elw2009, jenova swclos: a semantic web processor on clos advanced discussion seiji koide national...

ELW2009, Jenova

SWCLOS:A Semantic Web Processor on CLOSAdvanced Discussion

Seiji Koide

National Institute of Informatics

ELW2009, Jenova

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

ELW2009, Jenova

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?

ELW2009, Jenova

Denotational and Extensional Semantics of RDF

based on RDF Semantics by Patrick Hayes and Brian McBride

ELW2009, Jenova

Russell&Norvig AIMA

ELW2009, Jenova

Formal Semantics

Sentences SentencesEntails

Aspects of theReal World

Aspects of theReal Worldfollows

Representation

World

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Formal Semantics

Universe of Discourse

Set theory




Representation

World

ELW2009, Jenova

Formal Semantics





Representation

World

ELW2009, Jenova

Formal SemanticsS

tudy of O

ntology

Study of Formal Semantics


KB =αα




Representation

World

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Formal Semantics


Interpretation




Representation

World


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Formal Semantics

Universe of Discourse0 ×1 = 01 ×1 = 10 ＋ 1 = 11 ＋ 1 = 2




Representation

World

Interpretation


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Semantic Web LayerCake

RDF Semantics

RDFS Semantics

OWL Semantics

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RDFSemantics

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RDF Model Theory

• Directed labeled graph

ELW2009, Jenova

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” .




ELW2009, Jenova

RDF Vocabulary

rdf:_1

rdf:type rdf:predicate

rdf:object rdfs:comment

rdf:firstrdf:rest

rdf:type

rdf:value rdf:subjectrdf:_2

rdf:_3

rdf:Property

rdf:nil

rdf:List

rdf:Statement

rdf:Alt

rdf:Seq

rdf:Bag

rdf:XMLLiteral

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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 .

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RDF Simple Interpretationex:a ex:p"xx"^^rdf:XMLLiteral

“this is a literal”Representation

World

Interpretation

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IS (ex:a)


A set of resources; IR

ex:a ex:p"xx"^^rdf:XMLLiteral“this is a literal”

Representation

World

Interpretation

ELW2009, Jenova

IS (ex:p)


A set of propertes IP

ex:p

IS (ex:a)


ex:a"xx"^^rdf:XMLLiteral“this is a literal”

Representation

World

Interpretation

ELW2009, Jenova

RDF Simple InterpretationURI set

IR U IP

Mapping IS

IS (ex:p)


ex:p

IS (ex:a)



Representation

World

Interpretation

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IL ("xx"^^rdf:XMLLiteral)

RDF Simple InterpretationURI set

IR U IP

Mapping IS

IS (ex:p)


ex:p

IS (ex:a)



Representation

World

Interpretation

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Mapping IL

Typed literal set

IR


URI set

IR U IP

Mapping IS

IS (ex:p)


ex:p

IS (ex:a)



Representation

World

Interpretation

ELW2009, Jenova

Representation

Mapping IL

Typed literal set

IR


URI set

IR U IP

Mapping IS

IS (ex:p)


ex:p

IS (ex:a)



World

Interpretation


Set of literal values LV

Set of plain literals

“this is literal”

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〈 x, y 〉y Mapping IEXT from IP to 〈 x, y 〉

IS (ex:p)

x

Representation

World

Interpretation



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〈 x, y 〉

PowerSet IR × IR

y

x

IS (ex:p)

Representation

World

Interpretation




Mapping IEXT from IP to 〈 x, y 〉

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〈 x, y 〉

PowerSet IR × IR

y

x

IS (ex:p)

Representation

World

Interpretation






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:p ex:p y .


IS (ex:p)∈IR IS (ex:p)∈IP

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〈 x, y 〉

PowerSet IR × IR

y

x

IS (ex:p)

Representation

World

Interpretation








〈 IS (ex:p), y ∈〉 IEXT(IS (ex:p))

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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

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Simple Entailment between RDF Graphs

• I satisfies E 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

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Simple Entailment Rules of RDFRule

NameIf E contains: then add:

se1 uuu aaa xxx . uuu aaa _:nnn .

where _:nnn identifies a blank node allocated to xxx by rule se1 or se2.

se2 uuu aaa xxx . _:nnn aaa xxx .

where _:nnn identifies a blank node allocated to uuu by rule se1 or se2.

<ex:a> <ex:p> <ex:b> .<ex:c> <ex:q> <ex:a> .

<ex:a> <ex:p> <ex:b> .<ex:c> <ex:q> <ex:a> .

ex:a ex:b

ex:c

ex:q

ex:q

_:x <ex:p> <ex:b> .<ex:c> <ex:q> _:x .

_:x <ex:p> <ex:b> .<ex:c> <ex:q> _:x .

ex:b

ex:c

ex:q

ex:q

_:x <ex:q> <ex:a> .

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Literal Generalization/Instantiation Rule Rule


lg uuu aaa lll .

uuu aaa _:nnn .

where _:nnn identifies a blank node allocated to the literal lll by this rule.

gl

uuu aaa _:nnn .

where _:nnn identifies a blank node allocated to the literal lll by rule lg.

uuu aaa lll .

ex:aex:p

“literal1” ex:aex:p

“literal2”ex:q ex:q

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RDF entailment rules Rule


rdf1 uuu 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.

ex:aex:p

“1”^^xsd:integer ex:aex:p

rdf:XMLLiteral

rdf:type

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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:XMLLiteral rdf: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))

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RDF Axiomatic Triples

rdf:_1

rdf:type rdf:predicate

rdf:object rdfs:comment

rdf:firstrdf:rest

rdf:type

rdf:value rdf:subjectrdf:_2

rdf:_3

rdf:Property

rdf:nil

rdf:Litst

rdf:Statement

rdf:Alt

rdf:Seq

rdf:Bag

rdf:XMLLiteral

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 .

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RDFS Semantics

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RDFS Vocabulary

rdf:_1

rdfs:subClassOf rdfs:subPropertyOf rdf:type rdf:predicate

rdfs:domain rdfs:range rdfs:label rdf:object rdfs:comment

rdf:firstrdf:rest

rdfs:subClassOfrdfs:subPropertyOfrdf:type

class

instance

rdfs:seeAlso rdfs:isDefinedBy rdf:value rdf:subject rdfs:memberrdf:_2

rdf:_3

rdf:Property rdfs:ContainerMembershipProperty

rdf:nil

rdfs:Resource

rdf:List

rdf:Statement

rdfs:Container rdf:Alt

rdf:Seq

rdf:Bag

rdfs:Literalrdf:XMLLiteral

rdfs:Class rdfs:Datatype

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RDFS Semantic Condition

Universe of Discourse IR

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IR = ICEXT(IS(rdfs:Resource))

IS(rdfs:Resource)

x ∈ ICEXT(c) ， iff 〈 x,c ∈ 〉 IEXT(IS(rdf:type)) x ∈ ICEXT(c) ， iff 〈 x,c ∈ 〉 IEXT(IS(rdf:type))

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IS(rdfs:Resource)



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IS(rdfs:Resource)

IS(rdf:Property)


IP = ICEXT(IS(rdf:Property))

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RDFS Semantic ConditionIS(rdfs:Resource)

IS(rdfs:Literal)IS(rdf:Property)




LV = ICEXT(IS(rdfs:Literal))

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IS(rdf:Property)

IS(rdfs:Literal)IS(rdfs:Resource)IP = ICEXT(IS(rdf:Property))




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IC = ICEXT(IS(rdfs:Class))

IS(rdfs:Class)





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IS(rdfs:Class) IS(rdfs:Literal)

IS(rdfs:Resource)IP = ICEXT(IS(rdf:Property))




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RDFS Axiomatic Triples

rdf:_1



rdf:firstrdf:rest


class

instance


rdf:_3


rdf:nil

rdfs:Resource

rdf:Litst

rdf:Statement


rdf:Seq

rdf:Bag


rdfs:Class rdfs:Datatyperdfs:Class ∈ ICEXT(rdfs:Class) ， iff 〈 rdfs:Class,rdfs:Class ∈ 〉 IEXT(IS(rdf:type)) rdfs:Class ∈ ICEXT(rdfs:Class) ， iff 〈 rdfs:Class,rdfs:Class ∈ 〉 IEXT(IS(rdf:type))

ELW2009, Jenova

RDFS Axiomatic Triples

rdf:_1



rdf:firstrdf:rest


class

instance


rdf:_3


rdf:nil

rdfs:Resource

rdf:Litst

rdf:Statement


rdf:Seq

rdf:Bag



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: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 .

ELW2009, Jenova

RDFS Entailment RulesRule Name If E contains: then add:

rdfs1 uuu aaa lll.

where lll is a plain literal (with or without a language tag).

_: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 .

rdfs4a uuu aaa xxx . uuu rdf:type rdfs:Resource .

rdfs4b uuu 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 .

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RDFS Entailment RulesRule Name If E contains: then add:

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 .

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Hierarchical Structure of RDFS

rdf:_1



rdf:firstrdf:rest


class

instance


rdf:_3


rdf:nil

rdfs:Resource

rdf:List

rdf:Statement


rdf:Seq

rdf:Bag



InstanceInstance

Meta-classMeta-class

ClassClass

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Transitivity Rule implies …

rdf:_1



rdf:firstrdf:rest


class

instance


rdf:_3


rdf:nil

rdfs:Resource

rdf:List

rdf:Statement


rdf:Seq

rdf:Bag




rdfs:Resource rdf:Statement


rdf:Seq

rdf:Bag

rdfs:Literalrdf:XMLLiteralrdf:List


rdfs:Resource is a superclass of other classesrdfs:Resource is a superclass of other classes

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Transitivity Rule implies …

rdf:_1



rdf:firstrdf:rest


class

instance


rdf:_3


rdf:nil

rdfs:Resource

rdf:List

rdf:Statement


rdf:Seq

rdf:Bag




rdfs:Resource rdf:Statement


rdf:Seq

rdf:Bag

rdfs:Literalrdf:XMLLiteralrdf:List


rdfs:Resource is a superclass of other classes and meta-classesrdfs:Resource is a superclass of other classes and meta-classes

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Subsumption Rule implies …

rdf:_1



rdf:firstrdf:rest


class

instance


rdf:_3


rdf:nil

rdfs:Resource

rdf:List

rdf:Statement


rdf:Seq

rdf:Bag



rdf:_1



rdf:firstrdf:rest


rdf:_3

rdf:Property rdfs:ContainerMembershipPropertyrdf:Property rdfs:ContainerMembershipProperty

rdfs:Resource

rdf:nil

rdf:List

Every instance is an instance of rdfs:ResourceEvery instance is an instance of rdfs:Resource

ELW2009, Jenova


rdf:_1



rdf:firstrdf:rest


class

instance


rdf:_3


rdf:nil

rdfs:Resource

rdf:List

rdf:Statement


rdf:Seq

rdf:Bag



Every class is an instance of rdfs:ResourceEvery class is an instance of rdfs:Resource


rdfs:Resource

rdf:List

rdf:Statement


rdf:Seq

rdf:Bag


rdfs:Class rdfs:Datatyperdfs:Class rdfs:Datatype

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rdf:_1



rdf:firstrdf:rest


class

instance


rdf:_3


rdf:nil

rdfs:Resource

rdf:List

rdf:Statement


rdf:Seq

rdf:Bag



rdfs:Datatype and rdfs:Class are also instances of rdfs:Resourcerdfs:Datatype and rdfs:Class are also instances of rdfs:Resource

rdfs:Resource


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OWL Semantics

ELW2009, Jenova

Three sub languages of OWL• OWL Lite

– supports users primarily needing a classification hierarchy and simple constraints. It should be simpler to provide tool support for OWL Lite than the other sublanguages.

• OWL DL– supports users who want the maximum expressiveness while ret

aining computational completeness (all conclusions are guaranteed to be computable) and decidability (all computations will finish in finite time).

• OWL Full– is meant for users who want maximum expressiveness and the s

yntactic freedom of RDF with no computational guarantees. For example, in OWL Full a class can be treated simultaneously as a collection of individuals and as an individual in its own right.

ELW2009, Jenova

Conditions concerning the parts of the OWL universe and syntactic categories

If E is then

IS(E) ∈ ICEXT(IS(E))= and

owl:Class IC IOC IOC⊆IC

owl:Thing IOC IOT IOT⊆IR and IOT ≠ ∅

owl:Restriction IC IOR IOR⊆IOC

owl:ObjectProperty IC IOOP IOOP⊆IP

owl:DatatypeProperty

IC IODP IODP⊆IP

owl:AnnotationProperty

IC IOAP IOAP⊆IP

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RDF-Compatible Model-Theoretic Semantics

IRIOT

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IP

IRIOT

IOOP

IODPIOAP

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IP

IR

IC IOC

IOT

IOOP

IODPIOAP

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IP

IR

IC IOC

IOT

IOR

IOOP

IODPIOAP

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IP

IR

IC IOC

IOT

IOR

IOOP

IODPIOAP

OWL Full

IOT = IRIOOP = IPIOC = IC

IOT = IRIOOP = IPIOC = IC

OWL DL

LVI, IOT, IOC, IDC, IOOP, IODP, IOAP, IOXP, IL, and IX are all pairwise disjoint. For v in the disallowed vocabulary, IS(v) ∈ IR － (LV IOT IOC IDC IOOP IODP IOAP IOXP IL IX). ∪ ∪ ∪ ∪ ∪ ∪ ∪ ∪ ∪


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IP

IR

IC IOC

IOT

IOR

IOOP

IODPIOAP

OWL Full

IOT ⊆ IRIOOP ⊆ IPIOC ⊆ IC

IOT ⊆ IRIOOP ⊆ IPIOC ⊆ IC

OWL DL



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OWL-Full Style Connectionrdfs:subClassOfrdfs:subPropertyOfrdf:type

class

instance

rdf:Property

rdfs:Resource

rdfs:Class

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rdfs:Resource


class

instance

rdf:Property

rdfs:Class owl:Restrictionowl:Class

IOC IC⊆IOR IOC⊆

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rdfs:Resource

vin:Wine


class

instance

rdf:Property

rdfs:Class owl:Restrictionowl:Class

IOC IC⊆IOR IOC⊆

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rdfs:Resourcerdfs:Resource

vin:Winevin:Wine

OWL-Full Style Connection

• All classes under owl:Class are in the domain of rdfs:Resource.


class

instance

rdf:Property

rdfs:Class owl:Restrictionrdfs:Class owl:Classowl:Class

IOC IC ⊆ IR⊆IOR IOC⊆

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rdfs:Resourcerdfs:Resource

hasColor.RedhasColor.Red


• All restrictions under owl:Restriction are in the domain of rdfs:Resource.


class

instance

rdf:Property

rdfs:Class owl:Restrictionrdfs:Class owl:Classowl:Class

IOC IC ⊆ IR⊆IOR IOC ⊆ IC⊆ IR⊆

owl:Restriction

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rdfs:Resource

vin:Wine


class

instance

rdf:Property

rdfs:Class owl:Class owl:Restriction

owl:Thing

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class

instance

rdf:Property

rdfs:Resource


owl:Thing

vin:Wine vin:Zinfandel

vin:ElyseZinfandel

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• We need the new axiom to make OWL individuals be in RDFS universe.– owl:Thing rdfs:subClassOf rdfs:Resource .


class

instance

rdf:Property

rdfs:Resource


owl:Thing


vin:ElyseZinfandel

rdfs:Resource owl:Thing


vin:ElyseZinfandelIOT IR⊆

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class

instance

rdf:Property

rdfs:Resource


owl:Thing


owl:Thing


owl:Class

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class

instance

rdf:Property

rdfs:Resource


owl:Thing


rdfs:Resource owl:Thing


owl:Class

• We need the new axiom to make OWL classes be in OWL universe.– owl:Class rdfs:subClassOf owl:Thing .

IOC IOT⊆

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If E is then


owl:Class IC IOC IOC⊆IC





IC IODP IODP⊆IP


IC IOAP IOAP⊆IP

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If E is then


owl:Class IC IOC IOC IOT⊆ ⊆ IC





IC IODP IODP⊆IP


IC IOAP IOAP⊆IP

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• Classes may be treated as individual.


class

instance

rdf:Property

rdfs:Resource


owl:Thing

ELW2009, Jenova


• Classes may be treated as individual.– vin:Wine owl:sameAs food:Wine .


class

instance

rdf:Property

rdfs:Resource


owl:Thing

vin:Wine

food:Wine

ELW2009, Jenova

Equality in OWL

• Equivalency as Class– owl:equivalentClass, owl:intersectionOf, owl:unionOf,

owl:complementOf, owl:oneOf– owl:disjointWith, owl:complementOf,

• Equivalency as Individual– owl:sameAs, owl:FunctionalProperty,

owl:InverseFunctionalProperty– owl:differenceFrom, owl:distinctMembers– owl:oneOf

• Equivalency as Property– owl:equivalentProperty

http://www.w3.org/TR/owl-ref/#DescriptionAxiom

ELW2009, Jenova

Equivalent Propertyhttp://www.w3.org/TR/owl-ref/#equivalentProperty-def

• Property equivalence is not the same as property equality. Equivalent properties have the same "values" (i.e., the same property extension), but may have different intensional meaning (i.e., denote different concepts). Property equality should be expressed with the owl:sameAs construct. As this requires that properties are treated as individuals, such axioms are only allowed in OWL Full.

ELW2009, Jenova

Equality in RDF Graphhttp://www.w3.org/TR/2004/REC-rdf-concepts-20040210/#section-graph-equality

• M maps blank nodes to blank nodes. • M(lit)=lit for all RDF literals lit which are nodes of G. • M(uri)=uri for all RDF URI references uri which are

nodes of G. • The triple ( s, p, o ) is in G if and only if the triple

( M(s), p, M(o) ) is in G'.

Two RDF graphs G and G' are equivalent if there is a bijection M between the sets of nodes of the two graphs, such that:

With this definition, M shows how each blank node in G can be replaced with a new blank node to give G'.

ELW2009, Jenova

Non-Unique Name Assumption and Equality• In Semantic Webs, two or more different

names or URIs may denote same object.

• Negative identity of two or more graphs and nodes does not mean the difference.

ELW2009, Jenova

Graph Equality in RDFhttp://www.w3.org/TR/rdf-mt/#graphdefs

• Any instance of a graph in which a blank node is mapped to a new blank node not in the original graph is an instance of the original and also has it as an instance, and this process can be iterated so that any 1:1 mapping between blank nodes defines an instance of a graph which has the original graph as an instance. Two such graphs, each an instance of the other but neither a proper instance, which differ only in the identity of their blank nodes, are considered to be equivalent. We will treat such equivalent graphs as identical; this allows us to ignore some issues which arise from 're-naming' nodeIDs, and is in conformance with the convention that blank nodes have no label. Equivalent graphs are mutual instances with an invertible instance mapping.

ex:aex:p

ex:aex:p

<ex:a> <ex:p> _:x .<ex:a> <ex:p> _:x . <ex:a> <ex:p> _:y .<ex:a> <ex:p> _:y .

ELW2009, Jenova

Non-Unique Name Assumption and Equality• ex:a and ex:b may be identical (denoted by different URIs) in

non-UNA.• Two graphs that show different appearance may be identical.

ex:aex:p

ex:bex:p

<ex:a> <ex:p> 1 .<ex:a> <ex:p> 1 . <ex:b> <ex:p> 1 .<ex:b> <ex:p> 1 .

1 1

ELW2009, Jenova

Non-Unique Name Assumption and Equality

equal? different?

ex:aex:p

ex:bex:p

ex:aex:p

ex:aex:p

Yes. No.

ex:aex:p

ex:aex:p

Yes. No.ex:z ex:z

ex:aex:p

ex:bex:p

ex:z ex:z

ex:aex:p

ex:aex:p

ex:y ex:z

ex:p ex:pYes. No.

ex:p ex:pex:y ex:z

in UNA

No. Yes.

No. Yes.

No. Yes.

No. Yes.

ex:p ex:pex:z ex:z Yes. No.

ELW2009, Jenova


equal? different?

ex:aex:p

ex:bex:p

? ?

ex:aex:p

ex:aex:p

Yes. No.

ex:aex:p

ex:aex:p

Yes. No.ex:z ex:z

ex:aex:p

ex:bex:p

? ?ex:z ex:z

ex:aex:p

ex:aex:p

? ?ex:y ex:z

ex:p ex:p

Yes. No.

ex:p ex:p? ?ex:y ex:z

in non-UNA

ex:p ex:p

ex:z ex:z Yes. No.

ELW2009, Jenova


equal? different?

ex:aex:p

ex:bex:p

? ?

ex:aex:p

ex:aex:p

Yes. No.

ex:aex:p

ex:aex:p

Yes. No.ex:z ex:z

ex:aex:p

ex:bex:p

? ?ex:z ex:z

ex:aex:p

ex:aex:p

ex:y ex:z

ex:p ex:pYes. No.

ex:p ex:pex:y ex:z

Atomic UNA in non-UNA

No. Yes.

ex:p ex:pex:z ex:z Yes. No.

No. Yes.

ELW2009, Jenova


equal? different?

ex:aex:p

ex:bex:p

? ?

ex:aex:p

ex:bex:p

? ?ex:z ex:z

ex:aex:p

ex:aex:p

ex:y ex:z

ex:p ex:pex:y ex:z

Atomic UNA in non-UNA

No. Yes.

No. Yes.

Yes. No.

ex:y ex:z No. Yes.

Different names without slots

Same names with different slots

Different names with same slots

ELW2009, Jenova

Non-Unique Name Assumption and Equality• Two atomic objects must be different if the

two have different names, because they are basics of composite objects.

• If slots of two objects are different, then different.– intensional logics

• If slots of two objects are same, then same in non-UNA?

ELW2009, Jenova

Auto Epistemic Local Closed World

• Open World is troublesome.– owl:someValuesFrom restriction entails very few

entailments.• It may be satisfiable somewhere you do not know.

• After ontology building, agents want to infer the world which they know.

• User-Settable Closed World– owl:intersectionOf, owl:unionOf, owl:one of– owl:allValesFrom + owl:maxCardinality

ELW2009, Jenova

Russell&Norvig AIMA

ELW2009, Jenova

Formal Semantics




Representation

World

ELW2009, Jenova

Formal Semantics

triples a tripleEntails

RDF graph? a graph?follows

Representation

World

ELW2009, Jenova

Formal Semantics

Lisp Symbols A Lisp SymbolEntails

CLOS Objects? a CLOS object?follows

Representation

World

ELW2009, Jenova

Semantics in Lisp and RDF

based on Brian Cantwell Smith

1983

ELW2009, Jenova

A Simple Semantic Interpretation Function

Syntactic Domain S

Semantic Domain D

Mapping Φ Interpretation function

symbol s sign s

significance dinterpretation of s

1. The objects and events in the world in which a computational process is embedded, including both real-world objects like cars and caviar, and set-theoretic abstractions like numbers and functions.

2. The internal elements, structures, or processes inside the computer, including data structures, program representations, execution sequences and so forth.

3. The notational or communicational expressions, in some externally observable and consensually established medium of interaction, such as strings of characters, streams of words, or sequences of display images on a computer terminal.

1. The objects and events in the world in which a computational process is embedded, including both real-world objects like cars and caviar, and set-theoretic abstractions like numbers and functions.

2. The internal elements, structures, or processes inside the computer, including data structures, program representations, execution sequences and so forth.

3. The notational or communicational expressions, in some externally observable and consensually established medium of interaction, such as strings of characters, streams of words, or sequences of display images on a computer terminal.

ELW2009, Jenova

Semantic Relationships in a Computational Process

“ … ”

Structural Field

O Ψ

Φ

Φ(O(“T.S.Eliot”) = T.S.Eliot

ELW2009, Jenova

A Framework for Computational Semantics

Structure S1

Designation D1

Φ

Notation N1

O

Structure S2

Designation D2

Φ

Notation N2

Ψ

O － 1

ELW2009, Jenova

Russell&Norvig AIMA

Sentences

Aspects of the real world

Φ

Notation N1

O

Sentences

Aspects of the real world

Φ

Notation N2

O － 1

Entails

Follows

ELW2009, Jenova

LISP Evaluation vs. Designation

3

Three

Φ

Ψ(+ 1 2)

Three

Φ

Ψ3

Φ

T

Truth

Φ

Ψ'X

ΦΨ

X

(EQ 'A 'B)

Falsity

Φ

ΨNIL

Φ

(CAR '(A . B))

ΦΨ

A

CDR

the CDR function

Φ

???

ELW2009, Jenova

LISP’s “De-reference If You Can” Evaluation Protocol

Φ Ψ

Φ Ψ

… edge of the machine …

Internal Structures

External WorldΦ

Ψ

de-reference

ELW2009, Jenova

LISP Evaluation vs. Designation

3

Three

Φ

Ψ(+ 1 2)

Three

Φ

Ψ3

Φ

T

Truth

Φ

Ψ'X

ΦΨ

X

(EQ 'A 'B)

Falsity

Φ

ΨNIL

Φ

(CAR ‘(A . B))

ΦΨ

A

CDR

the CDR function

Φ

???

ELW2009, Jenova

Model Theoretic Semantics of RDF

ELW2009, Jenova


rdfs:Resource, rdf:Property, rdfs:subClassOf, rdfs:domain, rdfs:rangeeg:Agent, eg:Work, eg:author, eg:Person, eg:Documents

eg:authoreg:authorrdfs:Resourcerdfs:Resource

rdf:Propertyrdf:Property

rdfs:subClassOfrdfs:subClassOf

rdfs:domainrdfs:domain

rdfs:rangerdfs:range Information Management: A Proposal

“Information Management: A Proposal”, “Tim Berners-Lee”

Tim Berners-Leeeg:Agenteg:Agent

eg:Workeg:Work

eg:Personeg:Person

eg:Documentseg:Documents

ELW2009, Jenova









Tim Berners-Lee

URI References

Plane Literals

eg:Agenteg:Agent

eg:Workeg:Work

eg:Personeg:Person


PI

RI

Vocabulary V

Vocabulary V

ELW2009, Jenova









Tim Berners-Lee

SILV

eg:Agenteg:Agent

eg:Workeg:Work

eg:Personeg:Person


PI

RI

Vocabulary V

Vocabulary V

ELW2009, Jenova

A Framework for Computational Semantics for RDF

ComputationalObject1

Designation D1

Φ

URI_Reference1

O

ComputationalObject2

Designation D2

Φ

URI_Reference2

Ψ

O － 1

ELW2009, Jenova

SWCLOS’s “De-reference If You Can” Evaluation Protocol

Φ Ψ

Φ Ψ

… edge of the machine …

CLOS Objects

External WorldΦ

Ψ

de-reference

ELW2009, Jenova

Evaluation vs. Designation in SWCLOS

eg:Person

a Class Person

Φ

Ψ#<rdfs:Class eg:Person>

Φ

(typep eg:Person rdfs:Class)

Truth

Φ

Ψt

Φ

(slot-value a:Proposal 'dc:title)

“Information Management: A Proposal”

Φ Ψ

3

Three

Φ

Ψ

#<eg:Person TBL>

Tim Berners-Lee

Φ

ELW2009, Jenova

Continue to the paper

elw2009, jenova swclos: a semantic web processor on clos advanced discussion seiji koide national...

Documents

set of rdf triples

partial graph of rdf

partial set of triples

set ip

set of properties

extensional semantics

ground graph

set ir of resources