good way to implement NotSpecification: isSpecialCaseOf?

I'm implementing the specification pattern. The NotSpecification seems simple at first:

NotSpecification.IsSpecialCaseOf(otherSpecification)
    r开发者_如何学编程eturn !this.specification.isSpecialCaseOf(otherSpecification)

But it doesn't work for all Specifications:

Not(LesserThan(4)).IsSpecialCaseOf(Equals(5))

This should return false instead of 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?

I have tried to implement this in Java and it went without problems and remainderUnsatisfiedBy(). Probably you have some problem in your implementation, here is mine:

public boolean isSpecialCaseOf(Specification spec) {
    if (spec instanceof GreaterThan) {
        return ((GreaterThan) spec).boundary > this.boundary;
    }
    return false;
}

The catch is in the Not() method, which should correctly construct opposite type of its argument.

static final Specification Not(Specification spec) {
    return spec.not();
}

Then all I need is to have correct implementation of not() for every Specification, e.g. for LesserThan:

    @Override
public Specification not() {
    return new GreaterThan(boundary);
}

If you have any problems, please provide your implementation of GreatherThan.isSpecialCaseOf and of Not, I will try to help.