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AIList Digest Volume 3 Issue 146
AIList Digest Tuesday, 15 Oct 1985 Volume 3 : Issue 146
Today's Topics:
AI Tools - YAPS Info,
Bindings - Scheme Mailing List,
Opinion - Scaling Up,
Psychology & Logic - Modus Ponens
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Date: 14 Oct 85 15:58:27 EDT (Mon)
From: Liz Allen <liz@tove.umd.edu>
Subject: YAPS info
In response to the question about obtaining YAPS: YAPS is available
from the Univ of Maryland along with some other packages like a
flavors package. They run under Franz Lisp (we supply a slightly
hacked version of Opus 38.91) and on Vaxes running Berkeley Unix.
For more information, send mail to me.
-Liz
liz@tove.umd.edu or liz@maryland.arpa
------------------------------
Date: Mon, 14 Oct 85 20:37:24 EDT
From: Hal Abelson <HAL@MIT-MC.ARPA>
Subject: Scheme mailing list
Scheme@MIT-MC.ARPA is a network-wide mailing list for discussions
concerning the Scheme dialect of Lisp -- both as a vehicle for
investigating language development and as a vehicle for teaching
about computer science. To be added to the list, please send mail to
Scheme-Request@MIT-MC.ARPA. Remote sites with many entries are
encouraged to set up local distribution lists..
------------------------------
Date: Mon 14 Oct 85 07:50:00-PDT
From: Gary Martins <GARY@SRI-CSL.ARPA>
Subject: Scaling Up
In a recent issue of AIList [#145], Dave Wyland expresses a rather
common epistemological error, in his attempt to defend "AI" as we know
and love it today -- hype and all !
Mr. Wyland seems to think that finding problem solutions which "scale up"
is a matter of manufacturing convenience, or something like that. What
he seems to overlook is that the property of scaling up (to realistic
performance and behavior) is normally OUR ONLY GUARANTEE THAT THE
"SOLUTION" DOES IN FACT EMBODY A CORRECT SET OF PRINCIPLES.
To put it more simply, if the solution doesn't scale up, then it just
plain isn't a solution, even if the inventor feels he has made a lot
of "profound and impressive insights". The point is, these insights
aren't very profound or impressive (except perhaps to IJCAI referees)
if they fail the scaling test.
This principle is generally understood by persons with real engineering
backgrounds, but seems to come as news to "AI" folks.
G.R. Martins
------------------------------
Date: Wed, 9 Oct 85 16:43 EST
From: Mukhop <mukhop%gmr.csnet@CSNET-RELAY.ARPA>
Subject: Non-contradictory set of beliefs and dependencies
> Date: Thu, 3 Oct 85 18:28:03 PDT
> From: albert@UCB-VAX.Berkeley.EDU (Anthony Albert)
> Subject: Re: Counterexample to modus ponens
>
> As far as beliefs, a non-contradictory set could be:
>
> 1) If a Republican wins then Reagan will win.
> 2) If Reagan doesn't win then a Republican won't win.
> 3) Unless a Democrat wins, a Republican will win.
>
Beliefs 1) and 2) of this non-contradictory set are one and the same as far
as inferential power is concerned:
P => Q <=> ~Q => ~P
Also, this set of non-contradictory beliefs does not include the notion
that Reagan (or a Republican) will probably win. It merely states that
Reagan's chances are better than his Republican opponent.
Getting back to the original set of statements:
> (1) If a Republican wins the election then if the winner is not Ronald
> Reagan, then the winner will be John Anderson.
>
> (2) A Republican will win the election.
>
> Yet few if any of these people believed the conclusion:
>
> (3) If the winner is not Reagan then the winner will be Anderson.
>
My perception of the commonly held beliefs at that time is:
a) There are three contestants in the election.
b) Ronald Reagan has the highest probability of winning.
c) John Anderson has the lowest probability of winning.
d) John Anderson and Ronald Reagan are the only Republicans contesting
the elections.
The second statement in the original set ("A Republican will win the
election") was a commonly held belief, arrived at from:
- Ronald Reagan has the highest probability of winning, and
- Ronald Reagan is a Republican.
(Of course, John Anderson increased the odds in favor of a Republican)
If the assumption is now made that Ronald Reagan will not win the election,
then one can no longer make the assumption that a Republican will win.
The conclusion,
" If the winner is not Reagan then the winner will be Anderson,"
can no longer be made.
It seems that the dependencies of the belief structures need to be
taken into account in order to avoid contradictions. If it was
reasonable to believe that a Republican would win, irrespective of
the chances of Ronald Reagan, then it would be reasonable to believe:
"If the winner is not Reagan then the winner will be Anderson."
------------------------------
Date: Sat, 12 Oct 1985 21:09 EDT
From: MINSKY%MIT-OZ@MIT-MC.ARPA
Subject: Republicans and Probability
About Republicans and probability.
That paradox comes from all those causes -- ambiguities, shifts in
meanings from "intension" to "extension," and so forth. In my view,
adult psychology is too complicated to treat in terms of such simple
mathematical models as deduction and probability. You've heard my
complaints about logic too often to repeat, and surely everyone has
read the critiques of Kahnemann and Tversky about applications of
probabilistic models to human beliefs and reasoning.
I suggest another, simple example to examine. If you tell a "typical"
person that "Most A's are B's" and that "Most B's are C's," then the
most common inference is that "Most A's are therefore C's." More
sophisticated people may say --"No, not most, but at least 26 percent
of A's are C's, because they'll notice that "most" might mean 51
percent. Very few people will recognize that it is possible that no
A's are C's, or be able to construct a counterexample.
------------------------------
Date: Sun, 13 Oct 85 13:39:09 edt
From: pugh@GVAX.CS.CORNELL.EDU (William Pugh)
Subject: Bayesian inference or nested assumptions
Continuing on the subject of the Modus Ponens example, I have
worked out some results on using Bayesian Inference for nested
assumptions:
Notation:
A|B means assuming B is true, A is true
if B is false, the statement is neither
true nor false, it is untested.
P(X) - the probability of X
e.g. P(A|B) = the probability of A being true,
given that B is true
For the original example:
>> (1) If a Republican wins the election then if the winner is not
>> Ronald Reagan, then the winner will be John Anderson.
>>
>> (2) A Republican will win the election.
>>
>> Yet few if any of these people believed the conclusion:
>>
>> (3) If the winner is not Reagan then the winner will be Anderson.
>>
Let RW stand for "A Republican wins"
Let RR stand for "Ronald Reagan wins"
Let JA stand for "John Anderson wins"
We have:
1) P((JA|~RR)|RW) = 1
2) P(RW) = very high
3) P(JA|~RR) = ??
Well, nested assumptions don't really work with the normal
Bayesian calculations, so we first have to convert (1) to
a normal form.
To convert to a normal form, P((A|B)|C) = P(A|(B&C))
You can show this formally, but informally in English:
Assuming that C, then assuming that B, then A
is the same as
Assuming that C and B, then A
Alright, so now we have P(JA|(~RR&RW)) = 1. What can we do
with this??
P(JA)P((~RR&RW)|JA)
P(JA|(~RR&RW)) = -------------------
P(~RR&RW)
P(JA)P(RW|JA)P(~RR|(RW&JA))
= ---------------------------
P(RW)P(~RR|RW)
P(JA)P(RW|JA)P(~RR|(RW&JA))
so P(JA|(~RR&RW))P(RW) = ---------------------------
P(~RR|RW)
P(JA)
(since there can be only one winner) = ---------
P(~RR|RW)
Which, by other real world knowledge, you can reduce to P(RW).
Side note: I was explaining this problem to a friend who
does not have a background in logic. I when I told her that
A => B is true when A is false, she said "That's stupid... No
wonder logicians have trouble with the real world." :-)
One moral of this story: Be careful of "if" in english - it
oftens means something other than the standard logical meaning.
Bill Pugh
Cornell University
..{uw-beaver|vax135}!cornell!pugh
607-257-6994
------------------------------
Date: Sun, 13 Oct 85 20:02:19 -0200
From: Eyal mozes <eyal%wisdom.bitnet@WISCVM.ARPA>
Subject: Re: Counter-example to Modus Ponens
>> Before the 1980 presidential election, many held the two beliefs
>> below:
>> (1) If a Republican wins the election then if the winner is not
>> Ronald Reagan, then the winner will be John Anderson.
>> (2) A Republican will win the election.
>> Yet few if any of these people believed the conclusion:
>> (3) If the winner is not Reagan then the winner will be Anderson.
> I would say the problem with this analysis is that people believed,
> instead of statement 1, the following similar statement:
> (1a) If a Republican wins the election and the winner is not
> Ronald Reagan, then the winner will be John Anderson.
In classical philosophical logic, a conditional proposition (i.e., a
proposition of the form 'if A then B') asserts the necessity of a
certain sequence between two statements; the truth of 'if A then B'
does not depend on the truth of A and of B, but on the connection
between them - whether B's truth FOLLOWS NECESSARILY FROM A's truth.
For example, the statement 'if you are alive, then you are now reading
an ARPANET message' is FALSE; the condition and the consequent are both
true, but the consequent does not follow necessarily from the condition
(you could be alive and still be doing something else now).
Now, let us look at the meaning of (1a), (2) and (3).
(1a) asserts that if the winner is a Republican but not Reagan, it
follows necessarily that it will be Anderson. Given that there were
only two Republican candidates, (1a) is true, and everyone knew it is
true. The actual results of the elections determined the truth of the
two components (both turned out to be false), but made no difference
about the necessary connection between them.
(2) is a simple categorical proposition; before the elections, many
people believed it is true, others believed it is false; it turned out
to be true.
(3) asserts that if the winner is not Reagan, it FOLLOWS NECESSARILY
that it will be Anderson. This is obviously false, and I doubt if
anyone ever believed it. Again, the actual results of the elections
determined the truth of the two components (both turned out to be
false), but made no difference about the lack of any necessary
connection between them.
Given the classical logical interpretation, then, (3) does not follow
from (1a) and (2). People who believed (1a) and (2) but not (3) were
perfectly consistent (and they were also correct).
This example demonstrates one of the serious weaknesses of predicate
calculus. Predicate calculus has no way to express necessary
connections (mainly because its originators, Russell and Whitehead,
held a philosophy which denies the existence of such connections); the
result is the truth-functional interpretation of conditional
propositions, which leads to such anti-common-sense results as making
(3) follow from (1a) and (2).
As for (1), I'm not sure about its meaning, but it certainly doesn't
mean exactly the same as (1a). As far as I know, in all discussions, by
classical logicians, of conditional propositions or of Modus Ponens,
they only dealt with the case in which both components of the
conditional are simple categorical propositions. It is an interesting
question whether Modus Ponens remains valid in other cases as well (and
this, of course, depends on what exactly such 'multiple-conditional'
propositions mean).
Eyal Mozes
BITNET: eyal@wisdom
CSNET and ARPA: eyal%wisdom.bitnet@wiscvm.ARPA
UUCP: ..!decvax!humus!wisdom!eyal
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End of AIList Digest
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