Aspect in Ancient Greek - Nijmegen Centre for Semantics

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112 Chapter 4. An analysis of aoristic and imperfective aspecthowever, since if we wish, we can easily intensionalise the semantics of theaorist as well:(139) AOR ′ = λPλt w ′Inert t (w 0 ,w ′ ) → [eτ(e) ⊆ t ⊕P(w′ )(e)]The result, however, is identical to what we get with the simple semantics,proposed earlier. Since all inertia worlds are identical to the actual world untilthe end of the topic time, it follows from the fact that there is a P eventualityincluded in the topic time in all inertia worlds that there is such an eventualityin the actual world.The foregoing discussion shows how Dowty’s solution of the imperfectiveparadox can be integrated in the semantics of imperfective and aoristic aspect.In order to keep formulas simple, I will return to the simple, non-intensionalsemantics for the remainder of this work. It should be noted that this hasno effect on the proposed analyses as they can all be reformulated in theintensional semantics without affecting the results. 18Before we leave the subject of the imperfective paradox, I will discuss adifferent way to avoid this paradox, proposed by Gerö and von Stechow (2003).It is interesting to see how they deal with the paradox, since I have adoptedtheir semantics of imperfective and aoristic aspect. I will try to show that ananalysis along the lines described above is superior to their account.The imperfective paradox is probably the reason why Gerö and von Stechow(2003) propose their selectional restriction of imperfective aspect to unboundedpredicates (see section 3.2.4). The (implicit) reasoning behind this restrictionseems to be the following: The problem of the imperfective paradox arises onlywith bounded predicates. By restricting imperfective aspect to unboundedpredicates, no problem will arise.But then the question is what to do with the cases where the imperfectiveseemingly combines with a bounded predicate. The straightforward answer isto introduce for these cases a coercion operator that maps the bounded predicateonto an unbounded predicate. For this purpose, Gerö and von Stechow(2003) propose the operator PROG ′ which, like my IMP ′ , is based on Dowty’s(1979) semantics for the English progressive: 1918 This also holds for examples that involve habitual coercion, since a proper habitualityoperator returns unbounded predicates.19 I have reformulated their account in DRT and adapted the use of variables to my ownnotational conventions.
4.9 The conative and likelihood interpretations 113(140) PROG ′ = λPλe w ′Inert τ(e) (w 0 ,w ′ ) → [ t e ′τ(e) ·⊃ tτ(e ′ ) ⊆ t⊕P(w ′ )(e ′ )]The main difference with my account is that I intensionalise the semanticsof the imperfective itself, whereas they capture the intensional element with anadditional operator. As a result imperfectivity comes on top of progressivityin their account. For (134a) we get the logical form in (141) (for INCLUDED,see (87); for the full derivation, see (224) in Appendix B):(141) PAST(INCLUDED(PROG ′ (λwλe m cross(e,w))))= λQ[tTT ≺ n ⊕Q(t TT)](λPλt[eτ(e) ⊇ t ⊕P(e)](λPλe w ′Inert τ(e) (w 0 ,w ′ ) → [ t e ′τ(e) ·⊃ tτ(e ′ ) ⊆ t⊕P(w ′ )(e ′ )](λwλe m cross(e,w))))≡et e ′w ′Inert τ(e) (w 0 ,w ′ ) → m cross(e ′ ,w ′ )τ(e) ·⊃ tτ(e ′ ) ⊆ tτ(e) ⊇ t TTt TT ≺ nWithout going in too much detail, notice that the imperfective and progressiveoperators contribute three temporal relations in total. Stacking thesetemporal relations gives the wrong result that the complete eventuality ofcrossing the street e ′ can be included in the topic time t TT (see Figure 4.13).This completely undoes the intended ‘going on’ interpretation of imperfectiveaspect.
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Aspect in Ancient GreekA semantic a
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viNick Asher, David Beaver, the lat
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Contentsix8 Conclusions and discuss
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2 Chapter 1. Introductiongroundbrea
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4 Chapter 1. Introduction(4) µετ
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6 Chapter 1. Introductionimperfecti
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1.3 Organisation of the thesis 9In
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Chapter 2The interpretations of aor
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2.3 Additional interpretations of t
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2.5 The challenge 21scriptions of h
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24 Chapter 3. Aspect in formal sema
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3.2 The perfective-imperfective dis
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162 Chapter 7. Comparison to theori
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172 Chapter 8. Conclusions and disc
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178 Appendix A: The language of Com
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192 Appendix B: Examples spelled ou
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206 Appendix C: List of abbreviatio
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208 Appendix C: List of abbreviatio
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210 References(Eds.), Cross-linguis
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212 ReferencesGrice, P. (1975). Log
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214 ReferencesLemmon, E. J. (1962).
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216 Referencesvan der Sandt, R. (19
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218 References
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220 Samenvatting (Summary in Dutch)
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222 Samenvatting (Summary in Dutch)
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