Pitfalls of Interval Reasoning

In most circumstances, arithmetic constraints maintain bounds-consistency and detect bounds-entailment and -disentailment. There are cases where a bounds-consistency maintaining constraint may detect a contradiction when the constraint is not yet bounds-disentailed, as the following example illustrates. Note that X #\= Y maintains domain-consistency if both arguments are constants or variables:

| ?- X+Y #= Z, X=1, Z=6, Y in 1..10, Y #\= 5.
| ?- X+Y #= Z #<=> B, X=1, Z=6, Y in 1..10, Y #\= 5.
X = 1,
Z = 6,
Y in(1..4)\/(6..10),
B in 0..1

Since 1+5#=6 holds, X+Y #= Z is not bounds-disentailed, although any attempt to make it bounds-consistent wrt. the store results in a contradictory store.

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