 In order to account for these intuitions in a precise way Krifka assumes that the parts of the structure \(\mathcal{M} = (\mathfrak{O}, \mathfrak{E}, \mathfrak{T})\) consisting of objects \(\mathfrak{O}\), events \(\mathfrak{E}\) and times \(\mathfrak{T}\) are each structured as complete join semi-lattices without a bottom element (see Grätzer, 1978). This means that we have a two place relation \(\sqcup\) (join) and relations \(\sqsubseteq\), \(\sqsubset\), and \(\bigcirc\) (part, proper part and overlap) that impose part-whole relations (mereologies, see the entry mereology) on the sets of objects, events and times. We cannot list all the properties that must hold for these structures to serve as admissible interpretations of natural language but we illustrate these properties by giving two examples.