Aspect in Ancient Greek - Nijmegen Centre for Semantics

3.2 The perfective-imperfective distinction 41element(i), (ii), and (iii) together make the structure a join semi-lattice and (iv)ensures that there is no bottom element.A part-of relation ⊑ can be defined in terms of the operation ⊔:(57) e ⊑ e ′ iff e ⊔ e ′ = e ′The proper part-of relation is then defined as follows:(58) e ⊏ e ′ iff e ⊑ e ′ and e ≠ e ′Krifka defines the distinction between telic and atelic predicates formallywith the use of this proper part-of relation. He claims that telic predicates arequantised: 14(59) A property P is quantised iff for all e, e ′ if P(e) and e ′ ⊏ e then ¬P(e ′ )A predicate is quantised iff no eventuality that is a proper part of an eventualityin the extension of the predicate is also in its extension. For example, a properpart of an eventuality in the extension of the telic predicate John build a houseis not likewise in the extension of John build a house (in the same way as aproper part of a bottle of water does not count again as a bottle of water).Atelic predicates, on the other hand, are non-quantised (often called homogeneous).The predicate John walk, for example, is non-quantised, given thata part of an eventuality in the extension of this predicate is in its extensiontoo, except when the parts get too small to count as walking (in the same wayas a part of water still counts as water, up to the level of molecules). Krifkaseems to require moreover that atelic predicates are cumulative. 15 I postponethe discussion of cumulativity to a later point in this section.With this formalisation of telicity Krifka immediately derives a numberof phenomena that needed some stipulations in the DRT accounts discussedin the previous section. Let’s first consider the interaction with time-frameadverbials like on Sunday.(60) a. Mary wrote a letter on Sunday.b. Mary was ill on Sunday.c. Mary wrote on Sunday14 Strictly speaking, quanticity is a property of properties, and a predicate is quantised ina derived sense only, viz. if it denotes a quantised property.15 Krifka (1989a:90): “Basically, telic predicates can be reconstructed as quantised eventpredicates, and atelic predicates as event predicates which are strictly cumulative (or atleast, non-quantised).” Krifka (1989b:158): “Die Atelizität wird umgekehrt durch die Kumulativitätdes verbalen Prädikats erfaßt werden.” (“Atelicity, by contrast, will be capturedby the cumulativity of the verbal predicate.”)