I'm implementing the specification pattern. The NotSpecification seems simple at first: NotSpecification.IsSpecialCaseOf(otherSpecification) return !this.specification.isSpecialCaseOf(otherSpecification) But it doesn't work for all Specifications: Not(LesserThan(5)).IsSpecialCaseOf(GreaterThan(4)) This should be true. So far I think that the only way to accomplish the isSpecialCaseOf the NotSpecification is to implement the remainderUnsatisfiedBy (partial subsumption in the paper on the specification pattern). But maybe I am missing something more simple or a logical insight that makes this unnecessary. Question: Is there another way of implementing this by not using remainderUnsatisfiedBy?