OWL universal quantification -

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i half way reading owl2 primer , having problem understanding universal quantification

the example given is

equivalentclasses(     :happyperson      objectallvaluesfrom( :haschild :happyperson ) )

it says happy person if children happy persons. if john doe has no children can instance of happyperson? parent?

i find part confusing, says:

hence, our above statement, every childless person qualified happy.

but wouldn't violate objectallvaluesfrom() constructor?

i think primer quite job @ explaining this, particularly following:

natural language indicators usage of universal quantification words “only,” “exclusively,” or “nothing but.”

to simplify bit further, consider expression you've given:

happyperson ≡ ∀ haschild . happyperson

this says happyperson only has children happyperson (are happy). logically, says nothing existence of instances of happy children. serves universal constraint on children may exist (note includes instances of happyperson don't have children).

compare existential quantifier, exists (∃):

happyperson ≡ ∃ haschild . happyperson

this says happyperson has at least one child happyperson. in constrast (∀), expression implies existence of happy child every instance of happyperson.

the answer, albeit unintuitive, lies in interpretation/semantics of objectallvaluesfrom owl construct in first-order logic (actually, description logic). fundamentally, objectallvaluesfrom construct relates logical universal quantifier (∀), , objectsomevaluesfrom construct relates logical existential quantifier (∃).


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