See Three-valued logic.

Some problems are very awkwardly expressed in two-valued logic, mostly when we are dealing with uncertainty.

A typical example is flow analysis. Consider this piece of elisp code:

(let (a)
  (if x
      (setq a "a was set")
    (message "we do nothing"))
  a) ;; what is a?

If we now ask a question "is a a string?" the answer is not "definitely yes" nor "definitely no" but "maybe" because without knowing what x is we can't tell.

This and many more use-cases can be found in Elsa, the Emacs Lisp Static Analyzer.

• trinary-true
• trinary-maybe
• trinary-false

• trinary-true-p = true
• trinary-maybe-p = maybe
• trinary-false-p = false
• trinary-possible-p = true or maybe
• trinary-necessary-p = true

See Kleene logic.

• trinary-not
• trinary-and
• trinary-or
• trinary-happened
• trinary-add-maybe = X or maybe