On Sun, Apr 30, 2006 at 09:08:27AM -0400, Patrick Durusau wrote:
> Chris,
>
> Chris Menzel wrote:
>
> >On Sat, Apr 29, 2006 at 11:19:55AM -0400, Patrick Durusau wrote:
> >
> >
> >>...Finally, it is FOL that imposes limitations on mapping.
> >>
> >>Assume that we have an experienced analyst that is reviewing
> >>information that has been recorded in a subject map using subject
> >>proxies. Due to their experience, they have reached a conclusion that
> >>what appears to be two distinct individuals is actually one. A
> >>conclusion that would result in merging proxies that represent the
> >>purchaser of weaponized anthrax and a recent entry into the US.
> >>
> >>They may not have an articulable basis for that conclusion and so FOL
> >>is not going to be of any use.
> >
> >I'm not at all sure what an "articulable basis for a conclusion" is,
> >but why does one need such a basis any more in the case of an
> >identity assertion than in any other case? If the analyst comes to
> >believe that S1 is in Afghanistan, she writes: In(Afghanistan,S1).
> >If she comes to believe that individuals S1 and S2 are one and the
> >same, she writes: S1 = S2.
> >
> Quite true, but as I noted yesterday, there is a difference between
> using FOL to represent the conclusions of the analyst and saying, "see
> the power of an FOL based system." (01)
Sure thing, but I'm afraid I don't get the point. You said "FOL ...
imposes limitations on mapping" and, presumably, your example was meant
to demonstrate this. My response shows that your example demonstrates
no such thing. (02)
> In most contexts, FOL is touted as a means to "reason" about
> information in a knowledgebase. (03)
I don't know what contexts you are referring to, but in my experience
FOL is touted primarily as a means to *represent* information and it is
explicitly and pretty much universally acknowledged that full FOL has
severe and well-known limitations vis-a-vis reasoning -- hence the need
for description logics, WFS, defeasible reasoners, and other
non-classical reasoning systems. (04)
> In the example in dispute, FOL is simply representing the conclusion
> of a human analyst. (05)
Er, wasn't that the point? (06)
> >>Should they simply not request merging the proxies on the basis of
> >>their judgment (assume the analyst is also identified as a subject)
> >>since they have no way to express it in FOL? Hardly, one has a
> >>merging rule that says Analyst X says proxy A and proxy B represent
> >>the same subject. Utterly outside of FOL.
> >
> >Not at all, though of course you need to use first-order theories that
> >enable you to express information about the appropriate objects,
> >properties, and relations. In particular, your rule above is easily
> >formalized in a first-order theory that contains appropriate operators
> >and terms to represent beliefs and/or assertions. There are numerous
> >first-order frameworks in which this is possible.
> >
> Yes and as I note above, that is representation of the input of a
> human operator, not a conclusion reached by the use of FOL. (07)
Again, I am not seeing the point. Are you suggesting that an FOL
reasoner couldn't conclude S1 = S2? (08)
> >>Apologies for the length to anyone who has gotten this far. I deeply
> >>respect the power of FOL and think it should be used whenever
> >>appropriate. But the key word in that statement is *appropriate.*
> >
> >Seems to me it is *always* appropriate when the point is
> >representation; I mean, why tie your hands expressively if the point
> >is to get the nature and structure of the relevant information right?
> >That said, of course, one might well use a weaker logic, or a
> >non-classical logic, if, say tractable or defeasible reasoning is
> >needed.
>
> Let's separate out the use of FOL for representation and the use of FOL
> for reasoning, as you appear to do so in the last sentence of your post. (09)
Yes, this is a critical distinction to make in discussions of FOL for
knowledge representation and knowledge engineering. (010)
> Even assuming that FOL is sufficient for any representation (a point
> you assume and I don't want to be diverted onto), why should any
> system exclude other means of representation? (011)
I don't know. Do you see me making any such claim anywhere? (012)
Your question is revealing, though. You seem to be thinking of FOL as a
particular system of representation. I'm not. FOL encompasses many
many forms of representation. Topic Maps themselves can be expressed as
a theory in a first-order language. But it would be silly to present
Topic Maps in that form to users, as standard TM syntax provides a much
friendlier face, and that is tremendously important for knowledge
capture. My claim about FOL is simply that, if you have useful
representations at all -- ones that are syntactically and semantically
well-defined -- then you've got something that can be expressed in the
language of FOL. *That* is the sense in which FOL is fundamental to KR. (013)
> In other words, why should a college dean, chemistry professor,
> physician, stock trader, economist, or even an elected official, ;-) ,
> have to use FOL to represent their subjects in an information system? (014)
Well, that depends on what you mean by "using FOL". If you mean that
they have to master, say, KIF and become proficient at translating from
natural language into first-order logic, then of course it would be
silly to impose that upon ordinary types of users like those mentioned
here. What *is* required of such users is that they are able to use a
system of representation that is syntactically and semantically
well-defined if there is to be any hope whatsoever that their
representations carry information that can be usefully shared and
reasoned upon. And, once again, any such representation will be one
that can be translated into (perhaps some sublanguage of) the language
of first-order logic. (015)
> What do we gain by disenfranchising users who have non-FOL descriptions
> of their subjects? (serious question) (016)
This question embodies the same misunderstanding. Many different forms
of representation are useful and respectable. But they must be
syntactically and semantically well-formed, on the model of standard
first-order languages. My argument is really just that systems of
representation have to be rigorously defined, both syntactically and
semantically. Only then will representations in the system carry
information that is usefully shared and reused. Done right, any
well-formed system of representation is really just a first-order system
(or perhaps a subsystem of such) in disguise. (I ignore the matter of
systems that are *stronger* than FOL for purposes here.) (017)
> I have some ideas on what we lose by requiring only FOL descriptions:
>
> 1. The number of users who can usefully contribute information to a
> system is greatly reduced. (018)
This again confuses FOL with certain specific first-order systems of
representation, e.g., KIF. That's a mistake. (019)
> 2. The variety of descriptions of subjects is reduced. (020)
Simply untrue. Anything you can usefully describe -- in such a way that
the description is syntactically well-formed and semantically
meaningful -- is describable in a first-order system. If you think that
isn't so, then provide an example of such a description. (021)
> 3. The systems in which such descriptions were developed are not
> represented or at least not independently of FOL. (022)
I don't know what this means. (023)
> In other words, if all descriptions must be translated or reduced to
> FOL, (024)
That is again a red herring. If the descriptions are well-defined,
there is no need whatever to translate them to a more "standard" sort of
first-order language. They already *are* in effect first-order
representations, at least in the sense that they are within a framework
that could be embedded into a full first-order framework without any
loss of information. But no one is insisting that we actually do so;
quite the contrary. (025)
> then we have lost the original descriptions of subjects by those most
> concerned with them, the users. So why use a lossy system when it is
> unnecessary? (026)
Nobody is advocating any such thing. (027)
> Note that we are only talking about "description" using FOL. I don't
> think it is legitmate to say that if we have FOL descriptions then it
> follows that an FOL system can "reason" about those subjects. It
> certainly can, (028)
Then why say it is not legitimate to say so? (029)
> but then the question is whether the outcomes of that reasoning make
> any sense to the ultimate users. (030)
If the outcomes are expressed in the same system as the input, then of
course they will be. Again, this appears to be confusing FOL with a
particular system of representation. (031)
Regards, (032)
Chris Menzel (033)
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