This is the fortieth part of the ILP series. For your convenience you can find other parts in the table of contents in Part 1 – Boolean algebra

We already know how to implement binary logic in ILP, today we are going to utilize it to implement ternary logic.

# Implementation

Ternary logic is used widely in SQL databases. Zero and one (or false and true) are rather ordinary, third value is called `null`

or `unknown`

and represent situation when we don’t know exact value. It usually has value . Truth tables for ternary logic goes as follows:

Disjunction:

Conjunction:

We are going to represent any ternary logic value as a pair of boolean flags. You can intuitively treat this as a number in binary system with values multiplied by two, so false is , unknown is , and true is . We know that disjunction can be calculated as a function and conjunction as a function and in theory we can implement operations in this way. However, simply checking all cases is faster. This is disjunction:

Conjunction goes this way:

Of course we need to destructure result to have two boolean flags at the end.