N-ary relations and Qualified Cardinality Restrictions (QCRs) Alan Rector with The Bio Health Informatics Group The CO-ODE Team University of Manchester.

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N-ary relations and Qualified Cardinality Restrictions (QCRs) Alan Rector with The Bio Health Informatics Group The CO-ODE Team University of Manchester With acknowledgements to Natsha Noy and the Semantic Web Best Practice and Deployment Working Group (SWBP) OpenGALEN BioHealth Informatics Group © University of Manchester

2 Saying something about a restriction ►Not just ►that an a book is good but who said so ►And its price ►And where to buy it ►But can say nothing about properties ►except special thing ►Super and subproperties ►Functional, transitive, symmetric

N-ary Relations Binary Relation ►According to whom? "Lions: Life in the Pride" excellent quality

Adding attributes to a Relation "Lions: Life in the Pride" excellent NY Times Book review quality

Define a class for a relation: Reification "Lions: Life in the Pride" Description_1 Quality: Excellent Source: NY Times Book review quality description Class: Description instance-of

A Relation Between Multiple Participants John buys “Lions:Life in the Pride” from books.com for $15 ►Participants in this relation: ►John ►“Lions: Life in the Pride” ►books.com ►$15 ►No clear “originator”

Network of Participants John Class: Purchase This Purchase $15 "Lions: Life in the Pride" books.com buyer object seller price

Considerations ►Choosing the right pattern: often subjective ►Pattern 1: additional attributes for a relation ►Pattern 2: a network of participants ►Instances of reified relations usually don’t have meaningful names ►Defining inverse relations is more tricky

© University of Manchester 9 Qualified cardinality constraints ►Use with partonomy ►Use with n-ary relations

© University of Manchester 10 Cardinality Restrictions ►“All mammals have four limbs” ►“All Persons have two legs and two arms” ►“(All mammals have two forelimbs and two hind limbs)”

© University of Manchester 11 What we would like to say: Qualified cardinality constraints ►Mammal has_part cardinality=4 Limb ►Mammal has_part cardinality = 2 Forelimb has_part cardinality = 2 Hindlimb ►Arm = Forelimb AND is_part_of some Person Glossary: “Forelimb” = front leg or arm “Hindlimb” = back leg

© University of Manchester 12 What we have to say in OWL ►The property has_part has subproperties: has_limb has_leg has_arm has_wing ►Mammal, Reptile, Bird has_limb cardinality=4 Person has_leg cardinality=2 Cow, Dog, Pig… has_leg cardinality=4 Bird has_leg cardinality=2 ►Biped = Animal AND has_leg cardinality=2

© University of Manchester 13 Classification of bipeds and quadrupeds ►Before classification ►After classificaiton

© University of Manchester 14 Cardinality and n-ary relations ►Need to control cardinality of relations represented as classes ►An animal can have just 1 “dangerousness” ►Requires a special subproperty of quality: ►has_dangerousness_quality cardinality=1

© University of Manchester 15 Re-representing the property has_danger as the class Risk Animal Dangerous has_danger cardinality=1 ‘functional’ AnimalRisk has_Quality cardinality=1 Risk_type Seriousness Avoidance has_risk_type cardinality=1 has_seriousness cardinality=1 has_avoidance cardinality=1

© University of Manchester 16 In OWL 1.0 must add subproperty for each quality to control cardinality, e.g. has_risk_quality OWL 1.1 will add QCRs ►Leads to a proliferation of subproperties ►The issue of “Qualified Cardinality Constraints” Animal Risk has_Risk_Quality cardinality=1 Risk_type Seriousness Avoidance has_risk_type cardinality=1 has_seriousness cardinality=1 has_avoidance cardinality=1 special subproperty of has_quality