|From:||Ali Hashemi <ali.hashemi+ontolog@xxxxxxxxxxx>|
|Date:||Tue, 2 Mar 2010 20:49:22 -0500|
Dear Gary and Pat C,|
Gary, a reply to your query re "how does meaning change" is below the "======".
On Tue, Mar 2, 2010 at 6:30 PM, Patrick Cassidy <pat@xxxxxxxxx> wrote:
I understand the difficulties that PatH describes (below) and agree that
we allow anyone to call
If I'm correct in my understanding of you've written above, I agree wholeheartedly with most of it.
In fact, except for the quest to identify and create an special foundation ontology out of the primitives, what you are now proposing is indistinguishable from what is already underway via COLORE. COLORE is gathering all ontologies written using CLIF regardless of their terminology or quirks. It provides a growing platform (a repository) in which they may be inputted and relations between them explored, identified and formalized.
and http://ontolog.cim3.net/file/work/OpenOntologyRepository/2010-02-19_OOR-Developers-Panel/COLORE--MichaelGruninger_20100219.pdf )
If you will be using ontologies with first order expressiveness, I would suggest you consider reusing the work already being done in that framework. So far, the following families of ontologies have been inputted (totaling about 80):
Generic Ontologies: Temporal, Duration, Process, Mereotopology, Geometry
Mathematical Ont: Algebras, Graphs, Lattices, Linear Orderings, Partial Orderings, Vector Spaces
Adding Upper Ontology type ontologies would also be very useful and would serve your goals. One possible approach might be to pick whichever upper ontology you like and start writing axioms for it in Common Logic. Once that is done, relations between terms in the UO and those in the repository could be explored. I'm not sure what you would connect any UO to otherwise. Outside of COLORE, there is a paucity of FOL theories at the moment. And for the type of interoperability you hope for, we need at least first order expressiveness except for the most obvious cases.
Keep in mind, mappings / relations connecting the ontologies already in the repository have also been specified, so you can leverage that work and see how those Upper Ontology primitives are reusing or are being reused by these existing ontologies.
Additionally, in terms of addressing some of the practical issues, I've previously mentioned a paper that is appearing in FOIS 2010 (Gruninger et al - "Ontology Verification with Repositories"), here's a draft version that I'm pretty sure I can share: http://preview.tinyurl.com/yf7cmdn
This paper provides some of the vocabulary and grounding necessary to specify mappings at the level of rigour which support the kind of interoperability PatC envisions. It also provides two examples showing how ontologies can be mapped into one another and how these results can be expoited. Note all these results also apply to ontologies written in OWL or RDFS; however, at the moment one wouldn't be able to identify the appropriate mapping for most of these ontologies because so much of the semantics are left outside the system of representation. Don't be scared away by the mathematical logic notation, they're there to eliminate ambiguity. There are very concrete and practical uses for these results... feel free to ask questions.
Nicola Guarino's explication of a formal ontology is eminently useful when discussing what we mean when we speak about ... formal ontologies. To answer your initial question regarding when primitives might change:
From a formal perspective, there are two possible ways of extending axioms, Conservative or Nonconservative. (Ron, yes I'll add a proper version of this to the wiki).
In plain English, a conservative extension means that you are introducing new terms which you didn't have in your vocabulary before and specifically you need these new terms to prove new things based on your axioms.
So say i've an ontology for the elephants that was silent about colour. I later introduce "pink" to denote that I care about distinguishing / reasoning / noticing "pink elephants"- This is a conservative extension of elephant. You are introducing a completely new entity that wasn't describable in the previous language. We are extending the meaning of elephant conservatively. We can say new things about elephants that we couldn't before, but we had to develop new language to do so.
In comparison, a non-conservative extension does change the meaning of your primitives. Say I have an ontology of lineage which ranges over both sexual and asexual creatures. This means that any creature can have one or two parents. Later, I realize that I only want lineage to range over sexual creatures, so I add an axiom to that effect. Here, I have non-conservatively extended the meaning of lineage, since I could have used my existing vocabulary to describe the new insight.
In the example you provided, the parallel-postulate introduces a new relation called "parallel". This relation is describable in the language of the previous axioms, and it proves novel properties about each of the primitives. Hence, the fifth postulate is a non-conservative extension of the first four. It doesn't change what we mean (colloquially) when say "point" or "line", but it definitely changes what is meant when we use them in a formal ontology! We can now definitively prove something about lines (if they are in a particular configuration) that we couldn't before. Naiively, lines are still lines, however what we can say about them, and how we talk about them has changed...
Hope this helps,
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