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Re: [ontolog-forum] [ontology-forum] Intensional, Extensional, FO, HO &

To: <ian@xxxxxxxxxxxxxxxx>, "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rich Cooper" <rich@xxxxxxxxxxxxxxxxxxxxxx>
Date: Thu, 12 Feb 2009 09:44:15 -0800
Message-id: <20090212174505.67DB2138CEA@xxxxxxxxxxxxxxxxx>

Ian Bailey wrote:


>Hello Now,


>I’ve been watching this thread on standard ontologies for a bit now…I even dared stick my head in the >lion’s mouth a couple of times by posting.


>I realise the thread is supposed to be about using ontologies in standards. Although that doesn’t >preclude everyone doing their own thing (it certainly hasn’t before in the world of standards), it would >perhaps make sense if these standards *could* all descend from a common foundation. By >foundation, I mean what Rich was calling an Ultra-High-Level Ontology – i.e. ontic categories and >relationships.


>Has anyone looked into the possibility of a foundation that covers the whole gamut ?  First order, >higher order, intensional, extensional (my sense), etc. ? RDF/RDFS gives us classes, type-instance, and >sub-super. It just doesn’t have individuals (my sense, ”something with spatio-temporal extent”). RDFS >covers higher order and first order by dint of not restricting how RDF:type is used. All it lacks is a >grounding in physical extent, which is understandable as it was designed to refer to stuff in cyberspace >rather than stuff I can kick.


Hi Ian,


One reason I liked your fundamental ontology is that it is relatively compact, which I think is excellent for a UHLO FO.  Although the “whole gamut” is needed ultimately, I think the UHLO level should be slim and only model what people can agree on.  It appears that John Sowa, Pat Hayes and you still have differences with the concepts in your model, and Ed Barkmeyer wants axioms in addition to concepts before he is willing to call it an “ontology”.  Personally, I think axioms would be better added in ontologies below the FO seed ontology, since I believe defining the axioms will be a difficult process to reach agreement on. 


I think we need two tracks.  The first is what we can all (most?) agree on, perhaps your FO – that is what I’ve called a UHLO for lack of a better name.  The “whole gamut” can descend from whatever the UHLO is in gobs and bursts as specific needs are announced and met.  The pieces of the “whole gamut” might be developed by adding concepts which (probably) fewer will agree on, but which there are groups of agreement due to similar mission statements. 


But like you, I think a very slim highest level ontology would add some momentum to the work of this list by letting us have at least a few concepts in agreement among us.  If you want to modify your UHLO to meet the slimmest of widely agreed concepts, which process could make it fit the need very well.  Additions should be those which can be debated and ultimately agreed to by various groups of us. 


The result MIGHT initialize John Sowa’s lattice of theories like a coat rack for later ontologies.  That could make his idea of a registry of ontologies come to life.  Progress made after the UHLO could extend the lattice in areas needed to continue development.  The infinite lattice might be further away, but at least we could point to  progress in agreeing on and realizing some common structures. 


I have no dog in this fight.  Any ontology might be the UHLO – I just want SOMETHING we can agree on because it is small enough to be agreeable to (nearly) all of us. 






Rich Cooper


Rich AT EnglishLogicKernel DOT com




>The difficulty, I suspect is in the intensional vs extensional bit. In BORO/ISO15926/IDEAS, we would >have one class with many names (e.g. “Equiangular Triangle”, “Equilateral Triangle”), whereas the >intensional folks would have two classes, perhaps with an equivalence relationship between them. >Has anyone analysed the nature of these two approaches and come up with a common foundation for >both, or are they so fundamentally different it can’t be done ?  Surely some logician or philosopher >must have cracked this ?


>The SC4 resources, at one time, had class_by_intension and class_by_extension in them, not sure if >there was anything to join them up though. I think David Leal did the work on this.




>Ian Bailey


>T: +44 207 193 4605

>M: +44 7768 892362





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