Mapping Guide Mapping Ontologies and Data Sets in RDF/RDFS/OWL2 Michel Böhms

Basic Assumptions A “Mapping” is a set of one or more Mapping Rules relating two ontologies and their data sets bi-directionally These Mappings are just like the ontologies/data sets to be mapped, “Mapping Ontologies” fully described using RDF/RDFS/OWL2 following the same V-Con Modelling Guide Not bound to a particular software tool Not bound to a particular semantics/format (i.e. like MS Excel file format) Making full use of interoperable and well-defined RDF/RDFS/OWL2 semantics and Turtle syntax Enabling inferred information from asserted information via standard reasoners (instead of dedicated transformation software tools) January 22, 2015 Michel Böhms Mapping Guide 2

Relevant dimensions Three key Meta concepts: Classes (owl:Class) Properties (owl:DatatypeProperty & owl:ObjectProperty) Individuals (owl:NamedIndividual) 11 “Venn situations” 5 for classes, same 5 for properties, 1 other for individuals Three Semantic levels (for classes) Asserted versus Inferred information January 22, 2015 Michel Böhms Mapping Guide 3

Assume 2 ontologies: x and y x, y prefixes for name space URIs asserted or inferred 1 Class A in ontology x, x:A 1 Class B in ontology y, y:B 1 Property in ontology x: x:c 1 Property in ontology y: y:d 1 Individual in ontology x: x:a 1 Individual in ontology y: y:b January 22, 2015 Michel Böhms Mapping Guide 4

5 Venn situations for classes The “default”, unconstrained. Independent classes, no mapping rule relevant x:A rdfs:subClassOf y:B y:B rdfs:subClassOf x:A x:A rdfs:subClassOf y:B AND y:B rdfs:subClassOf x:A Same as: x:A owl:EquivalentClass y:B [] rdf:type owl:AllDisjointClasses ; owl:members ( x:A y:B ). No mapping rule relevant (only for ‘negative’ info) January 22, 2015 Michel Böhms Mapping Guide 5

5 Venn situations for properties The “default”, unconstrained. Independent properties, no mapping rule x:c rdfs:subPropertyOf y:d y:d rdfs:subPropertyOf x:c x:c owl:propertyDisjointWith y:d No mapping rule relevant (only for ‘negative’ info) x:c rdfs:subPropertyOf y:d AND y:d rdfs:subPropertyOf x:c Same as: x:A owl:EquivalentProperty y:B January 22, 2015 Michel Böhms Mapping Guide 6

1 Venn situation for individuals 1. x:a owl:sameAs y:b January 22, 2015 Michel Böhms Mapping Guide 7

Types of Mapping Rules (#7) x:A rdfs:subClassOf y:B y:B rdfs:subClassOf x:A x:A owl:EquivalentClass y:B x:c rdfs:subPropertyOf y:d y:d rdfs:subPropertyOf x:c x:A owl:EquivalentProperty y:B x:a owl:sameAs y:b January 22, 2015 Michel Böhms Mapping Guide 8

3 semantic levels for classes L1: Classes without restrictions L2: Classes with only “necessary” Restrictions L3: Classes with “necessary & sufficient (n&s)” Restrictions An ontology can have a mix of 1/2/3 An ontology can be “strong”, having only level 3 classes January 22, 2015 Michel Böhms Mapping Guide 9

Inference potential Depending on the semantic level of the class more or less can be inferred from asserted information Standard OWL2 inferences (entailments regimes) like: If (x:a rdf:type x:A AND x:A rdfs:subClassOf y:B) THEN (x:a rdf:type y:B) January 22, 2015 Michel Böhms Mapping Guide 10

Example x is some context ontology, y some common ontology following the V- Con Modelling Guide Ontology x asserts: x:RedCar rdf:type owl:Class x:colour rdf:type owl:DatatypeProperty x:colour rdfs:range xsd:string x:MyRedCar rdf:type x:RedCar x:MyRedCar x:colour “Red”^^xsd:string Ontology y asserts y:Car rdf:type owl:Class y:colour rdf:type owl:DatatypeProperty (note not the same as x:colour!) January 22, 2015 Michel Böhms Mapping Guide 11

Venn situation here Clearly the intended meaning of the mapping rules is: x:RedCar rdfs:subClassOf y:Car x:colour owl:EquivalentProperty y:colour January 22, 2015 Michel Böhms Mapping Guide 12

Semantic Level here (L1) x:RedCar and y:Car have no n&s restrictions Also both have no explicit restrictions at all: so we did not specify for instance that a RedCar has the value “red” for x:colour explicitly Note we could have never inferred “x:MyRedCar rdf:type x:RedCar” based on “x:MyRedCar x:colour “red”^^xsd:string”) i.e. No way to automatically classify So we have to assert (as we did) “x:MyRedCar rdf:type x:RedCar” Note we also cannot infer in any way that x:RedCar is a subclass of y:Car i.e. No way to automatically subclass So we have to assert “x:RedCar rdfs:subClassOf y:Car” as mapping rule Doing that we CAN infer: x:MyRedCar rdf:type y:Car X:MyRedCar y:colour “red”^^xsd:string And if we assert extra: y:MyCar rdf:type y:Car AND x:MyRedCar owl:sameAs y:MyCar We can extra infer: y:MyCar x:colour “red”^^xsd:string and y:MyCar y:colour “red”^^xsd:string Note that this had not been possible if he had not asserted x:MyRedCar x:colour “red”^^xsd:string in the first place (it would have been implicit in the RedCar class only January 22, 2015 Michel Böhms Mapping Guide 13

In case semantic level 2 So: x:RedCar and y:Car have again no set of n&s restrictions but this time we add an explicit restriction on the x:RedCar class: x:RedCar a owl:Class ; rdfs:subClassOf owl:Thing ; rdfs:subClassOf [ a owl:Restriction ; owl:hasValue "red"^^xsd:string ; owl:onProperty x:colour ]. January 22, 2015 Michel Böhms Mapping Guide 14

In case semantic level 2 Again, we can never infer that x:MyRedCar is of type x:RedCar i.e. again no way to automatically classify, even if x:MyRedCar x:clour “red” was asserted in the first place So we again have to assert x:MyRedCar rdf:type x:RedCar Again, we also cannot infer in any way that x:RedCar is a subclass of y:Car i.e. again no way to automatically subclass So we again have to assert x:RedCar rdfs:subClassOf y:Car Now we CAN infer: x:MyRedCar rdf:type y:Car (as before) And if we assert: y:MyCar AND x:MyRedCar owl:sameAs y:MyCar (as before) And x:MyRedCar x:colour “red” (because of the explicit restriction), no need to assert anymore! And even: y:MyCar x:colour “red” (as before) And even: y:MyCar y:colour “red” (as before) January 22, 2015 Michel Böhms Mapping Guide 15

In case semantic level 3 Now we add for both classes n&s restrictions like: In x ontology: x:RedCar owl:equivalentClass (…x:vehicleType=“car” and x:colour=“red”…) In y ontology: y:Car owl:equivalentClass (…y:vehicleType=“car” and y:colour=“red” In mapping ontology : “x:vehicleType owl:equivalentProperty y:vehicleType” AND “x:colour owl:equivalentProperty y:colour” which makes it possible to Infer that “x:MyRedCar rdf:type x:MyCar” (automatic classification) in case “x:MyRedCar x:colour “red”^^xsd:string” was asserted, but more important: Infer that “x:RedCar rdfs:subClassOf y:Car” (automatic subclassing based on the n&s class restrictions on both sides) So no need for mapping rules for the classes at all! Note: nice but unrealistic that all classes are defined on L3… January 22, 2015 Michel Böhms Mapping Guide 16

Bottom Lines In general we have to specify mapping rules explicitly for classes since strong L3 definitions are not likely We always need mapping rules for properties We need mapping rules for individuals to go beyond enrichment (and have all inferred data in both ontologies or in case such individuals are already asserted in both ontologies and actually refer to the same real world entity We need as much as necessary restrictions to make knowledge explicit on class level and to avoid the need to provide all this data on individual level (for all individuals) If this info is not explicitly at class level and not available at individual level this info is not really there at all (only in the name of the class) so inference will obviously also not create it (more positively: no info is really lost, is was never their in the first place) January 22, 2015 Michel Böhms Mapping Guide 17

Issues Other restriction types So far we discussed Restrictions of the form “owl:hasValue” Other types: hasRange (asphalt example) Or even (?) owl:minCardinality, owl:maxCardinality, owl:allValuesFrom, owl:someValuesFrom, …. What happens now (when inferring) Role of domain/range clauses for properties Datypes and Lexical values Do we also have to indicate that x:red = y:red or a bit more abstract x:datatype is y:datatype if not the same (like xsd:string) Do we also need rule x:c owl:differentFrom y:d ? January 22, 2015 Michel Böhms Mapping Guide 18

Simple CBNL Use Case /1 Ontology x (being CBNL) as entrance to ontology (and its individuals) y Where classes from y are equivalent or subclasses of classes in x (only classes since properties are also modelled as classes in CBNL) No need to move data Ontology y maybe not even an ontology, just connected via specific api/web services etc. January 22, 2015 Michel Böhms Mapping Guide 19

Simple CBNL Use Case /2 2 ontologies: x (CBNL) and y (ETIM) 1 Individual in some ontology c classified as an item in CBNL: c:a rdf:type x:A A being an “object-class” in CBNL 1 Class B in ontology y (ETIM), y:B In mapping rule: y:B owl:equivalentClass x:A or y:B rdfs:subClassOf x:A (being more realistic in case of specific restrictions in y) January 22, 2015 Michel Böhms Mapping Guide 20

Simple CBNL Use Case /3 (flow) You can now browse from c:a to x:A and search in all mapping ontologies for y:B like classes being equivalent or subclass and known more info on class level and existing individuals for y:B (here 2BA products) January 22, 2015 Michel Böhms Mapping Guide 21