Logical Translation of EnglishAuthor(s): Leon DavidsonSource: Journal of the Operations Research Society of America, Vol. 2, No. 4 (Nov., 1954), pp.446-448Published by: INFORMSStable URL: http://www.jstor.org/stable/166702 .

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446 LETTERS TO THlE EI)ITOR

THE APPIPIACATION OF TIIE OPERATIONS-RESEARCH APPROAC11 IN MAKING A DECISION OF NO

GREAT IMPORTANCE

GEOFFREY J. SIEGE',L Battelle .M1emorial Institute, Columibus, Ohio

(Received September 27, 19(5)

IT AMAY NOT be news to rea(ders of the JOURNAL that the operations-research approach is applicable to making small everyday decisions, but (clear-cut ex-

aflln)les of successful applications are rarely plesented. I found a 'scientific' metho(1 very helpful in decidIing what initials to place in

front of the name of a (colonel nanied Lewis, with whom I had to make an ap- pointment. I was sure of the last name, but I did not know the initials. It wxasn't really necessary to know the initials, and nothing drastic would have hap-

pened if I used the wrong ones. I just felt that an initial or two would look better on the forins that I had to fill out to arrange the appointment.

My problem was to select the initials to go with 'Lewis' that had the best chance of being right. The reference book nearest at hand was the telephone directory. Under LEwis-also see Louis, I counte(l the frequency that each letter of the alphabet occurred ats a first initial. Then I tabulated the frequency of seeon(l initials which occurre(l with the most common first initial.

'C' predominate(l as a first initial-40 'C.' Lewises, with the 'R.' Lewises in second place with 37. The '(C. H.' Lewises led the 'C. E1.' and the 'C. A.' Lewises by a slight margin.

The decision I made wras conservative; I use(l 'Colonel C. L ewis' in making arrangements for the visit. The moral of this story is that any data, no matter how scantv, may be a better basis for decision than a pure guess.

It turned out that the colonel really was 'C. H. Lewis.' In fact, he told me: "You should have used the Department of Defense phone directory. There were six Colonel C. HI. Lewises listed when I w-as stationed at the Pentagon."

LOGICAL'I., 'TIIANSLA'T..I()ON OF ,J.NGISH-l*

1LEON DAVIDSON 14 8oundliCw Avenue, 1Wh1ite Plains, New, York (Received August 26 and September 24, 1954)

I SHOULI) LIKE to comment on the paper by Robert S. Ledley which appeared in the August issue of .JORSA. On encountering the article I turned first to

the first example given (Example I, p. 265) to see the lay of the land. Ignoring the symbolism for the moment, I tried to reconcile a straightforward logical verbal

* The following are excerpts made by the Editor from two letters commenting on LEi)iFY'S ''Mathematical Foundations and Computational M-lethods for a D)igital Logic Mlachine" [J. Opns. IRes. Soc. Anm. 2, 249 (August 1954)1. Itobert Ledlev was given a chance to comment on the first, letterl alnd his comments were sent to David- son before the second letter was writtell.

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LEON DAVIDSON 447

analysis of statements 1 through 8 to the two conclusions containing "the most information" stated on p. 267.- I found that I could not agree with the -author's conclusions.

Statements 5 through 8, supposedly received from "fairly, though not completely reliable sources," read as follows:

5. Jet planes have heavy armor. 6. Heavy armored planes with a short range are fighters. 7. Either long-range planes or fighter planes have light armor. 8. Either conventional engine planes, or short range planes have heavy armor.

I find no basis, in the statements as given above, for any of the author's conclusions as stated.

Before proceeding, let us clarify the meaning of "either. . , or . . ." as used in statements 7 and 8. Either this means

[x] "Either A or B, but not both simultaneously" (the common English meaning) or it means

[y] "Either A or B, or both simultaneously" (the meaning indicated by the symbolic presentation of statement 7 at the bottom of p. 266, which uses the "+" symbol defined at the top of p. 251).

It should be noted that the " An" symbol is defined only as "or," however, and no symbol is ever defined for the word "either" in this paper.

I did not find fault with Ledley's logical system, but rather with his translation of the English statements into logical symbols.

On p. 264 there is a most apt discussion of "the difficulty of translating the practical worldly situation into these precise [propositional] statements. Part of this difficulty is the prevalent loose and often obscure use of language, and in particular of those very conjunctions that form the logical operations."

I submit that the simple point at issue is this: Ledley does not comprehend that there could be more than one logical translation of the "either..., or..." statements 7 and 8. This is unfortunate because on the next page he said "In the examples presented here, we have tried to restrict the initial sentences to those with relatively clear-cut intended meaning." I claim that the meaning which Ledley chooses to use is not the one which the ordinary person (or Lower- Slobbovian informant) would intend, when making the statements.

It is explicit in Ledley's reply that he understands statement 7 to say "that if the plane is a fighter, or if the plane has long range, or both, then it has light armor." This is, of course, the meaning of his symbolic translation A +C-+D. Now, I claim that this is a strained translation of 7, which contains no "ifs" as originally written.

The commonly understood meaning of 7, which the man in the street or the Lower-Slobbovian informant would undoubtedly mean when he made the statement, would be "either long range planes have light armor, or fighter planes have light armor." (Although I am sure that the man in the street would also have in mind adding "but not both simultaneously" to his meaning, I defer to the logicians and their 'logical or' and allow that we may add 'or both' to the foregoing translation, without affecting the following argument.) The logical symbolism for this commonly understood meaning of 7 would be (AN-D) +(C-+D).

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448 LETTERS TO THE EDITOR

It is obvious that the interpretation of 7 given in this paragraph is different from the interpretation used by Ledley, given in the preceding paragraph.

Ledley's methodology surely gives the correct results corresponding to what he feeds into it. I claim that what he fed in for 7 and 8 was incorrect, or was at least not the only correct interpretation. Thus his results were incorrect, for an intelligence agency cannot afford to lose a large fraction of the possible results because of a limited or erroneous interpretation of the raw intelligence data.

Let me add that I have great respect for symbolic logic and its facile prac- titioners, and I quite agree with many of the points in Ledley's reply concerning the utility of symbolic methods. I even admire the neatness and scope of his digital formulation of the logical system. I merely urge that care be taken in selecting the symbols to fit the statements, lest some of the possible conclusions be lost at the start. I do not wish to seem to imply that there is any error in the digital system or logical manipulations which Ledley utilizes. It is just that I find it disconcerting that we are not all aware that English, as she is spoke, is a very tricky language.

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