I remember reading an article (in Scientific American I think) back in grad school (late 1970’s) that proposed a 24-valued logic. The basic idea had to do with rust fungus on crops and the values corresponded to the month of the year and the presence or absence of rust. I have not been able to find this article again. Does anyone know of it? Thanks.
NOTE: I am not interested in a 24-valued logic per se. I am interested in the motivation for and application of such a system in a field far removed from formal disciplines such as mathematical logic and computer science. In other words, as far as the logic is concerned, I wanted to see what the researchers say in the informal metalanguage (English plus logicians' jargon).
Is this the article or would this link give some clue to find the article
https://ir.library.oregonstate.edu/xmlui/bitstream/handle/1957/8858/tec_bul_117.pdf?sequence=1
or would this give any clue
http://www.ars.usda.gov/SP2UserFiles/ad_hoc/36400500Publications/CerealRusts/The%20Cereal%20Rusts_VOLUME%20II.pdf
No success, but thanks for the effort Nilay & Peter. At the time I was writing a thesis on the individuation of events but often got sidetracked into other interesting stuff. I was looking at Carnap’s Introduction to symbolic logic and its applications where he had sections on axiomatic systems, including one for biology, which subsequently got me reading Woodger’s The axiomatic method in biology, and then I serendipitously came across the article in an old issue of Scientific American (?) in my department’s reading room. So the article’s reference to a 24-valued logic would have quite specific and literal, and not just something I inferred from its content. And yes, as I said in the blurb to my question, the 24 values corresponded to month of year plus presence or absence of rust. But the Chandra and Stockmeier article you mentioned, Peter, looks like something I will want to read too. Thanks for that.
I have seen a number of papers on 3-, 4-, 8-, 9- and 16-valued logics, such as 'Some Useful 16-Valued Logics: How a Computer Network Should Think' by Yaroslav Shramko and Heinrich Wansing, see http://kdpu.edu.ua/shramko/files/2005_JPL_Some_Useful_16-valued_Logics.pdf
So far, I haven't seen any papers that focus explicitly on 24-valued logic.
Karl Pfeifer, from the description that you give, I have the impression that the late 1970s article in Scientific American might have used a classical two-valued logic, possibly introducing 12 propositional atoms, each corresponding to the presence (or absence, depending on the valence true or false) of rust in a given month. Could that be the case?
As far as I remember, Chandra and Stockmeyer do not discuss a 24-valued logic in their 1979 paper "Intrinsically difficult problems" in Scientific American (which I cannot find freely downloadable on the Internet to check). I think they might have referred to 2^4, which search engines equate with 24.
I wish you the best of luck in finding the crop rust paper!
Dear Karl,
you should take the set of values {0, 1/22, 2/22, .... ,1}
and define: x or y = max(x, y), x and y = min(x, y), not x = 1 - x.
That way you get 24-valued logiC (so called Goedel logic G24).
Greetings, Tadeusz
Yes Reineke, what you suggest is definitely possible -- it's been so long ago I don't remember the details except that the phrase "24-valued logic" was used (or misused, if you are right).
Of course Chandra and Stockmeyer have nothing to do with this. but I just found their abstract independently interesting.
Cheers, Karl
Thanks Tadeusz. I realize there are many ways of developing a 24-valued logic. My interest is not so much in the formal technical aspects of such a system (or even in 24 values per se) but in the motivation for and application of such a system in a field removed from formal disciplines such as mathematical logic and computer science. In other words, as far as the logic is concerned, I wanted to see what the researchers say in the informal metalanguage (English plus logicians' jargon).
There are different finite-valued logics. The first 3-valued logic was introduced by the Polish logician Jan Lukasiewicz with value 1=truth, value 0=falsity and 1/2 - unknown. Its origin goes back to Aristoteles and is related to the logical value of sentences like A="Tomorrow will be sea battle". The value of this sentence today is unknown, (so v(A)=1/2), the value its negation ~A today is also unknown (hence v(~A)=1/2. The table of this Lukasiewich negation ~A is: ~0=1, ~1=0, ~1/2=1/2. Another, different meaning of Lukasiwech negation is as a negation by counterexample. More about different semantics of this logic can be seen in:
"Intuitive semantics for some three-valued logics connected with information, contrariety and subcontrariety" STUDIA LOGICA 48(4):565-575 · DECEMBER 1989.
Size does not matter. For any N, take a poset N, a topos SetN, and in this topos you will have N+1 logical values (points).
If you are referring to a student's work, I have had an article called 24 Alternatives for Comprehensive Models of Knowledge and Ethics published for some time. It has attracted some interest, and is available on Academia and AcademicRoom: https://www.academia.edu/14270121/24_Alternatives_for_Comprehensive_Models_of_Knowledge_and_Ethics
However, it is not peer-reviewed. But it does happen to discuss logic / knowledge, and has 24 models or values.
https://www.academia.edu/14270121/24_Alternatives_for_Comprehensive_Models_of_Knowledge_and_Ethics
If you are referring to a student's work, I have had an article called 24 Alternatives for Comprehensive Models of Knowledge and Ethics published for some time. It has attracted some interest, and is available on Academia and AcademicRoom: https://www.academia.edu/14270121/24_Alternatives_for_Comprehensive_Models_of_Knowledge_and_Ethics
However, it is not peer-reviewed. But it does happen to discuss logic / knowledge, and has 24 models or values.
https://www.academia.edu/14270121/24_Alternatives_for_Comprehensive_Models_of_Knowledge_and_Ethics
A lot of intuitionistic logics can be built so that the classifier has 24 different points.
E.g. take Set2 × Set3. Or Set23. By 2 and 23 I mean a linear order with as many elements. These two are just samples.
Several responders have indicated that a 24-valued logic could be set up in any number of ways, and indeed, that would be a trivial exercise. My interest is not in the formal technical aspects of such a system (or even in 24 values per se) but in the motivation for and application of such a system in a field far removed from formal disciplines such as mathematical logic and computer science. In other words, as far as the logic is concerned, I wanted to see what the researchers say in the informal metalanguage (English plus logicians' jargon). I have added a note to the original question to make this clear.