Documentation

Linglib.Semantics.Events.CEM

Event mereology #

The event domain as a classical extensional mereology ([Hov09]). Events carry a parthood partial order (Event.Mereology); when that order is a Mereology.ClassicalMereology — closed under unrestricted type-2 fusion with weak supplementation — the binary event sum is the unique fusion of a pair (instSemilatticeSupEvent, sup_isLUB) rather than a stipulated operation.

Implementation notes #

There is deliberately no single bundled event-mereology class. An event theory's two assumptions — that events form a classical mereology, and (separately) that a trace function such as the temporal trace Event.runtime is a Mereology.IsSumHom — are logically independent, so callers state the standard mixins directly: [ClassicalMereology (Event Time)] and, where τ-pullback is needed, [IsSumHom (fun e => e.runtime)] ([Cha17] §2.5; [Bac86] for the underlying event algebra).

Lexical cumulativity of a verb predicate is just Mereology.CUM over Event Time[Cha17] takes it as a working hypothesis, universal over verbal predicates (telic ones included) — so it is used directly with no event-specific re-spelling.

Main definitions #

Generic mereological vocabulary (CUM, QUA, IsSumHom, Overlap, IsFusion, ClassicalMereology, …) lives in Mereology; consumers open Mereology.

@[implicit_reducible]
noncomputable instance Semantics.Events.CEM.instSemilatticeSupEvent (Time : Type u_1) [LinearOrder Time] [Event.Mereology Time] [Mereology.ClassicalMereology (Event Time)] :
SemilatticeSup (Event Time)

The binary sum on events, derived from the classical-mereology fusion axioms: e₁ ⊔ e₂ is the unique type-2 fusion of {e₁, e₂}. Noncomputable because the fusion is extracted by choice from Fusion2E.

Equations
theorem Semantics.Events.CEM.sup_isLUB {Time : Type u_1} [LinearOrder Time] [Event.Mereology Time] [Mereology.ClassicalMereology (Event Time)] (e₁ e₂ : Event Time) :
IsLUB {e₁, e₂} (e₁e₂)

The event sum e₁ ⊔ e₂ is the least upper bound of {e₁, e₂} under parthood — i.e. the mereological fusion, not a stipulated operation.