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

[Murray Altheim]

Quoting Lars Marius Garshol <larsga at ontopia.net>:
>
> * Lars Marius Garshol
>>
>> The software tools that operate on that symmetry treat it as being   
>> symmetrical. They can't do anything else.
>
> * Murray Altheim
>>
>> Then in all relations that aren't symmetrical those tools will make
>> incorrect inferences: they are operating on a symmetry that doesn't
>> exist.
>
> Well, that's the point. In Topic Maps these associations actually  
> *are* symmetrical, because the Norway/Sweden example would look as  
> follows:
>
>   borders-with(norway : neighbour, sweden : neighbour)
>
> This association looks exactly the same, regardless of which  
> direction you see it from, and so software can't very well avoid  
> treating it as symmetrical.

You're either not using the term "symmetrical" in its logical
sense (perhaps in its grammatical one) or you're not making
sense. Simply because an association looks the same (by which
I assume you mean that both members have the same role type)
doesn't make it symmetrical. They simply have the same role
type. To make the relation symmetrical one needs logic, and
there is no logic in that statement. It's just a Topic Map
expression.

I think our failure to communicate here is that you are not
differentiating between (or are at least confusing across
multiple statements):

  a. statements of the English natural language
  b. statements of formal logic (grounded or not)
  c. statements of Topic Maps

> * Lars Marius Garshol
>>
>> 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.
>
> * Murray Altheim
>>
>> This seems to be mixing up what occurs at the Topic Maps level
>> and what happens at an inferencing/logic level.
>
> No. If you tried to say that
>
>   borders-with(norway : neighbour, sweden : neighbour)
>
> and
>
>   borders-with(sweden : neighbour, norway : neighbour)
>
> you would wind up with a single association in Topic Maps.
>
>> I.e., this has nothing to do with Topic Maps, which are just being  
>> used as the
>> vehicle for the expression.
>
> It does have to do with Topic Maps, because you'd get a single  
> expression in TMs instead of two, whereas most other representations  
> would give you two expressions.
>
>> 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
>
> No, this doesn't follow, because here the topics at the two ends of  
> the association play roles of different types.

Ah, but it was your human mind that noticed this. As I responded
to Aad Kamsteeg recently, you've made a rule that doesn't exist
in Topic Maps by virtue of your experience as a human. These
rules are only there when we program them in, they're not inherent
in the expression. Though I hear someone saying "yes they are". No,
they aren't. They're only there via the *interpretation* of the
statement, and computers don't do interpretation. They just follow
rules. And while you may see symmetry, or a lack of it, absent the
rules for symmetry (as part of a logic) there is no symmetry. It's
at very least unstated, and therefore rather dangerous.

>> 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.
>
> The point is that in Topic Maps you don't have to state this; the  
> associations will either be symmetrical, or they won't.

As I stated above, there is no symmetry in Topic Maps. Your
sense of symmetry is something you have added as a layer of
logic above the Topic Map layer. In Topic Maps you *do* have
to state this in order to express the logic, otherwise you'll
have to hardwire the rule. And if you hardwire a rule without
even knowing what logic is being used, that rule will fail
when the circumstances or context in which that logic is valid
are not at play. This would be like using OWL for something
other than a Description Logics purpose. Or perhaps not even
understanding what Description Logics entails (and I mean
"entails" in the formal sense).

>> * which might be simply the existing software being made aware
>>  of a property of the Association type -- this doesn't have to
>>  be complicated.
>
> In OWL it's simple: you make the association type an instance of  
> owl:SymmetricalProperty, but in Topic Maps there's no need.

Symmetry in OWL exists because of its roots in DL. That doesn't
mean you can use OWL outside of its DL confines just to gain
that rule, you need to take on the entire framework and all that
entails, otherwise you're guilty of using the wrong tool, with
whatever consequences (scarred hands, air traffic control
accidents, nuclear fallout, etc.) that might come from that...

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