See invisible operates on a scale that determines what level of invisible monsters the player is allowed to see. (A low-level monster that drinks a potion of invisibility should be visible even with weak see invisible, an arch-lich casting disappear should require very strong see invisible.) Invisibility should do this too and have a scale as well (one notable place on the scale being that invisibility is kept only until the invisible thing takes an offensive action). If rings of invisibility and see invisible are made chargeable, this is an obvious avenue for them.