[topicmapmail] Re: Logicians do not rule the world (fortunately)

[Murray Altheim]

Quoting Lars Marius Garshol <larsga at ontopia.net>:
>
> * Murray Altheim
>>
>> This statement can only be valid if there is a grounding in some
>> form of logic that would make it true. Either the symmetry of a
>> given statement must be made explicit (and the software tools
>> that operate on that symmetry must be trained to read the explicit
>> statement of symmetry and operate upon it accordingly),
>
> The software tools that operate on that symmetry treat it as being  
> symmetrical. They can't do anything else.

Then in all relations that aren't symmetrical those tools will make
incorrect inferences: they are operating on a symmetry that doesn't
exist. This sounds like a bug, not a feature inherent in either the
model or its implementation in software. I certainly wouldn't write
a tool that assumed symmetry -- most relations aren't. If anything,
I'd assume not, statistically speaking.

>> Well, you can tell me that, and you can express that (i.e., write
>> it down) in a Topic Map, but stating it in a Topic Map in such a
>> way that can be reasoned upon by machines is an entirely different
>> matter. If you want an even rudimentary reasoning engine to be
>> able to connect the idea that
>>
>>   if    Norway borders-with Sweden
>>   then  Sweden borders-with Norway
>>
>> then the symmetry of the 'borders-with' relation must be stated
>> and the engine programmed to make that inference.
>
> No, that's not necessary in Topic Maps, since there is no way in a  
> topic map to distinguish the one statement from the other. They are  
> one and the same.

This seems to be mixing up what occurs at the Topic Maps level
and what happens at an inferencing/logic level. I.e., this has
nothing to do with Topic Maps, which are just being used as the
vehicle for the expression. But if in stating the expression in
Topic Maps, incorrect inferences are being made (by virtue of
the expression being in Topic Maps), then being in Topic Maps
isn't a justification, it's simply an ungrounded assumption.

But if we're talking Topic Maps (and we are here), that the two
statements happen to use the same Association type hardly means
that there is a symmetrical relationship between them -- there
simply isn't enough information. The expression is occurring at
an entirely different level than the interpretation. If what you
state were true,

     if    Norway instance-of Country
     then  Country instance-of Norway

     if    Chelsea Clinton daughter-of Bill Clinton
     then  Bill Clinton daughter-of Chelsea Clinton

would also be true. If there's not a statement of a relation's
symmetry, it can't be assumed one way or another. Now, if the
inferencing engine is provided with the information* stating
that the 'borders-with' Association type is symmetrical (and
the 'instance-of' and 'daughter-of' types are not), then correct
inferences can be made in all cases. Absent that, no.

Making inferences absent enough information (whether grammatical,
logical, including also the *form* of logic, contextual, etc.)
is bound to cause errors. This reminds me of how I've seen OWL
logic misapplied because it was being taken out of the DL world,
such as ignoring its monotonicity. Sadly all too common though.
Logic isn't difficult, but ignoring its rules isn't an option
if one is going to use it, i.e., make inferences using it.

Murray

* which might be simply the existing software being made aware
  of a property of the Association type -- this doesn't have to
  be complicated. There might not be anything in Topic Maps that
  permits explicitly logical expressions (i.e., we've not
  grounded Topic Map expressions in a specific form of logic,
  except in XTM in deliberately loose prose), but there's
  nothing prohibiting them either.
...........................................................................
Murray Altheim <murray06 at altheim.com>                              ===  = =
http://www.altheim.com/murray/                                     = =  ===
SGML Grease Monkey, Banjo Player, Wantanabe Zen Monk               = =  = =

      In the evening
      The rice leaves in the garden
      Rustle in the autumn wind
      That blows through my reed hut.  -- Minamoto no Tsunenobu