This tool provides some functions related to ternary logic on values ⊥,0,1. Formulas may use the constants ⊥,false,true, the negation, conjunction, disjunction, implication written as !,&,|,-> (alternatively as ¬,∧,∨,→) as well as the sequential ITE operation (x?y1:y0). Moreover, there is the absent test abs(x) which is true if x=⊥ holds and false otherwise. Finally, there is the equality operation phi=psi which is a ternary function that is true for a variable assignment if phi and psi evaluate to the same ternary value for that assignment, and is false otherwise.
(x?y1:y0)
abs(x)
x=⊥
phi=psi
phi
psi
The ternary function may be entered either as partial function table or as a formula using variables x0,...,xN (to avoid confusion). The function table requires only the entries that are mapped to 0 or 1 since the missing entries will be automatically mapped to ⊥. For the formula input, do not use equivalence or xor since these are interpreted as equality and its negation. Also, best use variables x0,...,xN since other variables are mapped to these names after parsing.
Recall Some Laws of Ternary Logic