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

[Lars Marius Garshol]

* 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.

* 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.

> 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.

> * 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.

--
Lars Marius Garshol, Ontopian               http://www.ontopia.net
+47 98 21 55 50                             http://www.garshol.priv.no