Floppy logic is multi-valued logic with completely unique properties.
Multi-valued logics and their problems
The history of multi-valued logics began in 1920, when Jan Łukasiewicz (1878-1956) published a short, two-page article on three-valued logic.1 The basic idea was simple: in addition to the truth values “true” and “false”, introduce a third value which we can call, for example, “I don’t know”.
Already at that time, logicians were working to connect multi-valued logic with probability theory, but, in the words of Jan Łukasiewicz: “Previous attempts to connect multivalued logic with probability theory have encountered major problems.”2 It is worth noting that the desired connection was not achieved even during the next nearly one hundred years.
Multi-valued logic experienced periods of greater or lesser prosperity, but the crucial year was 1965, when Lotfi Zadeh (1921-2017) wrote the first article on fuzzy logic.3 Fuzzy logic found its way into technical applications that ranged from washing machines to space rockets. It is precisely fuzzy logic that is contained in a large proportion of the so-called smart devices.
Despite its huge technical success, fuzzy logic also has its problems. Although a whole number of specific fuzzy logics were created, each of them lost some of the beautiful properties that we know from two-valued logic and that we would like every logic system to have.
Typically, when a student asks whether there can be a multi-valued logic that retains all the beautiful properties of two-valued logic, the answer they get is, well, to quote Jan Łukasiewicz again: “Even a cursory examination of this idea leads to the conclusion that not all laws of two-valued logic can remain valid.”2
Floppy logic as a solution to these problems
The idea that the loss of some desirable properties is the price we necessarily have to pay to move to multi-valued logic is very natural. Natural, but not true. Floppy logic is exceptional precisely because it was able to successfully solve both problems – the connection with probability theory and the preservation of the laws of two-valued logic. Plus, it is a simple and very elegant theory.
To get acquainted with floppy logic, I can especially recommend a simple:
There is also an abundance of other materials covering floppy logic available.
Reference:
[1] ŁUKASIEWICZ J. O logice trójwartościowej. Ruch Filozoficzny. 1920, 6, pp. 170–171.
[2] ŁUKASIEWICZ J. Geneza logiki trójwartościowej. Nauka Polska. 1939, 24, pp. 215-223.
[3] ZADEH L.A. Fuzzy sets. Information and Control. 1965, 8(3), pp. 338–353.