[bunderbunder]

If there are exactly two possible values, TRUE and FALSE, you're working with Boolean logic.

If there are three possible values, TRUE, FALSE and NULL (unknown), then you're probably working with something like Kleene logic. You can't truly be working with Boolean logic, though, any more than you can be doing integer arithmetic when 15.37 is a member of your domain.

To put it another way, if we're talking about the mathematical definition of boolean algebra and not just some programming language's quirky implementation that happens to be called "bool", then boolean values would by definition be non-nullable. That logic that allows nulls has been implemented using the same unified set of keywords and operator names is a pragmatic decision that simplifies the language implementation and spec, not a principled one that tries to be pedantic about mathematical terminology.

[mrkeen]

> That logic that allows nulls has been implemented using the same unified set of keywords and operator names is a pragmatic decision

That's why it's name-squatting. Rather than introduce a 'kleene' datatype & operations, and let the user opt-in, they decided that in our 'bool' world, the following is not a truism:

  a = a or a <> a