[topicmapmail] Topic Maps, Description Logics and Semantic Networks

[Murray Altheim]

Lars Marius Garshol wrote:
> 
> * Murray Altheim
>>
>> [...]
>> but if not the language of DL can be linked directly to FOL so that
>> shouldn't be too much of a stretch (though of course one is a superset
>> of the other; you'd be left out on a limb for anything not defined in
>> FOL, which with DL is quite a bit).
> 
> Given that DL is a subset of first-order logic I find this a bit 
> confusing. What did you mean?

I'm assuming you mean that FOL is a subset of DL? If you look at it
that way there should be no confusion. By "subset" I simply meant
that FOL is a component in the construction of a Description Logic.

One might also note that DL is not a single logic but a family of
knowledge representation languages. It just happens that one flavour
of DL ended up being talked about to the exclusion of others by the
"Semantic Web" people (not to be confused with the "TV people"). To
my knowledge there isn't *one* DL that is better than any other;
they're all just tools to be used for specific purposes.

Or to put it another way, FOL is a fundamental and simple foundation,
one of the tools upon which a DL is built. There are a lot of things
in DL (i.e., a lot of things that can be expressed in DL) that go
beyond what can be expressed FOL, which would only make sense -- it's
a richer language. DL is basically frames plus FOL. I believe (and
someone can correct me if I'm wrong) that anything expressed in DL
can potentially be deconstructed to an FOL expression, in the same
way that one can build any TTL logic solely from NAND gates, but the
FOL expression might be either enormously complex or the transforma-
tion may be lossy. I think it also depends on which DL. I'd have to
look that one up, haven't played with DL in a few years... but I
believe this is what is meant by a "DL being subsumed by FOL".

If you compare the Wikipedia pages on DL and FOL:

   DL:  http://en.wikipedia.org/wiki/Description_logics
   FOL: http://en.wikipedia.org/wiki/First_order_logic

you can see that even at the symbolic level FOL is much simpler than
DL.

Is that any help?

Murray

...........................................................................
Murray Altheim <murray07 at altheim.com>                           ===  = =
http://www.altheim.com/murray/                                     = =  ===
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