Ignition is a tool for building custom rules engines, tailored towards SAT solvers

A rule engine is built two parts, items and rules

id: <unique_id>
attributes:
  - key: key_1      # attribute 1
    value: <value>
  - key: key_2      # attribute 2
    value: <value>
  - key: key_3      # attribute 3
    value: <value>
  - key: key_1      # overrides attribute 1
    value: <value>

For these examples, we will imagine the problem of choosing an outfit from a closet

A closet has families of clothing (ex. Shirts, Pants, etc.)
A family of clothing has many possible items (ex. Shirts has red and black, Pants has jeans, etc.)

An outfit is a selection of items, one from each family
In an outfit, you must have at exactly one selection per family (ex. You can't wear two shirts, You can't skip pants!)
Rules may be defined that exclude or include certain items, given a specific selection (ex. You can't wear jeans with a blue shirt)

If we represent the selection of an item as a boolean (T for selected, F for not selected), each rule in the system can be defined by a logical binary operation
The output of the binary operation is a boolean, telling us whether the combination is valid.

An item is a single piece of clothing. The attributes are color and family.

id: blue_shirt
attributes:
  - key: color      # attribute 1
    value: blue
  - key: family     # attribute 2
    value: shirt

A and B are items in the same family
A and B may not be selected at the same time, but one of them must be selected

Equation (DNF): (A * ~B) + (~A * B)

Truth table:

While this equation looks similar to an XOR, it doesn't scale in the same way
Where a 3-input XOR function allows all three inputs to be T at the same time, our sibling relationship does not
Lets look at the truth table for three items in the same family

Equation (DNF): (A * ~B * ~C) + (~A * B * ~C) + (~A * ~B * C)

Truth table:

The relationship holds true for three items, and the equation will scale quadratically for each item added

A and B are items in different families
Selection of A excludes the selection of B
Selection of B excludes the selection of A

Equation: A -> ~B or ~(A * B)
Equation (DNF): ~A + ~B

Truth table:

A and B are items in different families
Selection of A requires that B is also selected Selection of B does not require that A is also selected

Equation: A -> B or ~(A * ~B)
Equation (DNF): ~A + B
NOTE: A and B are not interchangeable

Truth table: