Tuesday 27 November 2007
After posting a somewhat abstruse comment at Apperceptual where I struggled to explain the reasons why I reject some forms of "obstinate rationality" (there is "one true answer" to whatever question in a perfect Platonic world) I had a mail exchange with Peter Turney in which we agreed that an important point in knowledge representation is the reification of relations as full fledged concepts.
Mathematically a relation is just a subset of the cartesian product of its arguments domains, colloqially and in all philosophical discourses it is a much richer object where many extra qualities (properties, attributes, connotations, etc...) are actually attached to the "core meaning" which holds between its arguments.
This shows quite appropriately in the Conceptual graphs formalism where what can be originally seen as a plain relation "sitting(cat, mat)" (a relation node) is turned into a
more complex concept node.
This allows within the same framework to actually represent more detailled information about the "sitting" than the bare 'agent' and 'location' arguments, for instance :
[Sitting *x] -(agent)-> [Cat Elsie]
-(location)-> [Mat *y]
-(modality)-> [Mood quietly]
One should note two points:
- The reified concept is still a relation but maybe only in a more "philosophical" sense in that it is not too clear which "weight" each argument of this now ternary relation (agent, location, modality) has to be given when looking for "comparable" relations, like when searching a database for matching instances.
- The "arguments" can in fact ALSO be viewed as relations over some domains :
So the questions which arise from this are :
- How do we deal in logic with the "extraneous" arguments to a reified relation which we somehow want to "consider a bit" but not too much since they are only "supplementary" to the core relation?
- Where do we stop the reification, when is it sensible to ALSO reify what was originally just an argument name ('agent' of an action verb for instance) and has been turned to a relation by the previous reification?
- Since the CG kind of formalism is entirely equivalent to First Order Logic (see about the "phi-operator" in Higher-Order KIF and Conceptual Graphs) what does it mean to play around with the "carving out" of various relations from an initial "master formulation" of a problem statement?
To me this means that there is surely an extra degree of freedom involved in the translation from the "intuitive" formulation of a problem into any kind of formalised logic (FOL or even higher) which is almost always OVERLOOKED.
This is one of the basis of my discontent whith the hard core rationalists who seem to have an absolute faith in their formalisations.
They just forget the messy business they had to come up with the said formalisations and keep rehashing irrelevant "metaphysical" considerations about consistency, truth and existence (the Platonists vices...).
While chatting about this with Peter Turney he suggested that Dedre Gentner's paper Why We're So Smart "may be of interest":
You'll need to translate from cognitive psychology to logic, but I think you'll
find that the paper is talking about the power of reifying and de-reifying.
and indeed it is!
She highlighted the critical role of relations in cognition while still viewing them as an instance the more general framework of "a concept":
First, relational concepts are critical to higher-order cognition, but relational concepts are both nonobvious in initial learning and elusive in memory retrieval.
I haven't yet came up with a "translation from cognitive psychology to logic" but I am working on it and will post whatever ruminations I can milk out of this.
Submitted by Kevembuangga [/html]