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ideas[f83,jmc] exotic circumscriptions,
1983 dec 27
From 1982 Nov 3 notebook
Suppose we say that if x ≤ y, minimizing at x is more important
than minimizing at y. What is the circumscription formula? Presumably
it is a restriction of the usual formula. Is it well defined?
In the notebook I have
A(x,p) ≡ ∀y. y<x ⊃ A(y,p)
∧ ∀P' ∀y.y<x ⊃ A(y,P') ∧ [E(x,P') ⊃ E(x,P)] ⊃ [E(x,P) ⊃ E(x,P')],
but it isn't now clear what this means.
1983 dec 30
Conjecture: A child will have earlier memories of the facts of stories
that have been read to him than of any of his actual experiences. The
reason would be that mentalese is changed several times as the child
grows and memories in old mentalese are lost, while story memories
are in natural language which is stable.
1983 dec 30
Consider the sentence S: "Whenever it rains Oak Streeet becomes impassible
between 5th and 6th Streets" assumed to be true. The fact is not part of
general common sense knowledge. Some people know it and others don't.
It may have been false in the past (or meaningless) and may become
false in the future. The sentence carries with it some assurance,
beyond normal presumptions, that there is no more prevalent circumstance
making Oak Street impassible. It can be used in a number of ways,
but of people who know it sometimes miss its applicability to a particular
circumstance. Here are some of its applications.
1. There reason all these cars are lined up is because of S.
2. Don't go by Oak Street, because it's raining and A.
3. While Oak Street was blocked, it hasn't rained since yesterday,
so it should be ok now.
4. Whenever it rains, it takes 10 minutes longer to get home.
5. The city should install better storm drains on that block.
6. Perhaps the McCarthy Construction Co. can get a contract
to improve the Oak Street storm drains.
7. The city is likely to overspend its street repair budget
again this year.
Actually the key question is the effect of adding S to an
existing database. Consider a system that will take some action
before it receives S. Then how does receiving S change the action
it will take, and what is the mechanism of this change.
We will explore the idea of a "formal natural language" that
is compiled into logic - most likely into a logic with circumscription.
The problem with adding S to a logic database directly is that
even with circumscription, we would have to know what aspects to
modify.