| CN | concept name |
| C,D,E | concept expression |
| RN | role name |
| R, R1, R2,... | role expressions, i.e. role name or inverse role |
| KRSS | OWLClassExpression |
| (at-least n R C) | (OWLObjectMinCardinality R n C) |
| (at-most n R C) | (OWLObjectMaxCardinality R n C) |
| (exactly n R C) | (OWLObjectExactCardinality R n C) |
| (some R C) | (OWLObjectSomeValuesFrom R C) |
| (all R C) | (OWLObjectAllValuesFrom R C) |
| (not C) | (OWLObjectComplementOf C) |
| (and C D E) | (OWLObjectIntersectionOf C D E) |
| (or C D E) | (OWLObjectUnionOf C D E) |
| KRSS | OWLObjectPropertyExpression |
| (inv R) | (OWLInverseObjectPropertiesAxiom R) |
| KRSS2 | OWLAxiom | KRSS syntax | Remarks |
| OWLDisjointClassesAxiom | (disjoint C D) | OWLDisjointClasses C D1 D2 ... Dn { (disjoint i(j) i(j+k)) | 1 <= j <=n, j<k<=n, j=|=k} | |
| OWLEquivalentClasses | (define-concept C D) | OWLEquivalentClasses C D1 D2...Dn will be translated to: (define-concept C (and D1 D2...Dn)) Only applicable if there is no OWLSubClassOf axiom. | |
| OWLSubClassOfAxiom | (define-primitive-concept C D) | OWLSubClassOfAxiom C D1...Dn (n > 1) will be translated to: (define-primitive-concept C (and D1...Dn)) Only applicable if there is no OWLEquivalentClasses axiom. In that case the class will be introduced via (define-concept...) and all subclass axioms are handled via implies | |
| OWLSubClassOfAxiom | (implies D C) | Only in case of GCIs with concept expression (not named class) D, or in case that D is a non-primitive concept. Otherwise superclasses are introduced via (define-primitive-concept D ...) | |
| OWLEquivalentObjectPropertiesAxiom | (roles-equivalent r s) | All roles are explicitly introduced via define-primitive-role. | |
| OWLSubPropertyChainOfAxiom | (role-inclusion (compose r s) t) | Role inclusions of the kind (role-inclusion (compose r s) r) resp. (role-inclusion (compose s r) r) are handled within the (define-primitive-role) statement as right- resp. left-identities iff it is the only role-inclusion wrt. the super property. | |
| OWLSubObjectPropertyAxiom | (define-primitive-role R :parent S) (define-primitive-role R :parents S T U) Additional attributes:
| This will be only used if there is no OWLEquivalentClasses axiom containing R (see define-role). The additional attributes are added if there is an OWLTransitiveObjectProperyAxiom, OWLSymmetricObjectPropertyAxiom, OWLReflexiveObjectPropertyAxiom, OWLObjectPropertyDomainAxiom, OWLObjectPropertyRangeAxiom resp. OWLInverseObjectPropertiesAxiom. If there are multiple OWLInverseObjectPropertiesAxioms only one inverse is handled here, all others are handled via (inverse) statements. Domains/ranges of multiple domain/range axioms are handled as (and C C1...Cn). | |
| OWLSubObjectPropertyAxiom | (implies-role r s) | Only applicable if r is an inverse property, otherwise superproperties are handled within the define-primitive-role statement. | |
| OWLInverseObjectPropertiesAxiom | (inverse r s) | Only inverse properties which are not introduced via define-primitive-role. | |
| OWLObjectPropertyRangeAxiom | see define-primitive-role | ||
| OWLObjectPropertyDomainAxiom | see define-primitive-role | ||
| OWLSymmetricObjectPropertyAxiom | see define-primitive-role | ||
| OWLTransitiveObjectPropertyAxiom | see define-primitive-role | ||
| OWLReflexiveObjectPropertyAxiom | see define-primitive-role | ||
| OWLClassAssertionAxiom | (instance i D) | ||
| OWLDifferentIndividualsAxiom | (distinct i1 i2) | OWLDifferentIndividualsAxiom i1 i2 ... in will be splitted into: { (distinct i(j) i(j+k)) | 1 <= j <=n, j<k<=n, j=|=k} | |
| OWLObjectPropertyAssertionAxiom | (related i1 P i2) | i1: subject, i2: object | |
| OWLSameIndividualsAxiom | (equal i1 i2) | OWLSameIndividual i1 i2 ...i(n-1) in in will be splitted into: { (equal i(j) i(j+k)) | 1 <= j <=n, j<k<=n, j=|=k} (equal i1 i2) (equal i1 i3) ... (equal i(n-1) in) |
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