1. Linked Data & Semantic Web Technology The Semantic Web Part 7. RDF Semantics Dr. Myungjin Lee

2. Linked Data & Semantic Web Technology RDF – an assertional language intended to be used to express propositions using precise formal vocabularies – to provide a basic foundation for more advanced assertional languages – to emphasize generality and precision in expressing propositions about any topic 2

3. Linked Data & Semantic Web Technology Semantics What is Semantics? – the study of meaning focused on the relation between signifiers, like words, phrases, signs, and symbols, and what they stand for Syntax and Semantics – Syntax character strings without meaning – Semantics meaning of the character strings Why we need semantics for RDF(S) – to share equally interpretable meaning from RDF(S) syntax 3

4. Linked Data & Semantic Web Technology Model Theory What is Model Theory? – a formal semantic theory which relates expressions to interpretations – If a model for a language satisfies a particular sentence or theory, it is called a model of the sentence or theory. 4 WorldInterpretation Daisy isA Cow Cow kindOf Animal Mary isA Person Person kindOf Animal Z123ABC isA Car  {,…}     a b Model Mary drives Z123ABC

5. Linked Data & Semantic Web Technology Terms interpretation – an interpretation is a world with each symbol and each expression assigned an extension model – an model of a logic theory is an interpretation of the theory that satisfies all constraints specified by the theory consistency – a logic theory is consistent if it has a model satisfiability – a symbol or expression x is satisfiable if it is possible to find a model of K that makes x true entailment – a logic theory K entails another logical theory K’ if every model of K is a model of K’ 5

6. Linked Data & Semantic Web Technology Logical Consequence (Entailment) logical consequence – if an RDFS document contains – then 6 u rdf:type ex:Textbook. ex:Textbook rdfs:subClassOf ex:Book. u rdf:type ex:Book. It is deduced (deduction) or inferred (inference). models of p 1 models of p 3 models of p 2 interpretations p1p1 p2p2 p3p3 ㅠ logical entailment propositions (statements) ㅠ ㅠ ㅠ

7. Linked Data & Semantic Web Technology RDF Semantics – a basic technique called model theory for specifying the semantics of a formal language the language refers to a 'world‘ – the minimal conditions that a world must satisfy in order to assign an appropriate meaning for every expression in the language a particular word  an interpretation model theory  ‘interpretation theory’ – defined as a mapping on the abstract syntax of RDF described in the RDF concepts and abstract syntax 7 RDFS-interpretation RDF-interpretation simple interpretation

8. Linked Data & Semantic Web Technology Graph Definitions RDF graph, simply graph – a set of RDF triples a subgraph of an RDF graph – a subset of the triples in the graph a ground RDF graph – one with no blank nodes a name – a URI reference of a literal a vocabulary – a set of names the vocabulary of a graph – the set of names which occur as the subject, predicate, or object of any triple in the graph 8

9. Linked Data & Semantic Web Technology Definition of a Simple Interpretation A simple interpretation I of a vocabulary V is defined by: 1.A non-empty set IR of resources, called the domain or universe of I. 2.A set IP, called the set of properties of I. 3.A mapping IEXT from IP into the powerset of IR x IR i.e. the set of sets of pairs with x and y in IR. 4.A mapping IS from URI references in V into (IR union IP) 5.A mapping IL from typed literals in V into IR. 6.A distinguished subset LV of IR, called the set of literal values, which contains all the plain literals in V 9

10. Linked Data & Semantic Web Technology Semantic Conditions for Ground Graphs if E is a plain literal "aaa" in V then I(E) = aaa if E is a plain literal "aaa"@ttt in V then I(E) = if E is a typed literal in V then I(E) = IL(E) if E is a URI reference in V then I(E) = IS(E) 10

11. Linked Data & Semantic Web Technology Semantic Conditions for Ground Graphs if E is a ground triple s p o. then I(E) = true if s, p and o are in V, I(p) is in IP and is in IEXT(I(p)) otherwise I(E)= false. if E is a ground RDF graph then I(E) = false if I(E') = false for some triple E' in E, otherwise I(E) =true. 11

12. Linked Data & Semantic Web Technology Simple Entailment between RDF graphs a set S of RDF graphs (simply) entails a graph E if every interpretation which satisfies every member of S also satisfies E Lemma – Empty Graph Lemma. The empty set of triples is entailed by any graph, and does not entail any graph except itself. – Subgraph Lemma. A graph entails all its subgraphs. – Instance Lemma. A graph is entailed by any of its instances. – Merging lemma. The merge of a set S of RDF graphs is entailed by S, and entails every member of S. – Interpolation Lemma. – Anonymity lemma. – Monotonicity Lemma. – Compactness Lemma. 12

13. Linked Data & Semantic Web Technology RDF Interpretations RDF vocabulary – The RDF vocabulary, rdfV, is a set of URI references in the rdf: namespace RDF axiomatic triples 13 rdf:type rdf:type rdf:Property. rdf:subject rdf:type rdf:Property. rdf:predicate rdf:type rdf:Property. rdf:object rdf:type rdf:Property. rdf:first rdf:type rdf:Property. rdf:rest rdf:type rdf:Property. rdf:value rdf:type rdf:Property. rdf:_1 rdf:type rdf:Property. rdf:_2 rdf:type rdf:Property.... rdf:nil rdf:type rdf:List. rdf:type rdf:type rdf:Property. rdf:subject rdf:type rdf:Property. rdf:predicate rdf:type rdf:Property. rdf:object rdf:type rdf:Property. rdf:first rdf:type rdf:Property. rdf:rest rdf:type rdf:Property. rdf:value rdf:type rdf:Property. rdf:_1 rdf:type rdf:Property. rdf:_2 rdf:type rdf:Property.... rdf:nil rdf:type rdf:List. rdf:type rdf:Property rdf:XMLLiteral rdf:nil rdf:List rdf:Statement rdf:subject rdf:predicate rdf:object rdf:first rdf:rest rdf:Seq rdf:Bag rdf:Alt rdf:_1 rdf:_2... rdf:value

14. Linked Data & Semantic Web Technology RDF Semantic Conditions x is in IP if and only if is in IEXT(I( rdf:type )) If "xxx"^^ rdf:XMLLiteral is in V and xxx is a well-typed XML literal string, then IL("xxx"^^ rdf:XMLLiteral ) is the XML value of xxx; IL("xxx"^^ rdf:XMLLiteral ) is in LV; IEXT(I( rdf:type )) contains If "xxx"^^ rdf:XMLLiteral is in V and xxx is an ill-typed XML literal string, then IL("xxx"^^ rdf:XMLLiteral ) is not in LV; IEXT(I( rdf:type )) does not contain 14

15. Linked Data & Semantic Web Technology RDF Entailments S rdf-entails E when every rdf-interpretation which satisfies every member of S also satisfies E 15

16. Linked Data & Semantic Web Technology RDFS Interpretations RDFS vocabulary – RDF Schema extends RDF to include a larger vocabulary rdfsV with more complex semantic constraints 16 rdfs:domain rdfs:range rdfs:Resource rdfs:Literal rdfs:Datatype rdfs:Class rdfs:subClassOf rdfs:subPropertyOf rdfs:member rdfs:Container rdfs:ContainerMembershipProperty rdfs:comment rdfs:seeAlso rdfs:isDefinedBy rdfs:label

17. Linked Data & Semantic Web Technology RDFS Semantic Conditions x is in ICEXT(y) if and only if is in IEXT(I( rdf:type )) IC = ICEXT(I( rdfs:Class )) IR = ICEXT(I( rdfs:Resource )) LV = ICEXT(I( rdfs:Literal )) If is in IEXT(I( rdfs:domain )) and is in IEXT(x) then u is in ICEXT(y) If is in IEXT(I( rdfs:range )) and is in IEXT(x) then v is in ICEXT(y) IEXT(I( rdfs:subPropertyOf )) is transitive and reflexive on IP If is in IEXT(I( rdfs:subPropertyOf )) then x and y are in IP and IEXT(x) is a subset of IEXT(y) 17

18. Linked Data & Semantic Web Technology RDFS Semantic Conditions If x is in IC then is in IEXT(I( rdfs:subClassOf )) If is in IEXT(I( rdfs:subClassOf )) then x and y are in IC and ICEXT(x) is a subset of ICEXT(y) IEXT(I( rdfs:subClassOf )) is transitive and reflexive on IC If x is in ICEXT(I( rdfs:ContainerMembershipProperty )) then: is in IEXT(I( rdfs:subPropertyOf )) If x is in ICEXT(I( rdfs:Datatype )) then is in IEXT(I( rdfs:subClassOf )) 18

19. Linked Data & Semantic Web Technology RDFS Axiomatic Triples 19 rdf:type rdfs:domain rdfs:Resource. rdfs:domain rdfs:domain rdf:Property. rdfs:range rdfs:domain rdf:Property. rdfs:subPropertyOf rdfs:domain rdf:Property. rdfs:subClassOf rdfs:domain rdfs:Class. rdf:subject rdfs:domain rdf:Statement. rdf:predicate rdfs:domain rdf:Statement. rdf:object rdfs:domain rdf:Statement. rdfs:member rdfs:domain rdfs:Resource. rdf:first rdfs:domain rdf:List. rdf:rest rdfs:domain rdf:List. rdfs:seeAlso rdfs:domain rdfs:Resource. rdfs:isDefinedBy rdfs:domain rdfs:Resource. rdfs:comment rdfs:domain rdfs:Resource. rdfs:label rdfs:domain rdfs:Resource. rdf:value rdfs:domain rdfs:Resource. rdf:type rdfs:range rdfs:Class. rdfs:domain rdfs:range rdfs:Class. rdfs:range rdfs:range rdfs:Class. rdfs:subPropertyOf rdfs:range rdf:Property. rdfs:subClassOf rdfs:range rdfs:Class. rdf:subject rdfs:range rdfs:Resource. rdf:predicate rdfs:range rdfs:Resource. rdf:object rdfs:range rdfs:Resource. rdf:type rdfs:domain rdfs:Resource. rdfs:domain rdfs:domain rdf:Property. rdfs:range rdfs:domain rdf:Property. rdfs:subPropertyOf rdfs:domain rdf:Property. rdfs:subClassOf rdfs:domain rdfs:Class. rdf:subject rdfs:domain rdf:Statement. rdf:predicate rdfs:domain rdf:Statement. rdf:object rdfs:domain rdf:Statement. rdfs:member rdfs:domain rdfs:Resource. rdf:first rdfs:domain rdf:List. rdf:rest rdfs:domain rdf:List. rdfs:seeAlso rdfs:domain rdfs:Resource. rdfs:isDefinedBy rdfs:domain rdfs:Resource. rdfs:comment rdfs:domain rdfs:Resource. rdfs:label rdfs:domain rdfs:Resource. rdf:value rdfs:domain rdfs:Resource. rdf:type rdfs:range rdfs:Class. rdfs:domain rdfs:range rdfs:Class. rdfs:range rdfs:range rdfs:Class. rdfs:subPropertyOf rdfs:range rdf:Property. rdfs:subClassOf rdfs:range rdfs:Class. rdf:subject rdfs:range rdfs:Resource. rdf:predicate rdfs:range rdfs:Resource. rdf:object rdfs:range rdfs:Resource. rdfs:member rdfs:range rdfs:Resource. rdf:first rdfs:range rdfs:Resource. rdf:rest rdfs:range rdf:List. rdfs:seeAlso rdfs:range rdfs:Resource. rdfs:isDefinedBy rdfs:range rdfs:Resource. rdfs:comment rdfs:range rdfs:Literal. rdfs:label rdfs:range rdfs:Literal. rdf:value rdfs:range rdfs:Resource. rdf:Alt rdfs:subClassOf rdfs:Container. rdf:Bag rdfs:subClassOf rdfs:Container. rdf:Seq rdfs:subClassOf rdfs:Container. rdfs:ContainerMembershipProperty rdfs:subClassOf rdf:Property. rdfs:isDefinedBy rdfs:subPropertyOf rdfs:seeAlso. rdf:XMLLiteral rdf:type rdfs:Datatype. rdf:XMLLiteral rdfs:subClassOf rdfs:Literal. rdfs:Datatype rdfs:subClassOf rdfs:Class. rdf:_1 rdf:type rdfs:ContainerMembershipProperty. rdf:_1 rdfs:domain rdfs:Resource. rdf:_1 rdfs:range rdfs:Resource. rdf:_2 rdf:type rdfs:ContainerMembershipProperty. rdf:_2 rdfs:domain rdfs:Resource. rdf:_2 rdfs:range rdfs:Resource.... rdfs:member rdfs:range rdfs:Resource. rdf:first rdfs:range rdfs:Resource. rdf:rest rdfs:range rdf:List. rdfs:seeAlso rdfs:range rdfs:Resource. rdfs:isDefinedBy rdfs:range rdfs:Resource. rdfs:comment rdfs:range rdfs:Literal. rdfs:label rdfs:range rdfs:Literal. rdf:value rdfs:range rdfs:Resource. rdf:Alt rdfs:subClassOf rdfs:Container. rdf:Bag rdfs:subClassOf rdfs:Container. rdf:Seq rdfs:subClassOf rdfs:Container. rdfs:ContainerMembershipProperty rdfs:subClassOf rdf:Property. rdfs:isDefinedBy rdfs:subPropertyOf rdfs:seeAlso. rdf:XMLLiteral rdf:type rdfs:Datatype. rdf:XMLLiteral rdfs:subClassOf rdfs:Literal. rdfs:Datatype rdfs:subClassOf rdfs:Class. rdf:_1 rdf:type rdfs:ContainerMembershipProperty. rdf:_1 rdfs:domain rdfs:Resource. rdf:_1 rdfs:range rdfs:Resource. rdf:_2 rdf:type rdfs:ContainerMembershipProperty. rdf:_2 rdfs:domain rdfs:Resource. rdf:_2 rdfs:range rdfs:Resource....

20. Linked Data & Semantic Web Technology Some Triples which are RDFS-Valid 20 rdfs:Resource rdf:type rdfs:Class. rdfs:Class rdf:type rdfs:Class. rdfs:Literal rdf:type rdfs:Class. rdf:XMLLiteral rdf:type rdfs:Class. rdfs:Datatype rdf:type rdfs:Class. rdf:Seq rdf:type rdfs:Class. rdf:Bag rdf:type rdfs:Class. rdf:Alt rdf:type rdfs:Class. rdfs:Container rdf:type rdfs:Class. rdf:List rdf:type rdfs:Class. rdfs:ContainerMembershipProperty rdf:type rdfs:Class. rdf:Property rdf:type rdfs:Class. rdf:Statement rdf:type rdfs:Class. rdfs:domain rdf:type rdf:Property. rdfs:range rdf:type rdf:Property. rdfs:subPropertyOf rdf:type rdf:Property. rdfs:subClassOf rdf:type rdf:Property. rdfs:member rdf:type rdf:Property. rdfs:seeAlso rdf:type rdf:Property. rdfs:isDefinedBy rdf:type rdf:Property. rdfs:comment rdf:type rdf:Property. rdfs:label rdf:type rdf:Property. rdfs:Resource rdf:type rdfs:Class. rdfs:Class rdf:type rdfs:Class. rdfs:Literal rdf:type rdfs:Class. rdf:XMLLiteral rdf:type rdfs:Class. rdfs:Datatype rdf:type rdfs:Class. rdf:Seq rdf:type rdfs:Class. rdf:Bag rdf:type rdfs:Class. rdf:Alt rdf:type rdfs:Class. rdfs:Container rdf:type rdfs:Class. rdf:List rdf:type rdfs:Class. rdfs:ContainerMembershipProperty rdf:type rdfs:Class. rdf:Property rdf:type rdfs:Class. rdf:Statement rdf:type rdfs:Class. rdfs:domain rdf:type rdf:Property. rdfs:range rdf:type rdf:Property. rdfs:subPropertyOf rdf:type rdf:Property. rdfs:subClassOf rdf:type rdf:Property. rdfs:member rdf:type rdf:Property. rdfs:seeAlso rdf:type rdf:Property. rdfs:isDefinedBy rdf:type rdf:Property. rdfs:comment rdf:type rdf:Property. rdfs:label rdf:type rdf:Property.

21. Linked Data & Semantic Web Technology Extensional Semantic Conditions is in IEXT(I( rdfs:subClassOf )) if and only if x and y are in IC and ICEXT(x) is a subset of ICEXT(y) is in IEXT(I( rdfs:subPropertyOf )) if and only if x and y are in IP and IEXT(x) is a subset of IEXT(y) is in IEXT(I( rdfs:range )) if and only if (if is in IEXT(x) then v is in ICEXT(y)) is in IEXT(I( rdfs:domain )) if and only if (if is in IEXT(x) then u is in ICEXT(y)) 21

22. Linked Data & Semantic Web Technology RDFS Entailments S rdfs-entails E when every rdfs-interpretation which satisfies every member of S also satisfies E – since every rdfs-interpretation is an rdf-interpretation, if S rdfs-entails E then it rdf-entails E – rdfs-entailment is stronger than rdf-entailment 22

23. Linked Data & Semantic Web Technology Entailment Rules What is Entailment Rules? – some inference patterns which capture some of the various forms of vocabulary entailment used as a guide for the design of software to check RDF graphs for RDF and RDFS entailment – to add a consequent triple to a graph when it contains triples conforming to a pattern a graph entails any larger graph that is obtained by applying the rules to the original graph Conventions – aaa, bbb, etc., stand for any URI reference – uuu, vvv, etc. for any URI reference or blank node identifier – xxx, yyy etc. for any URI reference, blank node identifier or literal – lll for any literal – _:nnn, etc., for blank node identifiers 23

24. Linked Data & Semantic Web Technology Simple Entailment Rules Literal Generalization Rule Literal Instantiation Rule 24 Rule Nameif E containsthen add se1uuu aaa xxx. uuu aaa _:nnn. where _:nnn identifies a blank node allocated to xxx by rule se1 or se2. se2uuu aaa xxx. _:nnn aaa xxx. where _:nnn identifies a blank node allocated to uuu by rule se1 or se2. Rule Nameif E containsthen add lguuu aaa lll. uuu aaa _:nnn. where _:nnn identifies a blank node allocated to the literal lll by this rule. Rule Nameif E containsthen add gl uuu aaa _:nnn. where _:nnn identifies a blank node allocated to the literal lll by rule lg. uuu aaa lll.

25. Linked Data & Semantic Web Technology RDF Entailment Rules 25 Rule Nameif E containsthen add rdf1uuu aaa yyy. aaa rdf:type rdf:Property. rdf2 uuu aaa lll. where lll is a well-typed XML literal. _:nnn rdf:type rdf:XMLLiteral. where _:nnn identifies a blank node allocated to lll by rule lg.

26. Linked Data & Semantic Web Technology RDFS Entailment Rules 26 Rule Nameif E containsthen add rdfs1 uuu aaa lll. where lll is a plain literal (with or without a language ta g). _:nnn rdf:type rdfs:Literal. where _:nnn identifies a blank node allocated to lll by rule rule lg. rdfs2 aaa rdfs:domain xxx. uuu aaa yyy. uuu rdf:type xxx. rdfs3 aaa rdfs:range xxx. uuu aaa vvv. vvv rdf:type xxx. rdfs4auuu aaa xxx. uuu rdf:type rdfs:Resource. rdfs4buuu aaa vvv. vvv rdf:type rdfs:Resource. rdfs5 uuu rdfs:subPropertyOf vvv. vvv rdfs:subPropertyOf xxx. uuu rdfs:subPropertyOf xxx. rdfs6 uuu rdf:type rdf:Property.uuu rdfs:subPropertyOf uuu. rdfs7 aaa rdfs:subPropertyOf bbb. uuu aaa yyy. uuu bbb yyy. rdfs8 uuu rdf:type rdfs:Class.uuu rdfs:subClassOf rdfs:Resource. rdfs9 uuu rdfs:subClassOf xxx. vvv rdf:type uuu. vvv rdf:type xxx. rdfs10 uuu rdf:type rdfs:Class.uuu rdfs:subClassOf uuu. rdfs11 uuu rdfs:subClassOf vvv. vvv rdfs:subClassOf xxx. uuu rdfs:subClassOf xxx. rdfs12 uuu rdf:type rdfs:ContainerMembershipProperty. uuu rdfs:subPropertyOf rdfs:member. rdfs13 uuu rdf:type rdfs:Datatype. uuu rdfs:subClassOf rdfs:Literal.

27. Linked Data & Semantic Web Technology Extensional Entailment Rules 27 Rule Nameif E containsthen add ext1 uuu rdfs:domain vvv. vvv rdfs:subClassOf zzz. uuu rdfs:domain zzz. ext2 uuu rdfs:range vvv. vvv rdfs:subClassOf zzz. uuu rdfs:range zzz. ext3 uuu rdfs:domain vvv. www rdfs:subPropertyOf uuu. www rdfs:domain vvv. ext4 uuu rdfs:range vvv. www rdfs:subPropertyOf uuu. www rdfs:range vvv. ext5 rdf:type rdfs:subPropertyOf www. www rdfs:domain vvv. rdfs:Resource rdfs:subClassOf vvv. ext6 rdfs:subClassOf rdfs:subPropertyOf www. www rdfs:domain vvv. rdfs:Class rdfs:subClassOf vvv. ext7 rdfs:subPropertyOf rdfs:subPropertyOf www. www rdfs:domain vvv. rdf:Property rdfs:subClassOf vvv. ext8 rdfs:subClassOf rdfs:subPropertyOf www. www rdfs:range vvv. rdfs:Class rdfs:subClassOf vvv. ext9 rdfs:subPropertyOf rdfs:subPropertyOf www. www rdfs:range vvv. rdf:Property rdfs:subClassOf vvv.

28. Linked Data & Semantic Web Technology References http://www.w3.org/TR/2004/REC-rdf-mt-20040210/ http://en.wikipedia.org/wiki/Semantics Pascal Hitzler, Knowledge Representation for the Semantic Web, Winter 2011. http://www.slideshare.net/baojie_iowa/rdf-semantics http://www.slideshare.net/lysander07/08-semantic-web-technologies-rdfs-semantics http://www.csee.umbc.edu/courses/691s/notes/06rdfsemantics.ppt 28

29. Linked Data & Semantic Web Technology 29 Dr. Myungjin Lee e-Mail : mjlee@li-st.com Twitter : http://twitter.com/MyungjinLee Facebook : http://www.facebook.com/mjinlee SlideShare : http://www.slideshare.net/onlyjiny/