Aspect in Ancient Greek - Nijmegen Centre for Semantics

188 Appendix A: The language of Compositional DRTf. λPλt[λiλj∃k[λiλj[i⌊e t ′ ⌋j ∧ τ(w(e)(j))(w(t ′ )(j))∧ ·⊃ (w(t ′ )(j))(w(t)(j))](i)(k) ∧P(e)(k)(j)]]g. λPλt[λiλj∃k[λj[i⌊e t ′ ⌋j ∧ τ(w(e)(j))(w(t ′ )(j))∧ ·⊃ (w(t ′ )(j))(w(t)(j))](k) ∧P(e)(k)(j)]]h. λPλt[λiλj∃k[[i⌊e t ′ ⌋k ∧ τ(w(e)(k))(w(t ′ )(k))∧ ·⊃ (w(t ′ )(k))(w(t)(k))] ∧P(e)(k)(j)]]λ=⇒λ=⇒And finally (210):(213) a. λe p kingeRWR2=⇒b. λe p king{e}ABB3=⇒c. λeλiλj[i⌊⌋j ∧p king(e)(j)]ABB1=⇒d. λeλiλj[i⌊⌋j ∧ λip king(w(e)(i))(j)]λ=⇒e. λeλiλj[i⌊⌋j ∧p king(w(e)(j))]Then we combine (212h) and (213e):(214) a. λPλt[λiλj∃k[[i⌊e⌋k ∧ τ(w(e)(k))(w(t ′ )(k))∧ ·⊃ (w(t ′ )(k))(w(t)(k))] ∧P(e)(k)(j)]](λeλiλj[i⌊⌋j ∧p king(w(e)(j))])λ=⇒b. λt[λiλj∃k[[i⌊e⌋k ∧ τ(w(e)(k))(w(t ′ )(k)) ∧ ·⊃ (w(t ′ )(k))(w(t)(k))]∧λeλiλj[i⌊⌋j ∧p king(w(e)(j))](e)(k)(j)]]λ=⇒c. λt[λiλj∃k[[i⌊e⌋k ∧ τ(w(e)(k))(w(t ′ )(k)) ∧ ·⊃ (w(t ′ )(k))(w(t)(k))]∧λiλj[i⌊⌋j ∧p king(w(e)(j))](k)(j)]]λ=⇒d. λt[λiλj∃k[[i⌊e⌋k ∧ τ(w(e)(k))(w(t ′ )(k)) ∧ ·⊃ (w(t ′ )(k))(w(t)(k))]∧λj[k⌊⌋j ∧p king(w(e)(j))](j)]]λ=⇒e. λt[λiλj∃k[[i⌊e⌋k ∧ τ(w(e)(k))(w(t ′ )(k)) ∧ ·⊃ (w(t ′ )(k))(w(t)(k))]∧ [k⌊⌋j ∧p king(w(e)(j))]]]And finally, we combine (214e) and (211h):(215) a. λQλiλj∃k[[i⌊⌋k ∧ ≺ (w(t TT )(k))(w(n)(k))] ∧Q(t TT )(k)(j)](λt[λiλj∃k[[i⌊e t ′ ⌋k ∧ τ(w(e)(k))(w(t ′ )(k))