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- 1. RDF Semantics by Patrick Hayes W3C Recommendation http://www.w3.org/TR/rdf-mt/ Presented by Jie Bao RPI Sept 4, 2008 Part 1 of RDF/OWL Semantics Tutorial http://tw.rpi.edu/wiki/index.php/RDF_and_OWL_Semantics
- 2. A Layer Cake of Languages OWL2 OWL (RDFS 3.0) You RDF(S) Are Here
- 3. Outline • What is Semantics? • RDF: Syntax • RDF Graph and Simple Entailment • RDF Interpretation • RDFS Interpretation
- 4. What is Semantics Semant Inferen Syntax Logic ics ce Merriam-Webster: the study of meanings Wikipedia: the study of meaning in communication.
- 5. What is Semantics? • Intensional Meaning – TW Students are Students with affiliation to the Tetherless World Group • Extensional Meaning – TW Students are the set {Jiao, Ankesh, Jesse,…}
- 6. Model Theory Used to link intensional meaning and extensional meaning “Model theory assumes that the language refers to a 'world', and Alfred Tarski describes the minimal conditions that 1901-1983 a world must satisfy in order to Picure source: wikipedia assign an appropriate meaning for every expression in the language.” --RDF Semantics
- 7. Model: an Example Expression: TW Students are Students with affiliation to the Tetherless World Group A Model: …
- 8. A Few Jargons • An interpretation is a world with each symbol and each Interpretation expression assigned an extension. • An model of a logic theory is an interpretation of the Model theory that satisfies all constraints specified by the theory • A logic theory is consistent if it has a model. Consistency • A symbol or expression x is satisfiable w.r.t. a logic theory Satisfiability K if there is a model of K with x’s extension not empty. • A logic theory K entails another logical theory K’ if every Entailment model of K is a model of K’
- 9. Outline • What is Semantics? • RDF: Syntax • RDF Graph and Simple Entailment • RDF Interpretation • RDFS Interpretation
- 10. RDF Family RDFS RDFS Interpretation Vocabulary RDF Vocabulary RDF Interpretation RDF Graph Simple Interpretation Syntax Semantics
- 11. Not Covered in the Talk • Blank Node (b-Node) • Literals (Datatypes) • Containers • Collections • Reification • Annotation • Entailment rules (rule inference)
- 12. RDF: Triple and Graph • Triple: (subject, property, object) – UB × U × UBL (Url, Blank node, Literal) – e.g., (Jim, is-a, Professor) – e.g., (Jim, has-surname, “Hendler”) – not covered – e.g.,(Jim, has-pet, _:x) – not covered is-a Professor Jim has-surname “Hendler” has-pet • Graph: A set of triples
- 13. Outline • What is Semantics? • RDF: Syntax • RDF Graph and Simple Entailment • RDF Interpretation • RDFS Interpretation
- 14. 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 We do not consider RDF vocabulary (e.g., rdf:type), yet.
- 15. Simple Interpretation V IS IP IR IEXT
- 16. Simple Interpretation Example V={a, b, c} Picture courtesy of “RDF Semantics”(Figure 1)
- 17. Simple Semantic Conditions • if E is a URI reference in V then I(E) = IS(E) • 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 • 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 blank node and A(E) is defined then [I+A](E) = A(E) • If E is an RDF graph then I(E) = true if [I+A'](E) = true for some mapping A' from blank(E) to IR, otherwise I(E)= false
- 18. Note to Simple Interpreation • IP may not be in IR • A property (an element in IP) and its extension (mapping by IEXT) are separated. – Thus avoids paradox like the barber paradox (A barber shaves only those men who do not shave themselves.)
- 19. Outline • What is Semantics? • RDF: Syntax • RDF Graph and Simple Entailment • RDF Interpretation • RDFS Interpretation
- 20. RDF Vocabulary (rdfV) • 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
- 21. RDF Semantic Conditions • x is in IP if and only if <x, I(rdf:Property)> is in IEXT(I(rdf:type)) – Thus, RDF properties (IP) must be resources (IR) in the universe. – (rdf:type rdf:type rdf:Property ) is always true • More conditions for literals
- 22. RDF Interpretation Example Vocabulary: rdfV + V={a,b,c} Picture courtesy of “RDF Semantics”(Figure 2)
- 23. Outline • What is Semantics? • RDF: Syntax • RDF Graph and Simple Entailment • RDF Interpretation • RDFS Interpretation
- 24. RDFS Vocabulary (rdfsV) • rdfs:domain rdfs:range rdfs:Resource • rdfs:Class rdfs:subClassOf rdfs:subPropertyOf • rdfs:Literal rdfs:Datatype • rdfs:member rdfs:Container rdfs:ContainerMembershipProperty • rdfs:comment rdfs:seeAlso rdfs:isDefinedBy rdfs:label
- 25. RDFS Semantic Conditions On classes • 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 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
- 26. RDFS Semantic Conditions On properties • 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) More for container and literals
- 27. RDFS Axiomatic triples Domains • 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 .
- 28. RDFS Axiomatic triples Ranges • 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 . More for container, reification, literal, and annotation…
- 29. RDFS-Valid Triples • rdfs:Resource rdf:type rdfs:Class . • rdfs:Class rdf:type rdfs:Class . • rdf:Property 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.
- 30. Conclusions • Model Theory gives semantics to RDF(S) • RDF and RDFS vocabularies pose semantic constraints on interpretations – RDF: type, Property – RDFS: domain, range, Resource, Class, subClassOf subPropertyOf • Will see OWL 1 and OWL 2 extensions to RDF(S) in the future
- 31. More on RDF Semantics • Herman J. ter Horst - Completeness, decidability and complexity of entailment for RDF Schema and a semantic extension involving the OWL vocabulary. In J. Web Sem. 3(2-3):79-115, 2005. • Jos de Bruijn, Stijn Heymans - Logical Foundations of (e)RDF(S): Complexity and Reasoning. In ISWC/ASWC pp. 86-99, 2007. • Jeff Z. Pan, Ian Horrocks - RDFS(FA) and RDF MT: Two Semantics for RDFS. In International Semantic Web Conference pp. 30-46, 2003.

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