[topicmapmail] Hierarchy PSIs

[tpassin@comcast.net]

Bernard Vatant wrote -
 
> I'm a bit confused with the current debate about hierarchy as defined - or
> not - by Techquila PSIs
> 
> http://www.techquila.com/psi/hierarchy/#hierarchical-relation-type
> http://www.techquila.com/psi/hierarchy/#subordinate-role-type
> http://www.techquila.com/psi/hierarchy/#superordinate-role-type
> 
> In Sowa's Knowledge Representation p.494, I read:
> "hierarchy : A partial ordering of entities according to some relation."
> Followed by examples like supertype-subtype, whole-part, broader-narrower
> ...
> 
> OTOH, I read Tom speaking about "virtual hierarchies" for display purposes,
> and Omnigator displaying hierarchies on the basis that they are declared as
> such by reference to the above PSIs, without any more requirement about
> formal properties.

I definitely had in mind only the partial ordering bit when I posterd about "virtual" hierarchies.

> 
> If one sticks to Sowa's definition of a hierarchy as a partial order
> (reflexive, transitive, antisymmetric relation), for example
> "predator-prey" is not a hierarchy, since it's not transitive, and can have
> non-trivial loops ...

I suspect that many, perhaps most, of the "hierarchy" cases that are interesting to people will turn out to be partial orderings but not strict hierarchies in Sowa's sense.  

> 
> So, seems to me that one should make distinct a "display-as-hierarchical"
> type of association type, which basically is what Techquila's PSIs are
> about, and a "formally-hierarchical" type of association type, the latter
> entailing the formal constraint that the relation is indeed globally a
> partial order, and that a topic map using it has been or can be checked to
> be conformant with the matching constraints by any relevant inference tool.
> 

Bernard, that is very astute of you!  You are suggesting, are you not, that there should be one "master" strict hierarchy association type (designated by a PSI)?  I could support such a thing.  I think it would be desirable to provide a partial-ordering-only association type as well.  Would you agree?  Any suggestions for a name for a virtual hierarchy association type?

Cheers,

Tom P