Hi
YKY,
The
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:
The
logic notation I use is nonstandard (but standard for Novamente ;), but
shouldn't
be too
difficult. Basically, the Python-style indent notation
A
B
C
is
used in place of the predicate-logic notation
A(B,C)
This
provides easier browsing of nested formulas. Also, I use the Novamente
notion
of
SatisfyingSet, defined by
SatisfyingSet( F) = the set of X so that F(x) is
true
Other
than that the logical relations used are fairly standard (ForAll,
ThereExists,
Inheritance, Member). There is some subtlety to
the Novamente Inheritance relationship
(which
combines intensional and extensional information) but that doesn't really
affect
the
formalization given here. Also, Novamente labels logical expressions with
numbers
representing their probabilistic truth value and their
importance to the system at a given
point
in time; these numbers are not included in the attached formalization, but they
are
of
course important to Novamente in the course of actually proving the
expressions
formalized here.
--
Ben
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]On Behalf Of Yan King Yin
Sent: Saturday, September 03, 2005 5:06 PM
To: AGI mailing list
Subject: [agi] Representing ThoughtsOne of the central issues in AGI would be how thoughts are represented.To give an example, consider the line of reasoning: "There are 4 apples on the table, and 5 people in the room. 5 is greater than 4. If each person eats one apple then there won't be enough apples for everyone."I wonder how this can be represented using formal logic. If this reasoning can be done using formal logic, I also doubt how that process is similar to the way humans do it. A sentence like "IsGreater(5,4)" does not capture the entire meaning of "5 is greater than 4" unless the meanings of entities like "5", "4", "IsGreater" are also defined. One question is whether formal logic can adequately represent these concepts. If it can, there are obvious advantages in using it to build an AGI.Any thoughts about this? =)yky
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