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SWCLOS: A Semantic Web Processor on CLOS Advanced Discussion

SWCLOS: A Semantic Web Processor on CLOS Advanced Discussion. Seiji Koide National Institute of Informatics. Formal Semantics. Platonic idealism (from Wikipedia)

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SWCLOS: A Semantic Web Processor on CLOS Advanced Discussion

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  1. SWCLOS:A Semantic Web Processor on CLOSAdvanced Discussion Seiji Koide National Institute of Informatics

  2. Formal Semantics • Platonic idealism (from Wikipedia) • Some contemporary linguistic philosophers construe “Platonism” to mean the proposition that universals exist independently of particulars (a universal is anything that can be predicated of a particular). • Ontology • Ontology is the philosophical study of the nature of being, existence or reality in general, as well as of the basic categories of being and their relations. • Formal … • How to describe things in objectivity • How to enable computation on ontology

  3. Formal Semantics • Equality • eq, eql, equal, equalp, = • Two names are lexically equal, then both equal? • Two names are different, then both different? • Two anonymous objects have the same structure and the same value, then both equal? • What do you mean by “same”? • Two classes share instances, then both equal?

  4. Denotational and Extensional Semantics of RDF based on RDF Semantics by Patrick Hayes and Brian McBride

  5. Russell&Norvig AIMA

  6. Formal Semantics Entails Sentences Sentences Representation World Aspects of the Real World Aspects of the Real World follows

  7. Formal Semantics Entails Sentences Sentences Representation World Aspects of the Real World Aspects of the Real World follows Universe of Discourse Set theory

  8. Formal Semantics Entails Sentences Sentences Representation World Aspects of the Real World Aspects of the Real World follows Universe of Discourse

  9. Formal Semantics Study of Formal Semantics Entails Sentences Sentences Study of Ontology Representation World Aspects of the Real World Aspects of the Real World follows Universe of Discourse KB =α α

  10. Formal Semantics Study of Formal Semantics Entails Sentences Sentences Interpretation Representation World Aspects of the Real World Aspects of the Real World follows Universe of Discourse 0 x 1 = 0 1 x 1 = 1 0 + 1 = 1 1 + 1 = 2

  11. Formal Semantics Study of Formal Semantics Entails Sentences Sentences Interpretation Representation World Aspects of the Real World Aspects of the Real World follows Universe of Discourse 0 ×1 = 0 1 ×1 = 1 0 ＋1 = 1 1 ＋1 = 2

  12. Semantic Web LayerCake OWL Semantics RDFS Semantics RDF Semantics

  13. Semantic Web LayerCake RDFSemantics

  14. RDF Model Theory Directed labeled graph

  15. RDF Model Theory An RDF graph is a set of RDF triples. Two graphs described by two N-triples documents that shares a set of triples, in which there is no difference except only blank node identifiers, are equal. A partial graph of RDF is a partial set of triples of the graph. A graph that have no blank node is called ground graph. http:/…/Proposal/ eg:author _:x1 . _:x1 eg:name “Tim Berners Lee” . http:/…/Proposal/ eg:author _:x2 . _:x2 eg:name “Tim Berners Lee” .

  16. RDF Vocabulary rdf:type rdf:Bag rdf:List rdf:XMLLiteral rdf:Seq rdf:Alt rdf:Statement rdf:Property rdf:nil rdf:value rdf:subject rdf:_1 rdf:_2 rdf:_3 rdf:object rdfs:comment rdf:first rdf:type rdf:predicate rdf:rest

  17. RDF Simple Interpretation • A non-empty set IR of resources, called the domain or universe of I. • A set IP, called the set of properties of I. • A mapping IEXT from IP into the powerset of IR × IR i.e., the set of sets of pairs <x,y> with x and y in IR . • A mapping IS from URI references in V into (IR ∪IP) . • A mapping IL from typed literals in V into IR. • A distinguished subset LV of IR, called the set of literal values, which contains all the plain literals in V .

  18. RDF Simple Interpretation "xx"^^rdf:XMLLiteral Interpretation Representation ex:p ex:a “this is a literal” World

  19. RDF Simple Interpretation "xx"^^rdf:XMLLiteral Interpretation Representation ex:p ex:a “this is a literal” World IS (ex:a) A set of resources; IR

  20. RDF Simple Interpretation "xx"^^rdf:XMLLiteral Interpretation Representation ex:p ex:a “this is a literal” World IS (ex:a) IS (ex:p) A set of resources; IR A set of propertes IP

  21. RDF Simple Interpretation "xx"^^rdf:XMLLiteral Interpretation Representation URI set ex:p ex:a “this is a literal” Mapping IS World IR U IP IS (ex:a) IS (ex:p) A set of resources; IR A set of propertes IP

  22. RDF Simple Interpretation "xx"^^rdf:XMLLiteral Interpretation Representation URI set ex:p ex:a “this is a literal” Mapping IS World IR U IP IS (ex:a) IL ("xx"^^rdf:XMLLiteral) IS (ex:p) A set of resources; IR A set of propertes IP

  23. RDF Simple Interpretation Typed literal set "xx"^^rdf:XMLLiteral Interpretation Representation URI set ex:p ex:a “this is a literal” Mapping IL Mapping IS World IR IR U IP IS (ex:a) IL ("xx"^^rdf:XMLLiteral) IS (ex:p) A set of resources; IR A set of propertes IP

  24. RDF Simple Interpretation Typed literal set Set of plain literals "xx"^^rdf:XMLLiteral Interpretation Representation URI set ex:p ex:a “this is a literal” Mapping IL Mapping IS World IR IR U IP IS (ex:a) IL ("xx"^^rdf:XMLLiteral) Set of literal values LV “this is literal” IS (ex:p) A set of resources; IR A set of propertes IP

  25. RDF Simple Interpretation Interpretation Representation World 〈 x, y 〉 y Mapping IEXT from IP to 〈 x, y 〉 x IS (ex:p) A set of resources; IR A set of propertes IP

  26. RDF Simple Interpretation Interpretation Representation World A set of resources; IR x 〈 x, y 〉 y Mapping IEXT from IP to 〈 x, y 〉 PowerSet IR × IR IS (ex:p) A set of resources; IR A set of propertes IP

  27. RDF Simple Interpretation Interpretation Representation World A set of resources; IR x 〈 x, y 〉 y Mapping IEXT from IP to 〈 x, y 〉 PowerSet IR × IR IS (ex:p)∈IR IS (ex:p)∈IP IS (ex:p) IEXT(IS (ex:p) ) is called a property extension of IS (ex:p). IP may be a partial set of IR. We distinguish IS (ex:p) as an element of pair from denotated property IS (ex:p), e.g., ex:pex:py . A set of resources; IR A set of propertes IP

  28. RDF Simple Interpretation Interpretation Representation World A set of resources; IR x 〈 x, y 〉 y Mapping IEXT from IP to 〈 x, y 〉 PowerSet IR × IR IS (ex:p) 〈IS (ex:p), y 〉∈IEXT(IS (ex:p)) IEXT(IS (ex:p) ) is called a property extension of IS (ex:p). IP may be a partial set of IR. We distinguish IS (ex:p) as an element of pair from denotated property IS (ex:p), e.g., ex:pex:py . A set of resources; IR A set of propertes IP

  29. 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) . 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 . “soccur@en-US” = “football”@en

  30. Simple Entailment between RDF Graphs IsatisfiesE if I(E) = true, and a set S of RDF graphs (simply) entails a graph E if every interpretation which satisfies every member of S also satisfies E. If A entails B, then any interpretation that makes A true also makes B true, so that an assertion of A already contains the same “meaning” as an assertion of B. Through the notions of satisfaction, entailment and validity, formal semantics gives a rigorous definition to a notion of “meaning”. Any process which constructs a graph E from some other graph(s), S is said to be (simply) valid if S entails E in every case, otherwise invalid. S ⊨ E

  31. Simple Entailment Rules of RDF ex:q ex:q ex:a ex:b ex:b ex:q ex:q _:x <ex:p> <ex:b> .<ex:c> <ex:q> _:x . <ex:a> <ex:p> <ex:b> .<ex:c> <ex:q> <ex:a> . ex:c ex:c _:x <ex:q> <ex:a> .

  32. Literal Generalization/Instantiation Rule ex:p ex:p ex:a “literal1” ex:a “literal2” ex:q ex:q

  33. RDF entailment rules rdf:XMLLiteral rdf:type ex:p ex:p ex:a “1”^^xsd:integer ex:a

  34. RDF Semantic Condition x ∈ IP，iff 〈x, I(rdf:Property)〉∈ IEXT(I (rdf:type)) xxx rdf:type rdf:Property . IEXT(I (rdf:type)) ∧ xxx is a well-typed XML literal ⇒IL(“xxx”^^rdf:XMLLiteral) is an XML value of xxx, IL(“xxx”^^rdf:XMLLiteral)∈ LV ,〈IL(“xxx”^^rdf:XMLLiteral), I (rdf:XMLLiteral) 〉∈IEXT(I (rdf:type)) “xxx”^^rdf:XMLLiteralrdf:type rdf:XMLLiteral . IEXT(I (rdf:type)) ∧ xxx is ill-typed XML literal ⇒IL(“xxx”^^rdf:XMLLiteral)∉ LV ，〈 IL(“xxx”^^rdf:XMLLiteral), I(rdf:XMLLiteral) 〉∉ IEXT(I (rdf:type))

  35. RDF Axiomatic Triples rdf:type rdf:Bag rdf:Litst rdf:XMLLiteral rdf:Seq rdf:Alt rdf:Statement rdf:Property rdf:nil rdf:value rdf:subject rdf:_1 rdf:_2 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:_3 rdf:object rdfs:comment rdf:first rdf:type rdf:predicate rdf:rest

  36. Semantic Web LayerCake RDFS Semantics

  37. RDFS Vocabulary rdfs:subClassOf rdfs:subPropertyOf rdf:type class instance rdfs:Class rdfs:Datatype rdf:Bag rdf:List rdf:XMLLiteral rdf:Seq rdfs:Literal rdfs:Container rdf:Alt rdfs:Resource rdf:Statement rdf:Property rdfs:ContainerMembershipProperty rdf:nil rdfs:seeAlso rdfs:isDefinedBy rdf:value rdf:subject rdfs:member rdf:_1 rdf:_2 rdf:_3 rdfs:domain rdfs:range rdfs:label rdf:object rdfs:comment rdf:first rdfs:subClassOf rdfs:subPropertyOf rdf:type rdf:predicate rdf:rest

  38. RDFS Semantic Condition Universe of Discourse IR

  39. RDFS Semantic Condition IS(rdfs:Resource) x ∈ ICEXT(c)，iff 〈x,c〉∈ IEXT(IS(rdf:type)) IR = ICEXT(IS(rdfs:Resource))

  40. RDFS Semantic Condition IS(rdfs:Resource) x ∈ ICEXT(c)，iff 〈x,c〉∈ IEXT(IS(rdf:type)) A set of propertes IP IR = ICEXT(IS(rdfs:Resource))

  41. RDFS Semantic Condition IS(rdfs:Resource) x ∈ ICEXT(c)，iff 〈x,c〉∈ IEXT(IS(rdf:type)) IS(rdf:Property) IP = ICEXT(IS(rdf:Property)) IR = ICEXT(IS(rdfs:Resource))

  42. RDFS Semantic Condition IS(rdfs:Resource) x ∈ ICEXT(c)，iff 〈x,c〉∈ IEXT(IS(rdf:type)) IS(rdfs:Literal) IS(rdf:Property) IP = ICEXT(IS(rdf:Property)) LV = ICEXT(IS(rdfs:Literal)) IR = ICEXT(IS(rdfs:Resource))

  43. RDFS Semantic Condition IS(rdfs:Resource) x ∈ ICEXT(c)，iff 〈x,c〉∈ IEXT(IS(rdf:type)) IS(rdfs:Literal) IS(rdf:Property) IP = ICEXT(IS(rdf:Property)) LV = ICEXT(IS(rdfs:Literal)) IR = ICEXT(IS(rdfs:Resource))

  44. RDFS Semantic Condition x ∈ ICEXT(c)，iff 〈x,c〉∈ IEXT(IS(rdf:type)) IS(rdf:Property) IP = ICEXT(IS(rdf:Property)) IS(rdfs:Resource) IS(rdfs:Literal) LV = ICEXT(IS(rdfs:Literal)) IR = ICEXT(IS(rdfs:Resource))

  45. RDFS Semantic Condition x ∈ ICEXT(c)，iff 〈x,c〉∈ IEXT(IS(rdf:type)) IS(rdfs:Class) IP = ICEXT(IS(rdf:Property)) IC = ICEXT(IS(rdfs:Class)) LV = ICEXT(IS(rdfs:Literal)) IR = ICEXT(IS(rdfs:Resource))

  46. RDFS Semantic Condition x ∈ ICEXT(c)，iff 〈x,c〉∈ IEXT(IS(rdf:type)) IP = ICEXT(IS(rdf:Property)) IS(rdfs:Resource) IS(rdfs:Class) IS(rdfs:Literal) LV = ICEXT(IS(rdfs:Literal)) IR = ICEXT(IS(rdfs:Resource))

  47. RDFS Axiomatic Triples rdfs:Class ∈ ICEXT(rdfs:Class)，iff 〈rdfs:Class,rdfs:Class〉∈ IEXT(IS(rdf:type)) rdfs:subClassOf rdfs:subPropertyOf rdf:type class instance rdfs:Class rdfs:Datatype rdf:Bag rdf:Litst rdf:XMLLiteral rdf:Seq rdfs:Literal rdfs:Container rdf:Alt rdfs:Resource rdf:Statement rdf:Property rdfs:ContainerMembershipProperty rdf:nil rdfs:seeAlso rdfs:isDefinedBy rdf:value rdf:subject rdfs:member rdf:_1 rdf:_2 rdf:_3 rdfs:domain rdfs:range rdfs:label rdf:object rdfs:comment rdf:first rdfs:subClassOf rdfs:subPropertyOf rdf:type rdf:predicate rdf:rest

  48. RDFS Axiomatic Triples 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 . rdfs:subClassOf rdfs:subPropertyOf rdf:type class instance rdfs:Class rdfs:Datatype rdf:Bag rdf:Litst rdf:XMLLiteral rdf:Seq rdfs:Literal rdfs:Container rdf:Alt rdfs:Resource rdf:Statement rdf:Property rdfs:ContainerMembershipProperty rdf:nil rdfs:seeAlso rdfs:isDefinedBy rdf:value rdf:subject rdfs:member rdf:_1 rdf:_2 rdf:_3 rdfs:domain rdfs:range rdfs:label rdf:object rdfs:comment rdf:first rdfs:subClassOf rdfs:subPropertyOf rdf:type rdf:predicate rdf:rest

  49. RDFS Entailment Rules

  50. RDFS Entailment Rules

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