Forty-four relations are found between an interval and an interval with a gap ( r_IIg ), capturing semantics that are distinct from those of the sets of constituting intervals and at a higher semantic level than pure pointbased models. The relations? conceptual neighborhood graph evolves as a refinement of the graph of Allen?s thirteen binary relations between intervals, primary due to more details revealed about five of the thirteen interval relations. The compositions of r_IIg with their converse relations r_IgI reveal that the interval compositions form an upper bound within which the gaps reduce the set of possible inferences, sometimes up to yielding unique inferences where interval compositions are fully undetermined.