From: scerir@libero.it
Date: Sun May 28 2000 - 05:28:55 MDT
If it's an algorithm, it's incomplete. There will be some undecidable
questions, which are decidable on another stronger algorithm. This
may not bother you, but it should tell you that Truth is not an
algorithm, that it cannot be reached, or even defined, algorithmically.
Dan Fabulich
Sure - but this isn't a practical problem anymore than the
incompleteness of number theory makes math useless. It's a good
objection though. Saying intelligence is an algorithm was sloppy of
me, I should say rather that intelligence is that which approximates
some particular uncomputable function in a tractable way. This opens
up the possibility of multiple viable solutions.
Matt Gingell
Minds are imperfect and heuristic, they only approximate a truth which
is, as you point out, uncomputable. A machine might out do us, as
Newton was out done by Einstein, by finding a better model than
ours. But any intelligent machine would have a concept of, say,
integer at least as an special case of something (perhaps vastly)
broader.
Matt Gingell
I wonder if some non standard logic, and (above all) the well-known
intensional logic, could help (AI) to find the right track.
http://www.earlham.edu/~peters/courses/logsys/nonstbib.htm#intensional
1)
Intensional logic.
Intensional (or indexical) logic is the study of assertions and other
expressions whose meaning depends on an implicit context or index, such as
time or spatial position. This type of logic was originally developed (by
Kripke, Carnap, Montague and others) to help understand natural language, in
which such expressions abound. The term ³indexical logic² is also used, Many
groups are interested in the indexical (Kripke-style) semantics, in which
context sensitive expressions are interpreted as denoting values which vary
over a space of indicies (or "possible worlds"). Many groups are interested
in the prescriptive use of indexical logic, to define new (programming)
languages equipped with indexical operators, rather than describe existing
(natural) languages.
2)
Intensional logic.
Intensional logic is a family of mathematical formal systems that allow
expressions whose value depends on hidden context or indices. Streams are
considered an intensional mapping, in the sense that neither the source nor
the destination need be aware of the "hidden" destination coordinates. Each
merely produces/consumes a one dimensional stream of data to be mapped by
whatever stream implementation using "hidden" state (coordinates) to direct
the mapping.
3)
Intensional logic.
Logics that include apparatus for signifying when two meanings (as opposed
to two wffs, truth-values, sets, predicates, functions) are identical, and
that analyzes inferences involving meanings. (Non-intensional logics are
called extensional.)
*Anderson, Anthony C., "General Intensional Logic," in Gabbay and Guenther,
vol. II.
*Benthem, Johan van. A Manual of Intensional Logic. Second ed., revised and
expanded. University of Chicago Press, 1985.
*Slater, B.H. Intensional Logic: An Essay in Analytical Metaphysics.
Avebury, 1994.
*Zalta, Edward N. Intensional Logic and the Metaphysics of Intentionality.
MIT Press, 1988.
5)
Non-monotonic logic.
Logics in which the set of implications determined by a given group of
premises does not necessarily grow, and can shrink, when new wffs are added
to the set of premises.
*Brewka, G. Nonmonotonic Reasoning: From Theoretical Foundation to Efficient
Computation. Cambridge University Press, 1990.
*Davis, M., "The Mathematics of Non-Monotonic Reasoning," Artificial
Intelligence, 13 (1980) 73-80.
*Gabbay, Dov M., et al. Handbook of Logic in Artificial Intelligence, Vol.
3: Nonmonotonic Reasoning and Uncertain Reasoning. Oxford University Press,
1994.
*Ginsberg, Matthew L. (ed.). Readings in Nonmonotonic Reasoning. Morgan
Kaufmann Pub. Inc., 1987.
*Rankin, Terry L., "When is Reasoning Nonmonotonic?" in James H. Fetzer
(ed.), Aspects of Artificial Intelligence, Kluwer Academic Publishers, 1988,
pp. 289-308.
scerir
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