CODEWITHSUNDEEP
owlprotege
Bill
Bill

Reputation: 179

universal quantification and vacuous entailment in OWL using Protege

I am trying understand cases where vacuous entailment occurs due to use of universal quantification in Protege. That is, axioms of the form:

A rel *only* B

Here is my setup:

I have created an ontology that (more or less) follows the one described in this Ontogenesis article:

http://ontogenesis.knowledgeblog.org/1260

It consists of an owns relation and two high level disjoint classes: person and pet.

Under the pet class, I have three primitive disjoint classes: dog, elephant, and newt.

Below the person class, I have a defined class pet owner, defined as follows:

'pet owner' equivalent_to person and (owns only pet)

Lastly, I have created and individual person, named person 1, that does not own any pets.

Universal quantification:

My understanding of universal quantification is that the only quantifier describes those individuals that only have relationships to individuals of a specific class. This entails that individuals that do not have any relationships to another individual would also be described by universal quantification.

In my example, I thought person 1 would be inferred to be a pet owner, since person 1 does not own any pets or stand in any other relationships. However, when I run the reasoner (HermiT and Pellet), this does not turn out to be the case. Person 1 is not inferred to be a member of pet owner.

So, it seems that I am not understanding universal quantification. Can someone please help me?

Upvotes: 1

Views: 152

Answers (1)

Dmitry Tsarkov
Dmitry Tsarkov

Reputation: 768

The problem here is that you didn't take into account Open World Assumption (OWA). By OWA the ontology only contains facts that are known; there might be other facts. If you say nothing about the things person 1 owns, it doesn't mean that it owns nothing. It might own other things, that are not in the ontology. So your universal restriction may prevent someone to be a pet owner (in case they own something that is not a pet, and the corresponding axiom is in the ontology). To make someone a pet owner, you might 'close' the information about it, e.g. saying that known pets are the only things that person owns. For this you may use owns only {pet1, pet2, pet3} construction.

Upvotes: 2

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