# Abstract Syntax DL Syntax Semantics Descriptions (C) A (URI ...

Abstract Syntax DL Syntax Semantics Descriptions (C) A (URI ...

Abstract Syntax DL Syntax Semantics

Descriptions (C)

A (URI reference) A A I ⊆ ∆ I

owl:Thing ⊤ owl:Thing I = ∆ I

owl:Nothing ⊥ owl:Nothing I = {}

intersectionOf(C1 C2 ...) C1 ⊓ C2 (C1 ⊓ C2) I = C I 1 ∩ C I 2

unionOf(C1 C2 ...) C1 ⊔ C2 (C1 ⊔ C2) I = C I 1 ∪ C I 2

complementOf(C) ¬C (¬C) I = ∆ I \ C I

oneOf(o1 ...) {o1, . . .} {o1, . . .} I = {o I 1,...}

restriction(R someValuesFrom(C)) ∃R.C (∃R.C) I = {x | ∃y.〈x, y〉 ∈ R I and y ∈ C I }

restriction(R allValuesFrom(C)) ∀R.C (∀R.C) I = {x | ∀y.〈x, y〉 ∈ R I → y ∈ C I }

restriction(R hasValue(o)) R : o (∀R.o) I = {x | 〈x, o I 〉 ∈ R I }

restriction(R minCardinality(n)) n R ( n R) I = {x | ♯({y.〈x, y〉 ∈ R I }) n}

restriction(R maxCardinality(n)) n R ( n R) I = {x | ♯({y.〈x, y〉 ∈ R I }) n}

restriction(U someValuesFrom(D)) ∃U.D (∃U.D) I = {x | ∃y.〈x, y〉 ∈ U I and y ∈ D D }

restriction(U allValuesFrom(D)) ∀U.D (∀U.D) I = {x | ∀y.〈x, y〉 ∈ U I → y ∈ D D }

restriction(U hasValue(v)) U : v (U : v) I = {x | 〈x, v I 〉 ∈ U I }

restriction(U minCardinality(n)) n U ( n U) I = {x | ♯({y.〈x, y〉 ∈ U I }) n}

restriction(U maxCardinality(n)) n U ( n U) I = {x | ♯({y.〈x, y〉 ∈ U I }) n}

Data Ranges (D)

D (URI reference) D D D ⊆ ∆ I D

oneOf(v1 ...) {v1, . . .} {v1, . . .} I = {v I 1 , . . .}

Object Properties (R)

R (URI reference) R R I ⊆ ∆ I × ∆ I

R −

(R − ) I = (R I ) −

Datatype Properties (U)

U (URI reference) U U I ⊆ ∆ I × ∆ I D

Individuals (o)

o (URI reference) o o I ∈ ∆ I

Data Values (v)

v (RDF literal) v v I = v D

Abstract Syntax DL Syntax Semantics

Class(A partial C1 ...Cn) A ⊑ C1 ⊓ ...⊓ Cn A I ⊆ C I 1 ∩ ...∩ C I n

Class(A complete C1 ...Cn) A = C1 ⊓ ...⊓ Cn A I = C I 1 ∩ ...∩ C I n

EnumeratedClass(A o1 ...on) A = {o1,...,on} A I = {o I 1 ,...,o I n}

SubClassOf(C1 C2) C1 ⊑ C2 C I 1 ⊆ C I 2

EquivalentClasses(C1 ...Cn) C1 = ...= Cn C I 1 = ...= C I n

DisjointClasses(C1 ...Cn) Ci ⊓ Cj = ⊥,i= j C I i ∩ C I j {},i= j

Datatype(D) D I ⊆ ∆ I D

DatatypeProperty(U super(U1)...super(Un) U ⊑ Ui

U I ⊆ U I i

domain(C1) ...domain(Cm) 1 U ⊑ Ci U I ⊆ C I i × ∆ I D

range(D1) ...range(Dl) ⊤⊑∀U.Di U I ⊆ ∆ I × D I i

[Functional]) ⊤⊑ 1 U U I is functional

SubPropertyOf(U1 U2) U1 ⊑ U2 U I 1 ⊆ U I 2

EquivalentProperties(U1 ...Un) U1 = ...= Un U I 1 = ...= U I ObjectProperty(R super(R1)...super(Rn) R ⊑ Ri

n

R I ⊆ R I domain(C1) ...domain(Cm) 1 R ⊑ Ci

i

R I ⊆ C I i × ∆ I

range(C1) ...range(Cl) ⊤⊑∀R.Ci R I ⊆ ∆ I × C I [inverseOf(R0] R =(

i

− R0) R I =(R I 0 ) −

[Symmetric] R =( − R) R I =(R I ) −

[Functional] ⊤⊑ 1 R R I is functional

[InverseFunctional] ⊤⊑ 1 R −

(R I ) − is functional

[Transitive]) Tr(R) R I =(R I ) +

SubPropertyOf(R1 R2) R1 ⊑ R2 R I 1 ⊆ R I 2

EquivalentProperties(R1 ...Rn) R1 = ...= Rn R I 1 = ...= R I n

AnnotationProperty(S)

Individual(o type(C1) ...type(Cn) o ∈ Ci o I ∈ C I i

value(R1 o1)...value(Rn on) 〈o, oi〉 ∈Ri 〈o I ,o I i 〉∈R I i

value(U1 v1)...value(Un vn)) 〈o, vi〉 ∈Ui 〈o I ,v I i 〉∈U I i

SameIndividual(o1 ...on) o1 = ...= on o I i = o I j

DifferentIndividuals(o1 ...on) oi = oj,i= j o I i = o I j ,i= j

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