhDLP in RIF functions, RIF predicates and RIF-URD 32 Talk Outline • Introduction and Motivation • DLP and Representation in RIF • Encoding Uncertainty in RIF • Fuzzy LP • Using RIF Functions • 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 Work 33 Conclusions •Presented two different principles of encoding uncertainty in RIF-BLD •Proposed an extension of RIF lditRIFleading to RIF-URD •Presented fhDLP, a fuzzy extension to Description Logic Programs 34 Future Work •Parameterize RIF-URD to support different theories of uncertainty in a unified manner •Complement RIF-URD presentation syntax with RIF-URD XML syntax •Exppglore further combination strategies of DL and LP 35 Questions?.