- From: Jonathan Rees <jar@creativecommons.org>
- Date: Thu, 26 Feb 2009 10:47:54 -0500
- To: Michael Hausenblas <michael.hausenblas@deri.org>
- Cc: Alan Ruttenberg <alanruttenberg@gmail.com>, AWWSW TF <public-awwsw@w3.org>, "Booth, David (HP Software - Boston)" <dbooth@hp.com>
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