Re: blog: semantic dissonance in uniprot

On Mar 29, 2009, at 10:48 AM, Oliver Ruebenacker wrote:

>     Hello Pat, All,
>
> On Sun, Mar 29, 2009 at 12:10 AM, Pat Hayes <phayes@ihmc.us> wrote:
>> On Mar 28, 2009, at 3:52 PM, Oliver Ruebenacker wrote:
>>>  Arithmetic can be described by ontologies.
>>
>> Not full arithmetic, because of Goedel's incompleteness theorem.  
>> You might
>> manage with Peano arithmetic, but I doubt it. I suspect you would  
>> need at
>> least complex analysis.
>
>  Isn't Goedel Incompleteness something that does not apply only to
> Math, but to Formal Logic in general? Wouldn't that imply that it is a
> concern for ontology building regardless of whether it is about Math
> or any other area?

In its original formulation it is entirely about arithmetic, but it  
has consequences for a wide variety of other topics which are  
commensurate with arithmetic in their expressivity.

>
>  The way I understand it: It depends on how deep you want to dig. For
> example, if you want to talk about the real number one, you could just
> declare a symbol for it and define in words that this is the real
> number one and rely on every one agreeing what it is and you will not
> be confronted with incompleteness.

Oh yes, I agree, you can always do things like that. And in practice  
that is often the best way to proceed. This is in effect what RDF and  
OWL do with integers, by relying on the XML Schema datatypes, which  
denote the natural numbers simply by fiat, without any pretense at  
formalizing them.

> Or you could try to formalize the
> definition of real numbers by formalizing field axioms. For example,
> you can base real numbers on set theory, and then you have the choice
> of naive set theory, which leaves some things undefined, or more
> sophisticated approaches, and then you would definitely be concerned
> about incompleteness.
>
>>>  What would you do?
>>
>> I wouldn't. Its far too complicated and too far from existing  
>> ontology work.
>> Statistical ensembles are just way outside the state of the
>> logical-formalizing art, I would guess. If you can cite any work,  
>> however,
>> I'd be delighted to be proved wrong.
>
>  Perhaps the question should read: What would you advice to some one
> who wants to build an ontology to describe pathways for Systems
> Biology purposes?

I really have no advice to give, as I know virtually nothing about  
systems biology. My remarks were based on your raising the topic of  
statistical ensembles, which is enough to make me want to go and do  
something else, I'm afraid.

Pat

>
>     Take care
>     Oliver
>
> -- 
> Oliver Ruebenacker, Computational Cell Biologist
> BioPAX Integration at Virtual Cell (http://vcell.org/biopax)
> Center for Cell Analysis and Modeling
> http://www.oliver.curiousworld.org
>
>

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Received on Monday, 30 March 2009 03:24:17 UTC