 With this formal background it is now possible to state exactly when a predicate of events corresponding to a verb-phrase is cumulative, telic etc.. Again we will just state one result. Let \(\phi = \{ e|\exists x(\alpha(e) \wedge \delta(x) \wedge \theta(e, x))\}\) be such a predicate where \(\alpha\) represents a verb - say draw - \(\delta\) the nominal predicate - pictures - and \(\theta\) a thematic relation - say theme. It then follows that one set of conditions for \(\phi\) being cumulative is that \(\delta\) is cumulative and \(\theta\) is summative. An example is the verb phrase draw pictures. Similar results  characterize, iterative, telic, atelic etc. readings.