Rules & Ontologies OWL 2 RL & SWRL Description Logic ... - LPIS

Rules & OntologiesDescription Logic Programs (DLP)4-1OWL 2 RL & SWRLRules & OntologiesA Semantic Web Primer, 3rd Edition4-2• Horn logic (rules) and description logics (ontologies) areorthogonal• The simplest integration approach is the intersection ofboth logics– The part of one language that can be translated in a semanticspreservingway to the other• OWL2 RL capture this fragment of OWL (previouslycalled Description Logic Programs - DLP)– Horn-definable part of OWL, or– OWL-definable part of Horn logicRules & OntologiesA Semantic Web Primer, 3rd EditionOWL 2 RLOpen-World Assumption (OWA)• OWL 2 is based on Description Logic.– A fragment of first-order logic– Inherits open-world assumption and non-uniquenameassumption• OWL 2 RL is an interesting sublanguage g ofOWL 2 DL– Above assumptions do not make a difference• We cannot conclude some statement x to befalse simply because we cannot show x to betrue.• The opposite assumption (closed world, CWA)would allow deriving falsity from the inability toderive truth.• OWL is strictly committed to the OWA– In some applications is not the right choice4-3Rules & OntologiesA Semantic Web Primer, 3rd Edition4-4Rules & OntologiesA Semantic Web Primer, 3rd Edition1

OWA vs. CWAExamplesUnique-Name Αssumption (UNA)4-5• Example in favor of OWA– Question: “Did it rain in Tokyo yesterday?”– Answer: “I don’t know that it rained, but that’s notenough reason to conclude that it didn’t rain.”• Example in favor of CWA– Question: “Was there a big earthquake disaster inTokyo yesterday?”– Answer: “I don’t know, but if there had been such adisaster, I’d have heard about it. Therefore I concludethat there wasn’t such a disaster.”Rules & OntologiesA Semantic Web Primer, 3rd Edition4-6• When two individuals are known by differentnames, they are in fact different individuals.– Sometimes works well and sometimes not• In favor: when two products in a catalog are knownby different codes, they are different• Against: two people in our social environmentinitially known with different identifiers (e.g., “Prof.van Harmelen” and “Frank”) are sometimes thesame personRules & OntologiesA Semantic Web Primer, 3rd EditionUnique-Name Αssumption (UNA)CWA vs. OWA• OWL does not make the unique-nameassumption• It is possible to explicitly assert of a set ofidentifiers that they are all unique– using owl:allDifferente • Databases and logic-programming systemssupport closed worlds and unique names• Knowledge representation systems andtheorem provers support open worlds andnon-unique names• Ontologies are sometimes in need of oneand sometimes in need of the other.– Big debate in the literature4-7Rules & OntologiesA Semantic Web Primer, 3rd Edition4-8Rules & OntologiesA Semantic Web Primer, 3rd Edition2

OWL 2 RLOWL 2 RL Advantages (1/2)• Debate resolved by OWL 2 RL• The largest fragment of OWL 2 on which thechoice for CWA and UNA does not matter– OWL 2 RL is weak enough so that the differencesbetween the choices don’t show up.– Still large enough to enable useful representationand reasoning tasks.• Applications that wish to make differentchoices on these assumptions (CWA, UNA,etc) can still exchange ontologies in OWL 2RL without harm.• Outside OWL 2 RL, they will draw differentconclusions from the same statements.– They disagree on the semantics.4-9Rules & OntologiesA Semantic Web Primer, 3rd Edition4-10Rules & OntologiesA Semantic Web Primer, 3rd EditionOWL 2 RL Advantages (2/2)OWL 2 RL constructs• Freedom to use either OWL 2 or rules (and associatedtools and methodologies) for modeling purposes• Description logic reasoners or deductive rule systemscan be used for implementation.– Extra flexibility - interoperability with tools• Preliminary experience with using OWL 2 has shownthat existing ontologies frequently use very fewconstructs outside the OWL 2 RL language.• Which constructs of RDF Schema and OWL 2can be expressed in Horn logic?– They lie within the expressive power of DLP• Some constructs cannot be expressed4-11Rules & OntologiesA Semantic Web Primer, 3rd Edition4-12Rules & OntologiesA Semantic Web Primer, 3rd Edition3

Allowed OWL constructors• Class and property equivalence• Equality- inequality between individuals• Inverse, transitive, symmetric and functionalproperties• Intersection of classes• Excluded constructors– Union, existential quantification, and arbitrarycardinality constraints4-13Rules & OntologiesA Semantic Web Primer, 3rd EditionSimple RDF constructs• A triple (a, P, b) is expressed as a fact P(a, b)• An instance declaration type(a,C),– a is an instance of class C– expressed as C(a)• C is a subclass of DC(X) → D(X)• Similarly for subpropertyP(X,Y) → Q(X,Y)4-14Rules & OntologiesA Semantic Web Primer, 3rd EditionMore RDF Constructs• Domain and Range Restrictions– C is the domain of property PP(X, Y) → C(X)– C’ is the range of property PP(X, Y) → C’(Y) C(Y)OWL Constructs• equivalentClass(C,D)– pair of rulesC(X) → D(X)D(X) → C(X)• Similarly for equivalentProperty(P,Q)P(X,Y) → Q(X,Y)Q(X,Y) → P(X,Y)4-15Rules & OntologiesA Semantic Web Primer, 3rd Edition4-16Rules & OntologiesA Semantic Web Primer, 3rd Edition4

More OWL ConstructsUnion (1)4-17• Transitive PropertiesP(X, Y ), P(Y,Z) → P(X,Z)• Boolean operators.– The intersection of C1 and C2 is a subclass of DC1(X), C2(X) → D(X)– C is a subclass of the intersection of D1 and D2C(X) → D1(X) C(X) → D2(X)– the opposite is outside the expressive power of HornlogicRules & OntologiesA Semantic Web Primer, 3rd Edition4-18• The union of C1 and C2 is a subclass of DC1(X) → D(X) C2(X) → D(X)• The opposite direction is outside theexpressive power of Horn logic.– To express that C is a subclass of the union of D1and D2 would require a disjunction in the head ofthe corresponding ruleRules & OntologiesA Semantic Web Primer, 3rd EditionUnion (2)OWL Restrictions allValuesFrom• There are cases where the translation ispossible– when D1 is a subclass of D2, then the ruleC(X) → D2(X)– is sufficient to express that C is a subclass of theunion of D1 and D2• There is not a translation that works in allcases• allValuesFrom(P,D)– the anonymous class of all x such that y must be aninstance of D whenever P(x, y)• C subClassOf allValuesFrom(P,D)C(X),P(X,Y)→ D(Y)• The opposite direction cannot in general beexpressed4-19Rules & OntologiesA Semantic Web Primer, 3rd Edition4-20Rules & OntologiesA Semantic Web Primer, 3rd Edition5

OWL Restrictions someValuesFromNon-expressible constructs• someValuesFrom(P,D)– the anonymous class of all x for which there existsat least one y instance of D, such that P(x, y).• someValuesFrom(P,D) subClassOf CP(X,Y), D(Y) → C(X)• The opposite direction cannot in general beexpressed.• Cardinality constraints and Complement ofclasses cannot be expressed in Horn logic inthe general case.4-21Rules & OntologiesA Semantic Web Primer, 3rd Edition4-22Rules & OntologiesA Semantic Web Primer, 3rd EditionOWL 2 RL – ConclusionsSemantic Web Rules Language(SWRL)• Allowed constructors allow usefulexpressivity for many practical cases• Guarantees correct interchange betweenOWL reasoners independent of CWA andUNA• Allows for translation into efficientlyimplementable reasoning techniques basedon databases and logic programs• A proposed Semantic Web languagecombining OWL 2 DL with function-free Hornlogic, written in Datalog RuleML• It allows Horn-like rules to be combined withOWL 2 DL ontologies.4-23Rules & OntologiesA Semantic Web Primer, 3rd Edition4-24Rules & OntologiesA Semantic Web Primer, 3rd Edition6

Rules in SWRLRule Heads4-25• B 1 , …,B n → A 1 , …,A m• commas denote conjunction on both sides ofthe arrow• A 1 , …,A m ,B 1 , …,B n can be– C(x), P(x, y), sameAs(x, y), differentFrom(x,y),– C is an OWL description, P is an OWL property,– x, y are Datalog variables, OWL individuals, orOWL data values.Rules & OntologiesA Semantic Web Primer, 3rd Edition4-26• If the head of a rule has more than one atomthe rule can be transformed to an equivalentset of rules with one atom in the head in astraightforward way– conjunction of atoms without shared variables• A(X,Y)→ B(X),C(Y)– A(X,Y)→ B(X)– A(X,Y)→ C(Y)Rules & OntologiesA Semantic Web Primer, 3rd EditionComplexity of SWRLSWRL vs. OWL 2 RL4-27• Arbitrary OWL expressions (e.g. restrictions),can appear in the head or body of a rule.• This adds significant expressive power toOWL, but at the high price of undecidability• There can be no inference engine that drawsexactly the same conclusions as the SWRLsemantics.Rules & OntologiesA Semantic Web Primer, 3rd Edition4-28• OWL 2 RL tries to combine the advantages of bothlanguages in their common sublanguage• SWRL takes a more maximalist approach and unitestheir respective expressivities.• The challenge is to identify sublanguages of SWRL thatfind the right balance between expressive power andcomputational tractability.– A candidate is the extension of OWL DL with DL-safe rules– Every variable must appear in a non-description logic atom in the rulebodyRules & OntologiesA Semantic Web Primer, 3rd Edition7

Example SWRL Rules:ReclassificationExample SWRL Rules:Property Value Assignment4-29Man(?m) → Person(?m)– Possible in OWL - subclassOf relation– Some rules are OWL syntactic sugarPerson(?m) hasSex(?m,male) → Man(?m)– Possible in OWL – hasValue (sufficient) restriction– Not all such reclassifications are possible in OWLRules & OntologiesA Semantic Web Primer, 3rd Edition4-30hasParent(?x, ?y) hasBrother(?y, ?z)→ hasUncle(?x, ?z)– Property chaining– Possible in OWL 2 - Not possible in OWL 1.0Person(?p) hasSibling(?p,?s) Man(?s)→ hasBrother(?p,?s)– Not possible in OWLRules & OntologiesA Semantic Web Primer, 3rd EditionExample SWRL Rules:Named IndividualsExample SWRL Rules:Built-insPerson(Fred) hasSibling(Fred, ?s) Man(?s)→ hasBrother(Fred, ?s)Person(?p) hasAge(?p,?age) swrlb:greaterThan(?age,17)→ Adult(?p)• Built-insins dramatically increase expressivity– most rules are not expressible in OWL 1– Some built-ins can be expressed in OWL 24-31Rules & OntologiesA Semantic Web Primer, 3rd Edition4-32Rules & OntologiesA Semantic Web Primer, 3rd Edition8

Example SWRL Rules:String Built-insPerson(?p) hasNumber(?p, ?number) swrlb:startsWith(?number, "+")→ hasInternationalNumber(?p, true)Example SWRL Rules:Built-ins / Argument BindingPerson(?p) hasSalaryInPounds(?p, ?pounds) swrlb:multiply(?dollars, ?pounds, 2.0)→ hasSalaryInDollars(?p, ?dollars)Person(?p) hasSalaryInPounds(?p, ?pounds) swrlb:multiply(2.0, ?pounds, ?dollars)→ hasSalaryInDollars(?p, ?dollars)4-33Rules & OntologiesA Semantic Web Primer, 3rd Edition4-34– Arguments can bind in any position– Usually implementations support binding of the 1 st argRules & OntologiesA Semantic Web Primer, 3rd EditionCan define new Built-in LibrariesSWRLTab Built-in Librarieshttp://protege.cim3.net/cgibin/wiki.pl?SWRLTabBuiltInLibraries4-35• Temporal built-ins:– temporal:before("1999-11-01T10:00", "2000-02-01T11:12:12.000")– temporal:duration(2, "1999-11-01", "2001-02-01",temporal:Years)• • TBox built-ins: ins:– tbox:isDatatypeProperty(?p)– tbox:isDirectSubPropertyOf(?sp, ?p)• • Mathematical built-ins:– swrlm:eval(?circumference, "2 * pi * r", ?r)Rules & OntologiesA Semantic Web Primer, 3rd Edition4-36Rules & OntologiesA Semantic Web Primer, 3rd Edition9

SWRL and Open World Semantics:sameAs, differentFromSWRL is Monotonic:does not Support Negated Atoms4-37Publication(?p) hasAuthor(?p, ?y) hasAuthor(?p, ?z) differentFrom(?y, ?z)→ cooperatedWith(?y, ?z)• Like OWL, SWRL does not adopt the uniquename assumption– Individuals must also be explicitly stated to bedifferent (using owl:allDifferents restriction)Rules & OntologiesA Semantic Web Primer, 3rd Edition4-38Person(?p) not hasCar(?p, ?c)→ CarlessPerson(?p)• Not possible - language does not supportnegation here• Potential invalidation - what if a person latergets a car?Rules & OntologiesA Semantic Web Primer, 3rd EditionSWRL is Monotonic:retraction (or modification) not supportedSWRL is Monotonic:counting not supported4-39Person(?p) hasAge(?p,?age) swrlb:add(?newage, ?age,1)→ hasAge(?p, ?newage)• Incorrect:– will run forever and attempt to assign an infinitenumber of values to hasAge property• There is no retraction of old value– Even if there was, it would run foreverRules & OntologiesA Semantic Web Primer, 3rd Edition4-40Publication(?p) hasAuthor(?p,?a) → SingleAuthorPublication(?p)• Not expressible - open world applies• Potential invalidation - what if author isadded later?Rules & OntologiesA Semantic Web Primer, 3rd Edition10

SWRLTabSWRLTab Wiki :http://protege.cim3.net/cgi-bin/wiki.pl?SWRLTab4-41• A Protégé-OWL development environment forworking with SWRL rules• Supports editing and execution of rules• Extension mechanisms to work with third-partyrule engines• Mechanisms for users to define built-in methodlibraries• Supports querying of ontologiesRules & OntologiesA Semantic Web Primer, 3rd Edition4-42Rules & OntologiesA Semantic Web Primer, 3rd EditionWhat is the SWRL Editor?SWRL Editor• The SWRL Editor is an extension to Protégé-OWL that permits the interactive editing ofSWRL rules.• The editor can be used to create SWRLrules, edit existing SWRL rules, and read andwrite SWRL rules.• It is accessible as a tab within Protégé-OWL.4-43Rules & OntologiesA Semantic Web Primer, 3rd Edition4-44Rules & OntologiesA Semantic Web Primer, 3rd Edition11

RIF – use of frames4-49Rules & Ontologies• An actor is a movie star ifhe has starred in more than3 successful movies,produced in a span of atleast 5 years.• A film is consideredsuccessful if it has receivedcritical acclaim (e.g. rating>8) or was financiallysuccessful (produced>$100M in ticket sales).• These rules should beevaluated against theDBpedia data set.A Semantic Web Primer, 3rd Edition4-50• The use of frames has a long tradition in OOlanguages and knowledge representation,– Has also been prominent in rule languages (e.g.FLogic).• The basic idea is to represent objects asframes, and their properties as slots.– E.g., a class professor with slots name, office, phone,department etc.oid[slot1 -> value1 … slotn -> valuen]Rules & OntologiesA Semantic Web Primer, 3rd Edition4-51Compatibility with RDF and OWL• The basic idea of combining RIF with RDF isto represent RDF triples using RIF frameformulas• A triple s p o is represented as s[p -> o]• Exampleex:GoneWithTheWind ex:FilmYear ex:1939ex:GoneWithTheWind[ex:FilmYear -> ex:1939]Rules & OntologiesA Semantic Web Primer, 3rd Edition4-52Inference in RIF and RDF• RIF rule: the Hollywood Production Code was in placebetween 1930 and 1968Group(Forall ?Film (If And( ex:?Film[ex:Year -> ?Year]External(pred:dateGreaterThan(?Year 1930))External(pred:dateGreaterThan(1968 ?Year)))Then ?Filmex:HollywoodProductionCode -> ex:True]))• Conclusionex:GoneWithTheWind[ex:HollywoodProductionCode -> ex:True]RIFex:GoneWithTheWind ex:HollywoodProductionCode ex:TrueRDF Rules & Ontologies A Semantic Web Primer, 3rd Edition13

4-53Rule Markup Language (RuleML)• RuleML is an effort to develop markup of rules on the Web.• It is a family of rule languages, corresponding to differentkinds of rule languages:– derivation rules, integrity constraints, reaction rules, …• The kernel of the RuleML family is Datalog– function-free Horn logic• RuleML is experimental– studies various features of rule languages that are far from beingstandardized (e.g. nonmonotonic rules)• These efforts may feed into future standards– RuleML results were important in the development of RIFRules & OntologiesA Semantic Web Primer, 3rd Edition4-54discountcustomerproduct7.5 percentpremiumcustomerluxuryproductRules & OntologiesThe discount for acustomer buyinga product is 7.5%if the customer ispremium and theproduct is luxuryA Semantic Web Primer, 3rd EditionSWRL andRuleML• SWRL is anextension ofRuleMLbrother(X,Y) childOf(Z,Y) uncle(X,Z)4-55Rules & OntologiesA Semantic Web Primer, 3rd Edition14