Hi,
I
didn't show how the reasoning itself would be done in Novamente because my time
was limited and the trains of reasoning would be pretty
long!
We
haven't yet tried NM on this kind of example but plan to do so in early
2006. This fall our main AGI goal is to get NM to automatically learn
Piagetan "object permanence" based on experience. Conservation rules like
conservation number come after that on our Piagetan learning trajectory.
However, we have worked out some inference trains of comparable
complexity. But to show you these inference trains would be tricky because
it would involve a lot of highly technical NM-inference-module terminology and
notation.
Regarding how the reasoning is done: Yes, in Novamente the reasoning is
spontaneous. Regarding the general problem of how to get logic
systems to do spontaneous inference, the real problem is defining what is a
"good conclusion." It's easy to get a logic system to produce consequences
of its premises, but, the question is how to get it to direct its course of
inference toward the "interesting" conclusions. One needs an
"interestingness" metric, then one can use an inference-control heuristic such
as tapered N-best search in a way that uses the interestingness metric to assess
"best"-ness. NM's current interesting metric values predicates with
surprising probability (based on the system's prior knowledge), high
amount-of-evidence, and small size (compactness). So, when acting in
spontaneous non-goal-oriented mode, Novamente "spontaneously" takes its
premises and tries to carry out inferences that will lead from its premises to
conclusions satisfying these merits.
--
Ben
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]On Behalf Of Yan King Yin
Sent: Tuesday, September 06, 2005 5:23 PM
To: [email protected]
Subject: Re: [agi] Representing ThoughtsThe example you give is an interesting one from a developmental psychology perspective, because it illustrates what Jean Piaget called "conservation of number," a cognitive skill that young children don't display but school-age children do.Regarding the formalization of the example in logical terms, this is not difficult, but it can be done in many different ways, and exploring these different ways brings up some interesting issues.Since the formatting of logical formulas in emails is difficult, I have put my reply to your email in HTML form and put it online at:Thanks for the clear exposition. You have shown how the premises and conclusion can be represented in formal logic, but not how the reasoning itself is done. There are 2 issues concerning this:1. Spontaneity: The reasoning should proceed spontaneously, after the thoughts of the premises somehow got into attention. Conventional formal logic does not tell us how to generate entailment automatically. It seems that we have to make a query like "Does there exist a person without an apple to eat?"
2. Neural plausibility: How does the brain actually do this reasoning? It seems that the sentence "5 > 4" (the number of one thing being greater than that of another thing) and the need for 1-1 correspondence directly leads to the notion that there are not *enough* of the second thing. It seems that the brain does not mentally do the 1-1 correspondence (which would be impractical when the number of items gets more than around 7).The challenge is how to get the AGI to arrive at the conclusion in a step by step way that does not involve external knowledge (ie not explicitly teaching it the pigeonhole principle etc). This may be the key to AGI design.The critical piece of knowledge may be represented as "A < B and 1-1 correspondence implies there is not enough A for B". The question is how does the brain (or AGI) acquire this knowledge from experience, which means generalizing from small cases of "2 > 1", "3 > 2", etc.What I noticed is that the sentences considered so far can all be represented easily in formal logic. The problem seems to be in the automatic generation of "rules of thinking" (like the pigeonhole principle). The AGI should be able to do this spontaneously.yky
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