I can write out the following CNF in various different ways:

In mathematical textbook notation: $(A \land B \land C) \lor (\lnot A \land B \land \lnot C) $

In C-like programming notation: (A && B && C) || (!A && B && !C)

In engineering logic notation: $(ABC) + (\overline{A}B\overline{C})$

So, I guess my question is in the title: why do we have so many different systems of boolean logic notation when boolean logic as a field is quite a recent invention?

  • $\begingroup$ Then there is the system using dots instead of parentheses. see math.stackexchange.com/q/311871/442 $\endgroup$ Jan 5, 2021 at 13:04
  • $\begingroup$ Why not? Boolean logic is used in many different fields for many different purposes, and each adopts the notation that suits their needs best. They also have different historical roots, the more algebraic notation goes back to Boole, the one with conjunctions and disjunctions to mathematical logic, and programming languages generally introduce many notational variations. $\endgroup$
    – Conifold
    Jan 5, 2021 at 20:40

1 Answer 1


The software part is easy: it uses standard ASCII characters so the source code can be universally applied.

"Engineering Logic" has its own variations,but notice that "addition" is similar to "OR" and "multiplication" is similar to "AND" when dealing with base-2 numbers -- and that Boolean logic is fundamentally binary.

As to tilde vs. exclamation point vs. overbar, my guess is that different groups or locales got started independently.

  • 1
    $\begingroup$ The internal logic of the engineering notation is clear enough, but my question is really why does the engineering notation exist at all when the ∧/∨ notation presumably already existed. Did that notation somehow fail to meet the needs of the engineering group? I do appreciate your answer for the ASCII observation, however. $\endgroup$
    – Ben I.
    Jan 7, 2021 at 19:35
  • $\begingroup$ As to the overbar for negation, I'd say that you simply have different needs for brevity in different contexts. If you are dealing with lots of negated signals, overbar gives a compact notation. $\endgroup$ Nov 30, 2022 at 0:02

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