[topicmapmail] Hierarchy PSIs

[Bernard Vatant]

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