Aspect in Ancient Greek - Nijmegen Centre for Semantics

A.9 Example 189∧ ·⊃ (w(t ′ )(k))(w(t)(k))] ∧ [k⌊⌋j ∧p king(w(e)(j))]]])λ=⇒b. λiλj∃k[[i⌊⌋k ∧ ≺ (w(t TT )(k))(w(n)(k))] ∧ λt[λiλj∃k[[i⌊e t ′ ⌋k∧τ(w(e)(k))(w(t ′ )(k)) ∧ ·⊃ (w(t ′ )(k))(w(t)(k))] ∧ [k⌊⌋j∧p king(w(e)(j))]]](t TT )(k)(j)]λ=⇒c. λiλj∃k[[i⌊⌋k ∧ ≺ (w(t TT )(k))(w(n)(k))] ∧ [λiλj∃k[[i⌊e t ′ ⌋k∧τ(w(e)(k))(w(t ′ )(k)) ∧ ·⊃ (w(t ′ )(k))(w(t TT )(k))] ∧ [k⌊⌋j∧p king(w(e)(j))]]](k)(j)]RBV=⇒d. λiλj∃k[[i⌊⌋k ∧ ≺ (w(t TT )(k))(w(n)(k))] ∧ [λiλj∃k ′ [[i⌊e t ′ ⌋k ′∧τ(w(e)(k ′ ))(w(t ′ )(k ′ )) ∧ ·⊃ (w(t ′ )(k ′ ))(w(t TT )(k ′ ))] ∧ [k ′ ⌊⌋j∧p king(w(e)(j))]]](k)(j)]λ=⇒e. λiλj∃k[[i⌊⌋k∧ ≺ (w(t TT )(k))(w(n)(k))] ∧ [λj∃k ′ [[k⌊e t ′ ⌋k ′∧τ(w(e)(k ′ ))(w(t ′ )(k ′ )) ∧ ·⊃ (w(t ′ )(k ′ ))(w(t TT )(k ′ ))] ∧ [k ′ ⌊⌋j∧p king(w(e)(j))]]](j)]λ=⇒f. λiλj∃k[[i⌊⌋k ∧ ≺ (w(t TT )(k))(w(n)(k))] ∧ ∃k ′ [[k⌊e t ′ ⌋k ′∧τ(w(e)(k))(w(t ′ )(k ′ )) ∧ ·⊃ (w(t ′ )(k ′ ))(w(t TT )(k ′ ))] ∧ [k ′ ⌊⌋j∧p king(w(e)(j))]]]g. λiλj∃k[[i⌊⌋k∧ ≺ (a TT )(a n )] ∧ ∃k ′ [[k⌊e t ′ ⌋k ′∧τ(w(e)(k ′ ))(w(t ′ )(k ′ )) ∧ ·⊃ (w(t ′ )(k ′ ))(a TT )] ∧ [k ′ ⌊⌋j∧p king(w(e)(j))]]]AX3=⇒Viewed as a computer program, (215g) brings a machine from state i to statej via k and k ′ .The resulting truth conditions are:(216) ∃j∃k[[i⌊⌋k∧ ≺ (a TT )(a n )] ∧ ∃k ′ [[k⌊e t ′ ⌋k ′ ∧ ·⊃ (w(τ(e))(k ′ ))(a TT )]∧ [k ′ ⌊⌋j ∧p king(w(e)(j))]]]Following the Unselective Binding Lemma this can be reduced to (217):(217) ≺ (a TT )(a n ) ∧ ∃b∃a 1 [τ(b)(a 1 ) ∧ ·⊃ (a 1 )(a TT ) ∧p king(b)]Or, written in a more familiar notation:(218) a TT ≺ a n ∧ ∃b∃a 1 [τ(b,a 1 ) ∧ a 1 ·⊃ a TT ∧p king(b)]which means that there is an eventuality b of Periandros being king whoseruntime a 1 includes the topic time a TT which is in the past of the moment ofspeech a n . This is exactly what I said that (105) meant.