# Re: Possible semantic bugs concerning domain and range

```>  >
>>  Range(P, A) -> (forall x,y P(x,y) -> A(y) )
>>
>>  You want
>>
>>  Range(P,A) <-> (forall x,y P(x,y) -> A(y) )
>>
>>  They are about equally clear and intuitive; but the latter rules out
>>  some possibilities which the former permits. I believe that all the
>>  'intuitive' entailments that people want in fact hold in both these
>>  cases; and that the former is therefore to be preferred.
>
>I am agnostic about which of these is to be preferred - as a humble
>engineer, all I need to know is which one it is so that I have a clear
>spec to which I can build my systems.
>
>One point that is worth making though is that there are a number of
>similar statements that can be made about OWL properties, and that it
>may make sense to give them a uniform semantics, i.e., all treated as
>implication or all treated as bi-implication. E.g., we also have:
>
>Domain(P,C) implies/iff (forall x,y P(x,y) -> C(x))
>TransitiveProperty(P) implies/iff (forall x,y,z (P(x,y) ^ P(y,z)) -> P(x,z))
>SymmetricProperty(P) implies/iff (forall x,y P(x,y) -> P(y,x))
>FunctionalProperty(P) implies/iff (forall x,y,z (P(x,y) ^ P(x,z)) -> y=z)
>InverseFunctionalProperty(P) implies/iff (forall x,y,z (P(y,x) ^
>P(z,x)) -> y=z)
>inverseOf(P,Q) implies/iff (forall x,y P(x,y) -> Q(y,x))

How about all the unary properties of properties having an IFF
semantics? That would make sense, but it would leave domain, range
and inverse up for discussion.

>functional). I argued for implies semantics, but the general view
>seemed to be that iff semantics should hold (and by extension that it
>should hold for all the above statements).

This is now post-F2F and we had this discussion briefly, but let me
expand on my reasons for the particular choices I prefer. First, I
don't buy the argument (rather, I don't hear any actual argument) for
the idea that we should treat all these cases uniformly. Seems to me
that we should in each case make the language conform as far as
possible to what might be called a reasonable pre-theoretic intuition

Given that, it seems to me that the notions of properties being
transitive, symmetric, functional and inverse functional really do
only have what might be called mathematical pre-theoretic meanings.
The only possible meanings one can attach to these terms are the
purely extensional ones. That is what it *means* to be transitive,
right? And similarly for the others. Also, note that these are all
simple predicates on properties, so giving them an IFF semantics
doesn't impose any identity conditions on properties (that is, it
doesn't force users to agree that properties are identical when they
don't think they should be).

InverseOf is more debatable: I can see someone wanting to say that
the inverse of the property 'isFatherOf' really is the unique
property 'hasAsFather', even if some other property has the same
extension. So I agree, there could be a case made there for an
intensional reading; but I havn't heard anyone particularly
requesting it. In contrast, domain and (especially) range not only
could have intensional readings, they seem to often actually be given
intensional readings in practice. Many people get a sharp intuitive
sense that there is something wrong when they are told that the
class, say, union(people, loaves of bread) is a range of Ancestor, or
that the universe is a range of every function; and many people see
nothing logically incoherent in the idea of restricting range classes
to, say, XML datatypes. I see no reason, therefore, to impose a
condition which rules out such intuitive usage, particularly when it
has no obvious utility in any case.

Pat

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Received on Friday, 11 October 2002 19:07:59 UTC