The Semantic Web #7 - RDF Semantics
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The document provides an in-depth exploration of RDF (Resource Description Framework) semantics, focusing on the formalization of meaning in linked data and semantic web technologies. It discusses key concepts such as model theory, entailment, and interpretation, along with the definitions and properties of various RDF and RDFS vocabulary elements. Additionally, the document covers semantic conditions, entailment rules, and the relationship between RDF and RDFS entailments, emphasizing the significance of logical consistency and satisfiability in semantic representation.
The Semantic Web #7 - RDF Semantics
- 1. Linked Data & Semantic Web Technology The Semantic Web Part 7. RDF Semantics Dr. Myungjin Lee
- 2. RDF • 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 Linked Data & Semantic Web Technology
- 3. 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 Linked Data & Semantic Web Technology
- 4. 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. World Model Interpretation Daisy isA Cow Cow kindOf Animal Mary isA Person Person kindOf Animal a Z123ABC isA Car b Mary drives Z123ABC {<a,b>,…} 4 Linked Data & Semantic Web Technology
- 5. 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 Linked Data & Semantic Web Technology
- 6. Logical Consequence (Entailment) • logical consequence – if an RDFS document contains u rdf:type ex:Textbook. ex:Textbook rdfs:subClassOf ex:Book. – then u rdf:type ex:Book. It is deduced (deduction) or inferred (inference). propositions (statements) ㅠ logical entailment p1 p2 p3 ㅠ ㅠ ㅠ models models models of p1 of p3 of p2 interpretations 6 Linked Data & Semantic Web Technology
- 7. RDF Semantics • 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 RDFS-interpretation RDF-interpretation simple interpretation 7 Linked Data & Semantic Web Technology
- 8. 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 Linked Data & Semantic Web Technology
- 9. 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 <x,y> 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 Linked Data & Semantic Web Technology
- 10. 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) = <aaa, ttt> • 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 Linked Data & Semantic Web Technology
- 11. 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 <I(s),I(o)> 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 Linked Data & Semantic Web Technology
- 12. 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 Linked Data & Semantic Web Technology
- 13. RDF Interpretations • RDF vocabulary – The RDF vocabulary, rdfV, is a set of URI references in the rdf: namespace 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 • RDF axiomatic triples 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 . 13 Linked Data & Semantic Web Technology
- 14. RDF Semantic Conditions • x is in IP if and only if <x, I(rdf:Property)> 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 <IL("xxx"^^rdf:XMLLiteral), I(rdf:XMLLiteral)> • 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 <IL("xxx"^^rdf:XMLLiteral), I(rdf:XMLLiteral)> 14 Linked Data & Semantic Web Technology
- 15. RDF Entailments • S rdf-entails E when every rdf-interpretation which satisfies every member of S also satisfies E 15 Linked Data & Semantic Web Technology
- 16. RDFS Interpretations • RDFS vocabulary – RDF Schema extends RDF to include a larger vocabulary rdfsV with more complex semantic constraints 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 16 Linked Data & Semantic Web Technology
- 17. RDFS Semantic Conditions • x is in ICEXT(y) if and only if <x,y> is in IEXT(I(rdf:type)) IC = ICEXT(I(rdfs:Class)) IR = ICEXT(I(rdfs:Resource)) LV = ICEXT(I(rdfs:Literal)) • If <x,y> is in IEXT(I(rdfs:domain)) and <u,v> is in IEXT(x) then u is in ICEXT(y) • If <x,y> is in IEXT(I(rdfs:range)) and <u,v> is in IEXT(x) then v is in ICEXT(y) • IEXT(I(rdfs:subPropertyOf)) is transitive and reflexive on IP • If <x,y> is in IEXT(I(rdfs:subPropertyOf)) then x and y are in IP and IEXT(x) is a subset of IEXT(y) 17 Linked Data & Semantic Web Technology
- 18. RDFS Semantic Conditions • If x is in IC then <x, I(rdfs:Resource)> is in IEXT(I(rdfs:subClassOf)) • If <x,y> 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: <x, I(rdfs:member)> is in IEXT(I(rdfs:subPropertyOf)) • If x is in ICEXT(I(rdfs:Datatype)) then <x, I(rdfs:Literal)> is in IEXT(I(rdfs:subClassOf)) 18 Linked Data & Semantic Web Technology
- 19. RDFS Axiomatic Triples rdf:type rdfs:domain rdfs:Resource . rdfs:domain rdfs:domain rdf:Property . rdfs:member rdfs:range rdfs:Resource . rdfs:range rdfs:domain rdf:Property . rdf:first rdfs:range rdfs:Resource . rdfs:subPropertyOf rdfs:domain rdf:Property . rdf:rest rdfs:range rdf:List . rdfs:subClassOf rdfs:domain rdfs:Class . rdfs:seeAlso rdfs:range rdfs:Resource . rdf:subject rdfs:domain rdf:Statement . rdfs:isDefinedBy rdfs:range rdfs:Resource . rdf:predicate rdfs:domain rdf:Statement . rdfs:comment rdfs:range rdfs:Literal . rdf:object rdfs:domain rdf:Statement . rdfs:label rdfs:range rdfs:Literal . rdfs:member rdfs:domain rdfs:Resource . rdf:value rdfs:range rdfs:Resource . rdf:first rdfs:domain rdf:List . rdf:Alt rdfs:subClassOf rdfs:Container . rdf:rest rdfs:domain rdf:List . rdf:Bag rdfs:subClassOf rdfs:Container . rdfs:seeAlso rdfs:domain rdfs:Resource . rdf:Seq rdfs:subClassOf rdfs:Container . rdfs:isDefinedBy rdfs:domain rdfs:Resource . rdfs:ContainerMembershipProperty rdfs:subClassOf rdfs:comment rdfs:domain rdfs:Resource . rdf:Property . rdfs:label rdfs:domain rdfs:Resource . rdf:value rdfs:domain rdfs:Resource . rdfs:isDefinedBy rdfs:subPropertyOf rdfs:seeAlso . rdf:type rdfs:range rdfs:Class . rdf:XMLLiteral rdf:type rdfs:Datatype . rdfs:domain rdfs:range rdfs:Class . rdf:XMLLiteral rdfs:subClassOf rdfs:Literal . rdfs:range rdfs:range rdfs:Class . rdfs:Datatype rdfs:subClassOf rdfs:Class . rdfs:subPropertyOf rdfs:range rdf:Property . rdfs:subClassOf rdfs:range rdfs:Class . rdf:_1 rdf:type rdfs:ContainerMembershipProperty . rdf:subject rdfs:range rdfs:Resource . rdf:_1 rdfs:domain rdfs:Resource . rdf:predicate rdfs:range rdfs:Resource . rdf:_1 rdfs:range rdfs:Resource . rdf:object rdfs:range rdfs:Resource . rdf:_2 rdf:type rdfs:ContainerMembershipProperty . rdf:_2 rdfs:domain rdfs:Resource . rdf:_2 rdfs:range rdfs:Resource . ... 19 Linked Data & Semantic Web Technology
- 20. Some Triples which are RDFS-Valid 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 . 20 Linked Data & Semantic Web Technology
- 21. Extensional Semantic Conditions • <x,y> 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) • <x,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) • <x,y> is in IEXT(I(rdfs:range)) if and only if (if <u,v> is in IEXT(x) then v is in ICEXT(y)) • <x,y> is in IEXT(I(rdfs:domain)) if and only if (if <u,v> is in IEXT(x) then u is in ICEXT(y)) 21 Linked Data & Semantic Web Technology
- 22. 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 Linked Data & Semantic Web Technology
- 23. 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 Linked Data & Semantic Web Technology
- 24. Simple Entailment Rules • Simple Entailment Rules Rule Name if E contains then add uuu aaa _:nnn . se1 uuu aaa xxx . where _:nnn identifies a blank node allocated to xxx by rule se1 or se2. _:nnn aaa xxx . se2 uuu aaa xxx . where _:nnn identifies a blank node allocated to uuu by rule se1 or se2. • Literal Generalization Rule Rule Name if E contains then add uuu aaa _:nnn . lg uuu aaa lll . where _:nnn identifies a blank node allocated to the literal lll by this rule. • Literal Instantiation Rule Rule Name if E contains then add uuu aaa _:nnn . gl uuu aaa lll . where _:nnn identifies a blank node allocated to the literal lll by rule lg. 24 Linked Data & Semantic Web Technology
- 25. RDF Entailment Rules Rule Name if E contains then add rdf1 uuu aaa yyy . aaa rdf:type rdf:Property . uuu aaa lll . _:nnn rdf:type rdf:XMLLiteral . rdf2 where lll is a well-typed XML literal . where _:nnn identifies a blank node allocated to lll by rule lg. 25 Linked Data & Semantic Web Technology
- 26. RDFS Entailment Rules Rule Name if E contains then add uuu aaa lll. _:nnn rdf:type rdfs:Literal . rdfs1 where lll is a plain literal (with or without a language ta where _:nnn identifies a blank node allocated to lll by rule g). rule lg. aaa rdfs:domain xxx . rdfs2 uuu rdf:type xxx . uuu aaa yyy . aaa rdfs:range xxx . rdfs3 vvv rdf:type xxx . uuu aaa vvv . rdfs4a uuu aaa xxx . uuu rdf:type rdfs:Resource . rdfs4b uuu aaa vvv. vvv rdf:type rdfs:Resource . uuu rdfs:subPropertyOf vvv . rdfs5 uuu rdfs:subPropertyOf xxx . vvv rdfs:subPropertyOf xxx . rdfs6 uuu rdf:type rdf:Property . uuu rdfs:subPropertyOf uuu . aaa rdfs:subPropertyOf bbb . rdfs7 uuu bbb yyy . uuu aaa yyy . rdfs8 uuu rdf:type rdfs:Class . uuu rdfs:subClassOf rdfs:Resource . uuu rdfs:subClassOf xxx . rdfs9 vvv rdf:type xxx . vvv rdf:type uuu . rdfs10 uuu rdf:type rdfs:Class . uuu rdfs:subClassOf uuu . uuu rdfs:subClassOf vvv . rdfs11 uuu rdfs:subClassOf xxx . vvv rdfs:subClassOf xxx . uuu rdf:type rdfs12 uuu rdfs:subPropertyOf rdfs:member . rdfs:ContainerMembershipProperty . rdfs13 uuu rdf:type rdfs:Datatype . uuu rdfs:subClassOf rdfs:Literal . 26 Linked Data & Semantic Web Technology
- 27. Extensional Entailment Rules Rule Name if E contains then add uuu rdfs:domain vvv . ext1 uuu rdfs:domain zzz . vvv rdfs:subClassOf zzz . uuu rdfs:range vvv . ext2 uuu rdfs:range zzz . vvv rdfs:subClassOf zzz . uuu rdfs:domain vvv . ext3 www rdfs:domain vvv . www rdfs:subPropertyOf uuu . uuu rdfs:range vvv . ext4 www rdfs:range vvv . www rdfs:subPropertyOf uuu . rdf:type rdfs:subPropertyOf www . ext5 rdfs:Resource rdfs:subClassOf vvv . www rdfs:domain vvv . rdfs:subClassOf rdfs:subPropertyOf www . ext6 rdfs:Class rdfs:subClassOf vvv . www rdfs:domain vvv . rdfs:subPropertyOf rdfs:subPropertyOf www . ext7 rdf:Property rdfs:subClassOf vvv . www rdfs:domain vvv . rdfs:subClassOf rdfs:subPropertyOf www . ext8 rdfs:Class rdfs:subClassOf vvv . www rdfs:range vvv . rdfs:subPropertyOf rdfs:subPropertyOf www . ext9 rdf:Property rdfs:subClassOf vvv . www rdfs:range vvv . 27 Linked Data & Semantic Web Technology
- 28. 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 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/ 29 29 Linked Data & Semantic Web Technology