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Re: Learning from other disciplines?

From: Jonathan Rees <jar@creativecommons.org>
Date: Thu, 26 Feb 2009 10:47:54 -0500
Cc: Alan Ruttenberg <alanruttenberg@gmail.com>, AWWSW TF <public-awwsw@w3.org>, "Booth, David (HP Software - Boston)" <dbooth@hp.com>
Message-Id: <69F88D9B-7CB6-45BA-945A-40AD03D2EAE8@creativecommons.org>
To: Michael Hausenblas <michael.hausenblas@deri.org>
I have a favorite account of "ambiguity" that comes from a completely  
different direction: model theory.

As I've said before model theory (as in: RDF semantics, OWL DL  
semantics, OWL Full semantics, etc.) explains "ambiguity" not as a  
problem in definition of terms, but of interpretation of theories.  
That is, you start with a set of logical axioms and some logic,  
consider the deductive closure (= theory), and then look for models of  
the theory. One way to find a model is by looking at rdfs:comment,  
rdfs:label, and other properties, which, however ill formed or blurry  
they may be, might constitute adequate hints to lead you to a model.

Now suppose you're talking to someone else about a theory, and you  
realize that the model they have in mind is one that you wish you had  
ruled out when you put the theory together. You have a choice: You can  
start speaking to the person in natural language to attempt to steer  
them toward the model you had in mind; or you can add constraining  
axioms to the theory, and agree with your interlocutor to consider the  
modified theory in place of the original. The latter approach, when it  
succeeds in converging, is called "knowledge representation" (or so  
Pat tells me), while the former is more in the direction of  
"controlled vocabulary". Choosing to communicate informally instead of  
formally is a sort of a failure of the method, but is often expedient.  
I think each method has its place, and typical RDF and OWL practice  
probably sits somewhere in between.

For example: Suppose I have a logical theory with three symbols P, A,  
and B, and I say that P is a relation that holds between A and B (in  
RDF: A P B.). It is very easy to come up with models of this theory;  
too easy in fact. We could have 2 < 3, ice is-frozen-state-of water,  
etc. Very "ambiguous". Now I tell you, at the meta-level or in  
rdfs:comment, that P means has father, A means Jonathan, and B means  
Gerald. This doesn't say Jonathan who, or what exactly is meant by  
"father", so there are still many plausible models, and nothing has  
changed from a logical point of view, but now you will probably not be  
interested in considering models in which A is not someone named  
Jonathan, B is not someone named Gerald, or P is not the has-father  
relation (i.e. B is not the father of A). Instead you will look for  
real-world scenarios to which the logic might apply (i.e. that are  
models of the theory). There is "ambiguity" (multiple interpretations)  
but less of it.

In the model theoretic account ambiguity is simply the existence of  
multiple models, and in the model theoretic + hints account ambiguity  
is the existence of multiple plausible models, where plausibility is  
not an operational notion. Interpretation ambiguity cannot always be  
isolated to individual terms, cannot always be detected, cannot
always be proven (to everyone's satisfaction), and can never be  
eliminated. It is inherent in the framework because models can't be  
communicated. This is the reason we use formal theories - they *can*  
be communicated, and over centuries people have become pretty  
successful at articulating, agreeing on, and following the rules of  
the game.

I steer toward a particular model as I add more axioms to the theory  
(last name, date of birth, clarification that a "father" is a "parent"  
but not a "mother", etc. etc.), because as the logical structure  
accumulates, accidental construction of unintended models becomes  
increasingly difficult. Pat tells me that there is some point in such  
an endeavor where it becomes so hard to interpret the logic  
incorrectly (at variance with intent) that one is justified in saying  
that "knowledge" has been "represented" logically.

Anyhow this is my argument for forgetting about the metatheory  
(logical systems containing symbols such as "denotes",  
"Interpretation", "Model", "splitting", etc.), and focusing on a  
simple first-order logical model of a domain first. We have a  
perfectly good account of ambiguity of interpretation already.  
Attempting a theory of the metatheory will just push an unsolvable  
problem off to an even worse place.

Jonathan
Received on Thursday, 26 February 2009 15:48:36 UTC

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