From 4b9b761cc990f9247083ea28a32d9123bb752818 Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Sat, 18 Jul 2020 23:35:02 -0400 Subject: Add a main repository link to html files and titles to spec files --- docs/doc/logic.html | 1 + 1 file changed, 1 insertion(+) (limited to 'docs/doc/logic.html') diff --git a/docs/doc/logic.html b/docs/doc/logic.html index 2235259a..7ac951d8 100644 --- a/docs/doc/logic.html +++ b/docs/doc/logic.html @@ -1,4 +1,5 @@ +
BQN

Logic functions: And, Or, Not (also Span)

BQN retains the APL symbols ∧ and ∨ for logical and and or, and changed APL's ~ to ¬ for not, since ~ looks too much like ˜ and ¬ is more common in mathematics today. Like J, BQN extends Not to the linear function 1⊸-. However, it discards GCD and LCM as extensions of And and Or, and instead uses bilinear extensions: And is identical to Times (×), while Or is ×⌾¬, following De Morgan's laws (other ways of obtaining a function for Or give an equivalent result—there is only one bilinear extension).

If the arguments are probabilities of independent events, then an extended function gives the probability of the boolean function on their outcomes (for example, if A occurs with probability a and B with probability b independent of A, then A or B occurs with probability a∨b). These extensions have also been used in complexity theory, because they allow mathematicians to transfer a logical circuit from the discrete to the continuous domain in order to use calculus on it.

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