AIList-REQUEST@SRI-AI.ARPA (AIList Moderator Kenneth Laws) (10/15/85)
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 ---------------------------------------------------------------------- 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 ------------------------------ End of AIList Digest ********************