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AIList Digest Volume 3 Issue 135
AIList Digest Monday, 7 Oct 1985 Volume 3 : Issue 135
Today's Topics:
Query - TIMM Expert System Tool,
Psychology & Logic - Probabilistic Counterexample to Modus Ponens
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Date: Fri 4 Oct 85 23:49:55-EDT
From: Richard A. Cowan <COWAN@MIT-XX.ARPA>
Subject: Expert System Tool
Does anyone know anything about TIMM, an "expert system tool" put out
by General Research Corp? I hear it costs $50,000 or so. I'd be
interested to hear what a tool could do that costs that much money,
especially in comparison to KEE.
Don't want to hear much; just send a "thumbs up/thumbs down" reply
directly to cowan@mit-xx.
Thanks,
Rich
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Date: Tue, 1 Oct 85 20:07:27 PDT
From: Hibbert.pa@Xerox.ARPA
Subject: Re: A Counterexample to Modus Ponens
In a recent issue of AIList, John McLean cited an article about
inconsistencies in public opinion that apparently said:
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.
People may have been willing to say that they believed #1, but that's
only because they didn't know the difference bewtween 1 and 1a.
Chris
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Date: Wed, 2 Oct 85 14:11:34 edt
From: John McLean <mclean@nrl-css.ARPA>
Subject: Re: A Counterexample to Modus Ponens
Chris Hibbert says that the purported counterexample to modus ponens I reported
rests on a distinction between
(1) If a Republican wins the election then if the winner is not Ronald
Reagan, then the winner will be John Anderson.
and
(1a) If a Republican wins the election and the winner is not Ronald
Reagan, then the winner will be John Anderson.
He says that
People may have been willing to say that they believed #1, but that's
only because they didn't know the difference bewtween 1 and 1a.
I would like to see some further discussion of this since I'm afraid that
I don't see the difference between (1) and (1a) either. Certainly there
is no difference with respect to inferential power as far as classical
logic is concerned.
John
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Date: Thu, 3 Oct 85 13:24:56 PDT
From: Hibbert.pa@Xerox.ARPA
Subject: Re: A Counterexample to Modus Ponens
Oops. I didn't think through very clearly what I had in mind. (And
definitely didn't say clearly what I was thinking.) I'll try again.
People's thinking may have been closer to probabilities rather than
classical logic. (Since most people don't understand either in any
formal way.) I'd like to claim that people believed something more like
the following:
(1b) If a Republican wins the election, then if the winner is not Ronald
Reagan, then the winner will probably be John Anderson.
(2b) A Republican will probably win the election.
without believing:
(3b) If the winner is not Reagan then the winner will probably be
Anderson.
And these beliefs are entirely consistent. (Given that peoples
standards for what constitutes a high probability are remarkably
inconsistent.)
Thanks John for making me think out more clearly what I had in mind.
Chris
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Date: 2 Oct 85 08:33:00 EDT
From: "CUGINI, JOHN" <cugini@nbs-vms>
Reply-to: "CUGINI, JOHN" <cugini@nbs-vms>
Subject: A (supposed) Counterexample to Modus Ponens
> Date: Fri, 27 Sep 85 10:57:18 edt
> From: John McLean <mclean@nrl-css.ARPA>
>
> In the most recent issue of The_Journal_of_Philosophy, there is an
> article by Vann McGee that presents several counterexamples to modus
> ponens. I am not sure whether to count them as counterexamples or as
> cases where we hold inconsistent beliefs. If the latter view is right,
> it should be of interest to those who model belief systems. [...]
I think this is just a problem with imprecisely stated beliefs:
surely the reasonable interpretation is that one believes (1) in
the simple sense that it's (almost certainly) true, but one
believes: (2') it is *probable* that a Republican will win the election.
After all, if you believed it was *certain* that "a Republican
wins the election" was true (maybe because you woke up the
morning after the election and someone told you: a Republican
has won), you would then believe (3). "Normal" rules of logic
don't work with probabilistic statements in lots of cases, eg:
I believe:
(1) the die will not come up as a 1.
(2) the die will not come up as a 2.
...
(6) the die will not come up as a 6.
but I certainly don't believe the conjunction of (1)-(6).
Of course, (1)-(6) should really be stated as:
(1) the die will (probably) not come up as 1, etc.
So, I consider these cases as neither true counterexamples to modus
ponens, nor as examples of inconsistent beliefs.
John Cugini <Cugini@NBS-VMS>
Institute for Computer Sciences and Technology
National Bureau of Standards
Bldg 225 Room A-265
Gaithersburg, MD 20899
phone: (301) 921-2431
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Date: Thu, 3 Oct 85 16:40:49 edt
From: John McLean <mclean@nrl-css.ARPA>
Subject: Modus Ponens
I agree that probability is the way to go in modeling beliefs. It is easy
to construct a distribution where the probabilities for (1) and (2) are
both quite high but where the probability of (3) is quite low even though
(3) follows from (1) and (2). Hence if believing p means that one assigns
a high probability to it, it is possible to believe (1) and (2) without
believing their logical consequence.
John
------------------------------
Date: Thu, 3 Oct 85 18:28:03 PDT
From: albert@UCB-VAX.Berkeley.EDU (Anthony Albert)
Subject: Re: Counterexample to modus ponens
(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 don't think the given example is a counter-example of modus-ponens
or of contradictory belief systems. It is not modus-ponens because
the statements are not true or false, but are beliefs. You cannot make
a statement that is true or false about the future.
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.
A belief X can always be qualified, usually by an all things being equal
type of default qualification. The given example ignores these implicit
conditions and so leads to a contradiction.
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End of AIList Digest
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