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Re: [ontolog-forum] Heterarchy & Hierarchy, oh my my

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Cc: bfo-discuss@xxxxxxxxxxxxxxxx, obo-relations@xxxxxxxxxxxxxxxxxxxxx
From: Wacek Kusnierczyk <Waclaw.Marcin.Kusnierczyk@xxxxxxxxxxx>
Date: Fri, 02 May 2008 21:30:26 +0200
Message-id: <481B6BD2.5030908@xxxxxxxxxxx>
Pat Hayes wrote:
> At 9:08 PM -0400 5/1/08, ZENG, MARCIA wrote:
>> Check: http://sig.biostr.washington.edu/projects/fm/FAQs.html
>> Foundational Model of Anatomy (FMA) ontology
>> Modeling questions...
>> 4) What does a merged hierarchy mean and why use one?
> Here's a toy example. Suppose you classify people 
> as male vs. female and married vs. single. You 
> can make this into a two-level hierarchy tree in 
> two ways, depending which distinction you make 
> 'higher' than the other. But this choice is 
> arbitrary; and arbitrary decisions like this are 
> bad for interoperation, since they tend to be 
> made essentially at random, producing 
> incommensurate classification systems. Moreover, 
> if you make the male/female division nearest the 
> root, then there is no place in the tree for the 
> class 'married people (regardless of gender)'. A 
> merged hierarchy would have these two divisions 
> of the root class represented independently, so 
> that there would be two routes back from 'married 
> men' to 'people', one representing the selection 
> of male (not-female) and the other representing 
> the selection of married (not-single). 
> Inheritance works as usual within each hierarchy 
> tree, and they may be independent, although more 
> complex schemes can be used.
> The chief advantages are already noted, but 
> others include increased efficiency of reasoning 
> and greater 'naturalness' in connecting 
> classifications with associated properties and 
> facts. And, contrary to initial expectations, 
> multiple-hierarchy schemes are almost as easy to 
> implement as single-tree taxonomies.
That's an interesting point.  I was repeatedly complaining on the OBO- 
and BFO-related lists about the insistence, within that framework, on 
single inheritance.  Illustrative cases of the arbitrariness of choice 
which distinction is to be prioritized over others (i.e., placed higher 
in the taxonomic tree) can be found in virtually any OBO ontology; for 
example, PATO starts at quality, distinguishes qualities of occurrents 
from qualitites of continuants, and then within each of these 
distinguishes, independently, monadic and relational qualities.  It 
could well have been the other way round.    (01)

I mention this because the answer to my complaints, if any, was 
invariably that single inheritance a) increases efficiency of reasoning, 
b) is more natural and easier to use, and c) is good for interoperability.
To my simple mind, these claims do not correspond well to yours above.  
It would be interesting to see a discussion on this issue, though the 
argumentation provided by proponents of the other view typically did not 
go beyond rather vague handwaving.    (02)

> Hope this helps. There is a lot more on this 
> general topic (including a foundational 
> mathematical theory based on lattice theory) on 
> John Sowa's excellent website, which I commend to 
> your attention.
>       (03)

Is there a precise pointer to precise results which say that it is (or 
is NOT) the case that:
a) single inheritance is more natural than multiple inheritance;
b) single inheritance is less problematic for reasoning than multiple 
c) single inheritance improves,  wrt multiple inheritance, interoprability?    (04)

vQ    (05)

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