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Re: [ontolog-forum] Self Interest Ontology

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 16 Aug 2011 13:51:55 -0400
Message-id: <4E4AAE3B.1010103@xxxxxxxxxxx>
Rich and Chris,    (01)

>> Any formal theory can only express one version at a time.    (02)

> That is why I chose the And/Or search algorithm class for my database
> context discovery methods.    (03)

Your and/or search algorithms need to be applied to some structure
for storing the information.    (04)

> Using different heuristic metrics, multiple viewpoints of the same
> factual structures (represented in the graph) can be visited sequentially
> as the solution subtree switches among the alternative interpretations.
> Each such solution subtree is itself consistent, and the forest of subtrees
> is based on the same facts and rules which establish any one of the subtrees.    (05)

Each of those viewpoints can be described by a collection of statements,
which could be called the axioms of a theory.    (06)

You can organize all those theories in a hierarchy by generalization
and specialization:  adding axioms makes a theory more specialized,
and deleting axioms makes it more generalized.  In whatever logic you
choose to state those theories, the implication operator corresponds
to generalization:    (07)

    If the axioms of theory A imply the axioms of theory B,
    then B is more a more general theory than A.    (08)

Given this hierarchy of theories, the And/Or algorithms walk up
and down that hierarchy.  If you fill the hierarchy with all
possible theories expressible in the given logic, you get a
Lindenbaum Lattice.  Since the lattice is infinite, you can't
store the whole thing, but you can construct as many theories
as you like to adding and deleting axioms.    (09)

For further discussion of the lattice, see slides 70 to 81 of    (010)

    http://www.jfsowa.com/talks/iss.pdf    (011)

> Do these "database context discovery methods" actually exist in code,
> in a form people can actually use for doing real-world knowledge
> engineering, or are you just sketching an architecture that you think
> can be coded and that you think would work if it were?    (012)

That depends on how much code you want to start with.  The simplest
implementation is a repository that organizes all the theories (or
their axiomatizations) in a tree that puts theory A under theory B
iff the axioms in B are a subset of the axioms of A.    (013)

That is very easy to implement, but more sophisticated software
would be useful.  See slides 70 to 81 of iss.pdf for more info.    (014)

John    (015)

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