[Ogi89]: Temporal Reference in English and Japanese

[Ogi89] §2.3 reconciles [Pri67]'s operator analysis of tense with [Par73]'s referential analysis: tense is a variable that picks a time and must satisfy a temporal presupposition (the picked time is past/present/future). The referential analysis picks the time; the operator imposes the constraint. They are complementary layers, not competitors (referential_past_decomposition).

theorem Ogihara1989.referential_past_decomposition {W : Type u_1} {Time : Type u_2} [LinearOrder Time] (P : Intensional.Index W Time → Prop) (g : Tense.TemporalAssignment Time) (n : ℕ) (w : W) (speechTime : Time) : Tense.PAST P { world := w, time := Tense.interpTense n g } { world := w, time := speechTime } ↔ g n < speechTime ∧ P { world := w, time := g n }

The Priorean PAST operator, applied at a referentially determined time g(n), decomposes into the conjunction of (1) the referential time precedes the speech situation and (2) the predicate holds at the referential time: the referential analysis picks the time, the operator imposes the constraint.