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

[Murray Altheim]

Quoting Aad Kamsteeg <a.kamsteeg at diderottrack.nl>:

> Murray, Lars,
>
> Amazing discussion, this is. Isn't it logic that reasoning goes 
> astray when you leave out information?

Yes, I would consider that logical (which is my assumption
about what you meant). Like the statement about the borders
between Norway and Sweden wasn't true prior to those
countries existing, and absent the context of a discussion
of national boundaries, we don't know if we are talking
about political boundaries or social ones, or anything else,
but we as humans are capable of making enormous inferential
jumps that go beyond logic, into the realms of intuition,
which is often based on experience.

But *computers* understand literally nothing. They only do
what they've been programmed to do, not one bit more. They
don't infer, not even a bit. They can be programmed to
follow rules, that's all.

> Think that the proper use of types and roles would make a lot of 
> sense here. Why don't you?

I'm not sure how to parse that question, as it would seem
that I'm suggesting the same thing as you. I do think so.

> There is no constraint that would stop you from doing so,
> if you need that information.

Agreed.

> Maybe I'm silly, but the statement that logic is either simple or 
> complex does depend on the amount of explicit statements available.

I don't understand what you're trying to say here when you
say "available."

> Murray Altheim wrote:
>
>>>>   if    Norway borders-with Sweden
>>>>   then  Sweden borders-with Norway
>>>
> If both Norway and Sweden are of type country and both are assigned 
> the same role (like: neighbour?), symmetry becomes obvious?

Only to a human. You're reading the statements as a human reads
them, and you then interpret those statements. Computers can do
the reading part okay, but they don't do interpretation, they
just follow rules. If there's a rule stating that the
'borders-with' relation is symmetrical, the computer can be
programmed (provided with a rule) to respond to that. If there
is no such rule the computer can have no proper response. Computers
don't assume anything, though programmers might erroneously do
so. And a programmer who assumed that any form of two statements

    if    ( a  relation b )
    then  ( b  relation  a )

implies symmetry, then they'd be wrong, as shown in my examples.

>>     if    Norway instance-of Country
>>     then  Country instance-of Norway
>>
>>     if    Chelsea Clinton daughter-of Bill Clinton
>>     then  Bill Clinton daughter-of Chelsea Clinton
>
> Again: Chelsea would be assigned the role of 'daughter' and Bill 
> 'father'. Isn't that what TM is about? Allowing good enough
> precision to make clear statements?

Yes, absolutely. There is precision in being able to assign
roles to the members of a relation. But this is orthogonal
to the current discussion. Even if we assign roles we still
haven't made any statement about symmetricality, though
there is a method of *inference* that can be made when the
roles have been assigned, whereby if two association members
have identical roles the relation can be considered symmetrical,
in certain forms of logic. Not all forms of logic have symmetry.

But this is *still* outside of the realm of Topic Maps, as we
still have to program our inference engine with this rule. We
are consistently operating at a level above the Topic Map level,
up in the world of logical inference. And to do that correctly,
it's really, really, really a good idea to ground all of the
statements in a *specific* form of logic so that when a group
of statements are taken together we can understand what to do
with them. In some forms of logic, you can't permit statements
of certain types, in some types no statement may invalidate an
earlier one (this is what is called monotonicity, which is what
OWL is, as it's based on Description Logics). Various forms of
logic treat these things differently, and as you said earlier,
"reasoning goes astray when you leave out information." You can't
do good reasoning on incorrect rules or incomplete information.

As I mentioned previously, once the ISO Common Logic standard
is available there will be a PSI set (a set of URI identifiers)
for a subset of the common logical features we've been talking
about, a set also capable of being used to build more useful,
complicated logics. And yes, some grounding in a specific logic
will be necessary to do proper inferencing, other than that we're
still talking toys. Or in the case of people using either a
completely unspecified or a wrong logic for a task, broken toys.

One thing I've learned from hanging around with logicians
is that they view logic as a set of tools, and they're quite
adamant about using the appropriate tool for a purpose. As a
part-time carpenter, I couldn't agree more. The few scars I
have on my hands are each the result of using a wrong tool.

Murray

...........................................................................
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