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Regarding the following quote from the article: "A statement either does hold (it has value 1, with some probability p) or it does not (it has value 0, with so
by triska 8y ago
Regarding the following quote from the article:
"A statement either does hold (it has value 1, with some probability p) or it does not (it has value 0, with some probability 1-p; the Law of the Excluded Middle means that there is no probability that the statement has any other value)."
This holds for example in classical logic, but it is not a universal principle in logic. For example, the statement does not apply to intuitionistic logic:
https://en.wikipedia.org/wiki/Intuitionistic_logic https://en.wikipedia.org/wiki/Intuitionistic_logic
The fact that (A ∨ ¬A) is not a tautology in intuitionistic logic reflects the limits of logical proof: By Gödel's first incompleteness theorem, if a consistent formal system is sufficiently powerful, then it can express statements that can be neither proven nor refuted within the system. Intuitionistic logic lets you reason about such situations.
If you are interested in learning a programming language where you can conveniently express "anything at all" without even a trace of "null", a logic programming language may be suitable. For example, in Prolog, a logical variable stands for anything at all, and as such is truly a variable as in predicate logic.