[topicmapmail] Hierarchy PSIs

[Thompson, Bryan B.]

Sounds right.  I  dealt with a similar issue developing automated content
classification software to leverage topic maps.  I was not being perhaps
as formal about things, but essentially you would indicate the relationship
that imposed the partial ordering and then "read" the topic map in terms of
that relationship as a hierarchy.

Happy new year,

-bryan

-----Original Message-----
From: topicmapmail-admin@infoloom.com
[mailto:topicmapmail-admin@infoloom.com] On Behalf Of Bernard Vatant
Sent: Monday, December 29, 2003 10:26 AM
To: topicmapmail@infoloom.com
Subject: [topicmapmail] Hierarchy PSIs



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.

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 (A eats B, B eats C, C eats D, D eats A). But nothing prevents from
declaring this relation as "hierarchical" by reference to the above PSIs,
and actually it would be interesting to display "locally" for each living
species its preys and/or predators using a tree-like structure (or lattice
more exactly in this case); although the "predator-prey" relation does not
define globally a formal hierarchy.

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 Vatant
Senior Consultant
Knowledge Engineering
Mondeca - www.mondeca.com
bernard.vatant@mondeca.com










Bernard Vatant
Senior Consultant
Knowledge Engineering
Mondeca - www.mondeca.com
bernard.vatant@mondeca.com


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