Saturday,
August 21, 2004
History and foundational work in Knowledge Science
Additional comment from
Richard Ballard ŕ
Paul:
I keep hoping you will discover that the semantic network in the forms inclusive of John's categories 1, 2, 3, and 5 [1] in his last post are sufficient to provide a full representation for every form of information and theory, once the relationship is extended to n-aries, where n >= physical degrees of freedom (number of independent variables arguably influential in changing an observable behavior).
The information content within the answer to any question is proportional [2]to the sum over all i of n, weighted by the number of bits, log N(i), needed to span all relevant N(i) variable instances (distinct observable values or states). [3]
The semantic network itself enforces all the rational (a' priori) constraints imposed by the theories deemed ontologically acceptable during the construction and subsequent updates (theory learning or modifications) to the network. Theory changes happen just once at the moment when learned or updated. [4]
By contrast, the (a' posteriori) information or reality constraints are imposed whenever a question is asked -- by "selection" of those particular observable instances deemed immediately operant or conditionally testable as in planning or decision assessment.
Those selections make just certain conditional relationships relevant and operating and others irrelevant. [5]
For the n-ary to be deemed relevant all instances must ultimately be selected, but the interactive examination of alternative "what-if" selections is at the heart of semantic network navigation and decisive inspection and assessment of acceptable rational path alternatives. [6]
Human-like thinking is rarely in pursuit of idealistic perfections like logical "truth" after all. It is characterized by trade-offs where each choice seeks greatest practical advantage in pursuit of all most favored values while minimizing the risk and consequence of adverse outcomes to some. The network itself provides "theory knowledge (constraints)" describing "how" when relevant paths are navigated in one direction and "why" when navigated in reverse. Similarly when optional decision variables are tested via n-aries within a pure declarative network all-possible "what-if" paths can be found, navigated, and assessed. [7]
The insertion of executable algorithmic functions and attachments, as in John's categories 4 and 6, introduce relationships that often are not and rarely can be reversible in their direction of reasoning.
By contrast the whole set of n-aries
< a ŕ x1 ŕ x2 ŕ x3 ŕ ..... ŕ b >
can solve for any m potentially relevant variable instances given n-m variable assumptions. [8]
This n-ary form guarantees that the "what-if" alternatives map to all possible paths [9]. Every executable algorithmic conditional relationship introduces the virtually certainty that certain paths will become irreversible by virtue of their representational formalism and not by any other necessity.
So the pure semantic network has the potential for representing all knowledge, the executable algorithm has the potential for representing at most a tiny set of particular examples. The Knowledge Age bids us to seek the former as a basis for science.
The challenge is to find the means for representing and integrating everything knowable. Others need to stop branding something new and look at the reversibility issue I have made as plain as I can.
You picked up on the ontological primitives John and I put forward, now look at the pure semantic network (+ n-aries) as a potentially complete formalism without algorithmic embellishments that need someone's name attached. It is a declarative platform for stating simply what was known and accepted by those constructing it.
Other tasks, like learning new knowledge, or algorithmic parallel agent path tracing, sense making, and decision assessment, or direct hardware declarative processing of constraints are ample places for real (question) time procedure inventions built around and upon a globally complete platform. Those are precisely the new opportunities being offered. Or pick a psychological theory and model in n-ary bundles those uniquely human reasoning constraints that will forever distinguish human reasoning from any reductive mechanism you perceive or imagine within this formalism.
Dick
[1] I can not find the
references to “categories 1, 2, 3, and 5”, are these four of the 12 Sowa
semantic primitives? (For the reader,
the committee will look to get a reference to what these categories are, and
what category 4 and 6 (mentioned later in this communication) are. A link at this point will then be
provided. 8/21/2004 6:05 PM
[2] Information is not
proportional to other information.
There are structural measurements that can be imposed on the
co-occurrence of information in descriptive acts, whether using natural language
or not.
[3] As is pointed out by Lev
Goldfarb, one needs both numeric models and models based on patterns where
numeric measurement is not relevant.
[4] Semantics is constrained by
real time pragmatics, and the anticipatory web of information model takes this
into account.
[5] Of course we agree, that
the act of making a question is a driver for the anticipatory response. Where
we do not understand something in common when we talk about the completeness of
a theory. My understanding of what you
say is confused, because I think that you suggest that only the question is a
proper anticipatory response. But if
course this is something that might be lost in translation. In
some cases, investigations have no questions, and yet they are
anticipatory. In fact, the more that
the human becomes involved in an awareness of the present moment, the less
there is a formation of a question and the more the individual human becomes part
of an anticipatory flow. Perhaps you
agree?
[6] Again, there is very little
disagreement with what you are saying.
[7] Again, there is very little
disagreement with what you are saying.
[8] I do not see what your notation
is indicating. Would you take the time
to explain the notation?
[9] The traversal of paths is
the key to the Orb notion of convolution and is the reason why we have
preferred to talk about a Hilbert encoding.