Aspect in Ancient Greek - Nijmegen Centre for Semantics

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186 Appendix A: The language of Compositional DRTA.8 ReductionsThe semantics of the language (A.5) ensures a number of equivalences. LetFV be the function that gives the free variables of a well-formed expressionand let µ β [ξ α ↦→ν α ] stand for the expression that results from replacing in µ allfree occurrences of the variable ξ by the expression ν. Then:(i)(ii)λξ α µ β (ν α ) M,f = µ β [ξ α ↦→ν α ] M,f , if FV (λξµ(ν)) = FV (µ[ξ↦→ν])λξ α µ β M,f = λυ α µ β [ξ α ↦→υ α ] M,f , if FV (λξµ) = FV (λυµ[ξ↦→υ]) (idemfor ∃ or ∀ instead of λ)The syntactic operations corresponding to (i) and (ii) are called lambdaconversion(λ) and renaming bound variables (RBV), respectively.A.9 ExampleLet’s now work out one of the examples (cf. (105)):(206) λQ[tTT ≺ n ⊕Q(t TT)](λPλt[eτ(e) ·⊃ t ⊕P(e)](λe p kinge ))As mentioned, I treat τ as a predicate now, which gives:(207) λQ[tTT ≺ n ⊕Q(t TT)](λPλt[e t ′e τ t ′t ′ ·⊃ t⊕P(e)](λe p kinge))Let’s first treat the parts (208) to (210) separately and then combine them:(208) λQ[tTT ≺ n ⊕Q(t TT)](209) λPλt[e t ′e τ t ′t ′ ·⊃ t⊕P(e)](210) λe p kingeFirst (208):
A.9 Example 187(211) a. λQ[tTT ≺ n ⊕Q(t TT)]RWR1=⇒b. λQ[ ≺ {tTT ,n} ⊕Q(t TT)]ABB4=⇒c. λQλiλj∃k[ ≺ {tTT ,n} (i)(k) ∧Q(t TT)(k)(j)]ABB3=⇒d. λQλiλj∃k[λiλj[i⌊⌋j ∧ ≺ {t TT ,n}(j)](i)(k) ∧Q(t TT )(k)(j)]ABB1=⇒e. λQλiλj∃k[λiλj[i⌊⌋j ∧ λi ≺ (w(t TT )(i))(w(n)(i))(j)](i)(k)∧ Q(t TT )(k)(j)]λ=⇒f. λQλiλj∃k[λiλj[i⌊⌋j ∧ ≺ (w(t TT )(j))(w(n)(j))](i)(k)∧ Q(t TT )(k)(j)]λ=⇒g. λQλiλj∃k[λj[i⌊⌋j ∧ ≺ (w(t TT )(j))(w(n)(j))](k) ∧Q(t TT )(k)(j)]h. λQλiλj∃k[[i⌊⌋k ∧ ≺ (w(t TT )(k))(w(n)(k))] ∧Q(t TT )(k)(j)]λ=⇒Let’s now do (209):(212) a. λPλt[b. λPλt[e t ′e τ t ′t ′ ·⊃ te t ′τ{e,t ′ }·⊃ {t ′ ,t}c. λPλt[λiλj∃k[⊕P(e)]⊕P(e)]e t ′τ{e,t ′ }·⊃ {t ′ ,t}(i)(k) ∧P(e)(k)(j)]]RWR1=⇒ABB4=⇒ABB3=⇒d. λPλt[λiλj∃k[λiλj[i⌊e t ′ ⌋j ∧ τ{e,t ′ }(j) ∧ ·⊃ {t ′ ,t}(j)](i)(k)∧P(e)(k)(j)]]e. λPλt[λiλj∃k[λiλj[i⌊e t ′ ⌋j ∧ λiτ(w(e)(i))(w(t ′ )(i))(j)∧ ·⊃ (w(t ′ )(i))(w(t)(i))(j)](i)(k) ∧P(e)(k)(j)]]ABB1=⇒λ=⇒
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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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3.3 Aspectual coercion 673.3.1 Aspe
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3.3 Aspectual coercion 69bials ((88
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3.3 Aspectual coercion 71the term c
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3.3 Aspectual coercion 73in the ext
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76 Chapter 4. An analysis of aorist
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100 Chapter 4. An analysis of aoris
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122 Chapter 5. Aspect and performat
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134 Chapter 6. The temporal structu
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Page 168 and 169: 158 Chapter 7. Comparison to theori
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Page 188 and 189: 178 Appendix A: The language of Com
Page 202 and 203: 192 Appendix B: Examples spelled ou
Page 216 and 217: 206 Appendix C: List of abbreviatio
Page 218 and 219: 208 Appendix C: List of abbreviatio
Page 220 and 221: 210 References(Eds.), Cross-linguis
Page 222 and 223: 212 ReferencesGrice, P. (1975). Log
Page 224 and 225: 214 ReferencesLemmon, E. J. (1962).
Page 226 and 227: 216 Referencesvan der Sandt, R. (19
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Page 230 and 231: 220 Samenvatting (Summary in Dutch)
Page 232 and 233: 222 Samenvatting (Summary in Dutch)
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Aspect in Ancient Greek - Nijmegen Centre for Semantics

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