In a nonhierarchical schema, the schema
represents a graph. The links between tables represent arcs from one node
of the graph to another. Therefore a nonhierarchical schema can be
represented by a plurality of hierarchical traversal trees.
The best way to see that is to look at
Nils Nilsson’s 1972 or so book titled “Principles of Artificial
Intelligence” – or one of his later versions – where he
addresses graph search algorithms in detail, yet with the clarity of
presentation only Nilsson seems to be able to present. He shows numerous
figures on graph search algorithms, and the on the solution subtrees, which are
subtrees of the graph search forest.
Note that Nilsson’s book didn’t
specifically address tables (and other relational database components), and was
ahead of its time by at least five years. His graph search descriptions
predated relational DBs, and so you have to read among the lines to get that
His book was very thin – much less than
200 page – and covered theorem proving, all the major search algorithms,
the problem reduction paradigm, and many other things I don’t
remember. The figures were EXCELLENT in an area of study that seldom has
good figures by other authors. If you (or anyone else) wants to get a
thorough overview of AI, that is the first place to start.
I couldn’t find that original 1972 version
of the book on the web in a quick search, though it is in libraries that were
around at the time. Surely there are many copies still around because it
was a popular book back then. It was such a vivid book, I still carry
around some of the images and algorithms in my memory.
Below is a later version of his book –
though contaminated by other subjects such as neural networks, and elementary
Later versions were released in 1980 and
even more recently, but I still prefer the 1972 version, which was clearer and
more fundamental than his later publications, IMHO. Most appropriately, you
can see his AND-OR search formulation in my patent at:
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of David Eddy
Sent: Saturday, June 02, 2012 8:42
Subject: Re: [ontolog-forum] How long to useful?
On Jun 2, 2012, at 11:22 PM, Rich Cooper
Here is a recently released
patent I came across that shows how to use multiple taxonomies to traverse
That's WAY above my reading for comprehension ability.
What if the "data" isn't hierarchical?