Let's say we have a set of options which the user can select. Options can be related between them in two ways: one can depend on another, and two options can be mutually exclusive. That means that these equalities must always hold true (note: this is not code, those are logical equations):

• "A depends on B", or "for A to be selected, B needs to be selected"

ruleSet.AddDep(A, B) =>
if isSelected(A) then isSelected(B)

• "A and B are exclusive", or "B and A are exclusive", or "for A to be selected, B needs to be unselected; and for B to be selected, A needs to be unselected"

ruleSet.AddConflict(A, B) <=> ruleSet.AddConflict(B, A) =>
if isSelected(A) then !isSelected(B) && if isSelected(B) then !isSelected(A)

We say that a set of relations are coherent if the laws above are valid for that set. For example, this set of relations is coherent:

AddDep(A, B) // "A depends on B"
AddDep(B, C) // "B depends on C"
AddConflict(C, D) // "C and D are exclusive"

And these sets are not coherent:

AddDep(A, B)
AddConflict(A, B)

A depends on B, so it's a contradiction that they are exclusive. If A is selected, then B would need to be selected, but that's impossible because, by the exclusion rule, both can't be selected at the same time.

AddDep(A, B)
AddDep(B, C)
AddConflict(A, C)

The dependency relation is transitive; it's easy to see, from the rules above, that if A depends on B, and B depends on C, then A also depends on C. So this is a contradiction for the same reason as the previous case.