Aspect in Ancient Greek - Nijmegen Centre for Semantics

78 Chapter 4. An analysis of aoristic and imperfective aspectfor the data I am concerned with. If an ontological distinction would prove tomake things easier, I would not hesitate to adopt it, but I don’t think it would.On the contrary, and this is my main objection, it makes the formulation ofoperators that cause a shift in aspectual class much more complicated, as wewill see in section 4.6. For these reasons, I will restrict the distinction to thelevel of predicates.As a consequence of restricting aspectual class distinctions to the level ofthe predicate, a mismatch in aspectual class cannot be formalised as a typetheoreticor sortal clash in the way de Swart (1998) and Egg (2005) implementit. Instead we need an alternative way to do this, which I will present in section4.6.4.3 Completed vs. going on: the completiveand processual interpretationsThe evaluation of one-component theories of aspect (theories in which the primarycontribution of aspect is a change in aspectual class) in section 3.2.3 hasdemonstrated that such theories, when adapted to the Ancient Greek data,end up with a vacuous semantics for aoristic and imperfective aspect (on acoercion approach) or are forced to postulate an ambiguity for the two (ona non-coercion approach). Therefore, I propose a two-component theory ofaspect, that is, a theory in which the primary contribution of grammaticalaspect is something different from a change in aspectual class. I follow Klein’s(1994) proposal in positing that grammatical aspect concerns the relation betweenthe time of the eventuality and the topic time. More precisely, I adopta semantics for imperfective and aoristic aspect that is very similar to vonStechow et al.’s INCLUDED and INCLUDES (see (87)), respectively (see below forthe differences). Formulated in terms of DRSs I propose:(101) a. IMP λPλt[b. AOR λPλt[eτ(e) ·⊃ t ⊕P(e)]eτ(e) ⊆ t ⊕P(e)]= IMP= AORThree remarks on the notation. First, as one can see, IMP andIMP are not usedinterchangeably. IMP stands for the imperfective markers (morphemes) usedin natural languages, whereas IMP abbreviates the translation of IMP into ourformal language. Second, ‘τ(e) ·⊃ t’ reads as ‘t is a non-final subset of τ(e)’(see Appendix C.3). Third, whereas it is easiest to keep thinking of e and t asvariables over eventualities and times, respectively, they are actually constants