Re: resources and URIs

>On Sunday, Jul 20, 2003, at 03:26 US/Eastern, Graham Klyne wrote:
>
>>Tim,
>>
>>Your message below seems closer to my understanding, except your 
>>comment about "assumption of a single interpretation" -- maybe this 
>>is just a terminological slip, but if we're talking about 
>>interpretations in a model theoretic sense, I think it's important 
>>to not try and claim any *single* interpretation.
>
>I'm not claiming that there is any single *well defined* interpretation.

?? What do you mean, then? What is a ill-defined interpretation? A 
set of well-defined interpretations, maybe?

>What I do, as you do, is point out that under certain rules, the 
>deductions (and action)  your agent makes are indistinguishable from 
>those of an agent who does assume a single interpretation.

Well, actually that still isn't correct. Look, if an agent knew 
enough to be able to pin down a single interpretation, then the agent 
would know everything that could possibly be known about the entire 
world: it would be omniscient.  Such an agent would not need to 
perform any deductions and would probably behave very differently 
from most agents.  It might demand that they worship it and forsake 
all other gods, for example.

>>[Background terminology check:  An "interpretation" arbitrarily 
>>assigns a single value from some domain to each of a set of names. 
>>A "denotation" of a name is the value assigned to that name by some 
>>given interpretation.  Thus, for a given name there are multiple 
>>denotations corresponding to each interpretation that mentions the 
>>name.]
>
>Absolutely. ("arbitrarily"?.  An agent considers interpretations 
>which are consistent with the data.
>So when I see and chose to believe
>   <#pat> contact:mailbox <mailto:phayes@ihmc.us>.
>I immediately rule out the interpretation in which  `<#pat> denotes 
>China, `contact:mailbox` denotes geographical inclusion, and 
><mailto:phayes@ihmc.us> denotes France.
>To take an arbitrary example.).
>
>
>>So, picking up your line of consistency and experimentation, if an 
>>"identity" is derived from (is the set of denotations according to) 
>>a set of interpretations that are consistent to some level of 
>>observation, we always have the possibility that additional 
>>observations will detect inconsistencies, hence fragment the 
>>identity into several distinct "sub-identities", each derived from 
>>a subset of the interpretations of the original.  In this sense an 
>>"ideal" identity (e.g. in the sense intuitively/informally used for 
>>URIs) might be derived from the limit of some set of consistent 
>>interpretations as the number of observations considered tends to 
>>an infinitude of all possible observations.  That is, we can never 
>>know the identity completely, but may know it well enough for any 
>>given purpose.
>
>Yes.

What does it mean to 'know an identity'?

>(I am reminded of a playground argument, "How do I know you don't 
>see red as what I see as blue.  You would call it blue, because 
>everything I see as blue you would say was blue when in fact it 
>would be red."  While that which is "really" denoted can never be 
>itself measured, it doesn't make any difference)
>
>>(In saying this, I'm trying to paraphrase in non-mathematical terms 
>>the way that definitions of limits and continuity are used in 
>>differential calculus.)
>
>>(Reviewing what I wrote here, it seems that a corollary is that any 
>>identity corresponds to (or may in general correspond to) an 
>>infinite number of possible denotations.  I think that underscores 
>>the point about not assuming a single interpretation.)
>>
>
>For me what underscores the need for being aware of possible 
>differences in denotations is the actual possibility that new 
>information may turn up distinguishing two things.

That can't possibly happen in RDF, though, with the present design. 
There is no way to say, my use of this URI doesn't fit with your 
usage of the same URI.  Just by using the same URI you will be 
agreeing with the other agent about the possible referents.

>However the danger of being too aware off it is that we spend too 
>much time worrying about it, like the kids worrying about what 
>people really see.
>
>Another danger is that we loose the *intent* that URIs should be 
>used to represent globally unique things.

But there is no such intent. Or at any rate, there shouldn't be. What 
would be the point of this intention? It has no useful consequences. 
You only need to be able to uniquely identify a referent when you 
need to DO something to it (and not to anything else), as in your 
taking-Fido-out example, and when using HTTP to ping an information 
resource.  But most (all?) of the actual reasoning on the SW deals 
with representations, not by performing operations on the denoted 
things themselves; and representations, by their very nature, only 
represent imperfectly: they are almost never sufficiently detailed to 
completely specify only a single possible interpretation. The only 
place that OWL uses URIs in this way is in owl:imports, to refer to 
an ontology: and that is handled by the http protocols, since 
owl:imports has no real model-theoretic semantics in any case.

>For example, if this talk of multiple interpretation allows 
>sloppiness in modeling for example peoples' home pages, people's 
>mailboxes, and people themselves in the knowledge representation, 
>then automated inference is doomed.

Well, not doomed, but realistically complicated. But that discussion 
should be on another thread.

Pat
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