# FullSemanticsPropertyCharacteristics

From OWL

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**The OWL 2 Full semantics of the new Property Characteristics.**

## Contents

## Reflexive Properties

### Syntax

x rdf:type owl:ReflexiveProperty

### Semantics

Axiomatic triples:

owl:ReflexiveProperty rdfs:subClassOf owl:ObjectProperty

Main semantic condition:

p ∈ CEXT_I(S_I(owl:ReflexiveProperty)) IF AND ONLY IF p ∈ IOOP, x ∈ IOT → (x,x) ∈ EXT_I(p)

## Irreflexive Properties

### Syntax

x rdf:type owl:IrreflexiveProperty

### Semantics

Axiomatic triples:

owl:IrreflexiveProperty rdfs:subClassOf owl:ObjectProperty

Main semantic condition:

p ∈ CEXT_I(S_I(owl:IrreflexiveProperty)) IF AND ONLY IF p ∈ IOOP, x ∈ IOT → (x,x) ∉ EXT_I(p)

## Asymmetric Properties

### Syntax

x rdf:type owl:AsymmetricProperty

### Semantics

Axiomatic triples:

owl:AsymmetricProperty rdfs:subClassOf owl:ObjectProperty

Main semantic condition:

p ∈ CEXT_I(S_I(owl:AsymmetricProperty)) IF AND ONLY IF p ∈ IOOP, (x,y) ∈ EXT_I(p) → (y,x) ∉ EXT_I(p)

## Considerations

- The semantics defined here seem to be straightforward, and there do not seem to be very different alternatives.
- All semantics specified here correspond to the respective semantics in OWL 2 DL.
- Axiomatic triples: more specific than in OWL 1 Full, where the property characteristics were only unspecified classes. Now they are subclasses of owl:ObjectProperty.
- OWL 1 Full uses IF-AND-ONLY-IF semantic conditions for all property characteristics. This means that the property characteristics are fully defined by these semantic conditions. This approach is followed here, too.
- OWL 1 Full has "p ∈ IOOP" in the "THEN" branch of the property characteristics. This means that from a typing triple it can be concluded that the subject of the triple is a property, instead of explicitly stating this in the "IF" branch. This approach is followed here, too.
- A term of the form "(x,y) ∉ EXT_I(p)" corresponds to a negative property assertion.