Hi Paola, (01)
I think we have the perennial problem here of using the same terms with
different senses.
My comments below. (02)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of paola.dimaio@xxxxxxxxx
> Sent: 22 January 2009 13:05
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] Next steps in using ontologies as
> standards
>
> Chris
>
> thanks for reply and I do not intend to bother you with what is
> something which is occupying my mind as your write
>
> I am just working on a paragraph about this and I am also struggling
> to avoid writing things that can be easily disproven (got to avoid
> the proof freaks breathing on my neck), so I am glad I have the chance
> to share what i am thinking
>
> well, from my reading, axioms are essential artifacts in ontology,
> because
> any object relating too another object does so according to some logic
>
> an ontology must have relationships, and some of these relationships
> are fixed truths (axioms) (03)
If you regard relationships as axioms then this is true.
My guess is that for mathematicians, axioms are not the same things as
relations. http://en.wikipedia.org/wiki/Axiom (04)
>
> [although it can be argued that lightweight ontologies do not depend
> on axioms as much as upper ontologies, no valid (that can be proven)
> assertion (thus ontological statements) can exist without relation to
> at least one axiom]
>
> axioms represent logical statements.
> an ontology without axioms (relationships) is more of a taxonomy (05)
I think "an ontology without relationships is more of a taxonomy" is OK
But "an ontology without axioms is more of a taxonomy" is more debatable.
Furthermore, one needs to be careful whether one is talking about the
representation or what is being represented. If I have an axiom about
something, this represents (let us say) a set of states of affairs, it is
not the actual set of states of affairs. (06)
>
> there is no ontology without relationships between concepts, and these
> relationships, when they are fixed, are axioms (07)
It seems to me that there is some equivocation here between the
representation (axioms) and the represented (relationship). (08)
>
> therefore, ontology includes logic within itself
>
> (what you wrote earlier seemed to contrast ontology and logic, which
> in my understanding is not true) (09)
If logic is the study of (valid) inference and ontology the study of
existence, then, on the face of it, they seem different. And if one thinks
there is a relationship between inference and existence, one needs to
clarify what this is. (010)
It seems to me that your comments indicate that axioms in a logical language
can be interpreted as representing relationships in the world. This seems to
me fine, but I do not see how it gets you to saying ontology includes logic. (011)
Apologies if I have misunderstood your point. (012)
>
> Just thinking loud
>
> PDM
>
>
> On Thu, Jan 22, 2009 at 7:47 PM, Chris Partridge
> <mail@xxxxxxxxxxxxxxxxxx> wrote:
> > Hi Paola,
> >
> >> >
> >> > A less simple answer would have to do with the relationship
> between
> >> logic
> >> > (inference) and ontology. Traditionally logic studies inference
> and
> >> ontology
> >> > existence. (I realise that in CS ontology (or as Pat called it WC3
> >> ontology)
> >> > inference plays a big part.)
> >> >
> >>
> >> it strikes me that you write this as I am working on it
> >> (its either echelon, or colletive consciouness, or both)
> >>
> >> however, I cannot see the sharp distinction between the two, cause
> >> ontology (existence) includes logic in its axioms
> >> therefore I am lead to conclude that logic is part of ontology
> >>
> >> if we consider axioms (and constraints) necessary to inference
> >> then the two are dependent
> >>
> >> isnt that so?
> >
> > I must apologise, I am afraid I do not understand your comments.
> > I do not see how "ontology (existence) includes logic in its axioms".
> > Ontology, in the philosophical sense I am using it, is a set of
> things. It
> > does not have axioms, though I suppose one could argue axioms are
> objects in
> > some (mathematical or logical) ontology. I suspect we are using terms
> in
> > different ways.
> >
> > Also, I was not arguing for there being no relationship between
> ontology and
> > logic. A hundred years ago people like Russell and Husserl saw logic
> as
> > being the language that could be used to describe an ontology.
> However, over
> > the last 100 years or so, the notion of logic has been refined to the
> study
> > of inference. I suspect there is a relationship, but have not managed
> to
> > find much material describing it, so if anyone knows of some ...
> >
> > Regards,
> > Chris
> >
> >>
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