Roberts and Simons (2024): Preconditions and Projection: Explaining Non-Anaphoric Presupposition

Roberts and Simons explain the projective content of change-of-state predicates, factives and selectional restrictions without a lexical constraint on the context. That content describes the ontological preconditions of the event type the predicate denotes, the conditions any event of the type depends on, so a sentence describing the event entails them. Projection is the listener's inference that the speaker presumes a context entailing them, as in the models of Qing, Goodman and Lassiter and of Warstadt. A negated trigger is more informative relative to a context restricted to the precondition, and a precondition, unlike a consequence of the event, can hold where the event does not, so it is the safe thing to accommodate. Projection is suppressed where the presumption cannot be attributed to the speaker, and filtering is the case in which the speaker has asserted, supposed or entertained the precondition, so that the trigger is evaluated in a context that includes it.

Main statements

• cosOccurs_subset_cosPrecondition: a change of state entails its precondition.
• mem_cosPrecondition_diff_cosOccurs, inter_compl_cosOccurs_eq_empty: a precondition is consistent with the negated trigger, and an entailment holding only where the change occurs is not.
• uniformOn_raining_compl_knows: restricting the context to the precondition makes the negative answer less probable, so more informative.
• localContext_subset: a trigger is filtered where its local context entails the precondition.

Implementation notes

Indices are world–time pairs. A change of state occurs where the meaning of the phasal verb, Aspect.Phasal.denote, is defined and true, and its precondition is the presupposition of that meaning, the prior state at an earlier index, so that its occurrence entails its precondition. The paper's two diagnostics for preconditions, the "part of what allowed for" frame and the counterfactual, sort entailments into preconditions, consequences and concomitants ontologically rather than semantically, so they are not derived here. The cells of the question about Jane are equiprobable, the paper's "roughly equal" probabilities.

TODO

• The paper's (28) is Karttunen's contrast between discover and regret (Karttunen1971b.projection_rows). Only the conditional (28c) is derived here, not the question (28b) or the projection of regret.
• The reference-time account of the contrast between know and discover in (32)–(34).

References

• C. Roberts, M. Simons, Preconditions and Projection: Explaining Non-Anaphoric Presupposition (2024)
• L. Karttunen, Some observations on factivity (1971)
• L. Karttunen, Presuppositions of Compound Sentences (1973)
• R. C. Stalnaker, Pragmatic Presuppositions (1974)
• L. Karttunen, Presupposition and Linguistic Context (1974)
• I. Heim, On the Projection Problem for Presuppositions (1983)
• C. Qing, N. D. Goodman, D. Lassiter, A Rational Speech-Act Model of Projective Content (2016)
• A. Warstadt, Presupposition Triggering Reflects Pragmatic Reasoning about Utterance Utility (2022)

Ontological preconditions (§2)

def RobertsSimons2024.cosOccurs {ι : Type u_1} (t : Aspect.Phasal) (R : SetRel ι ι) (P : ι → Prop) : Set ι

A change of state occurs at an index when the prior state held at an earlier index and the result state holds at the index, which is where the phasal verb is defined and true.

Equations

• RobertsSimons2024.cosOccurs t R P = Trivalent.posExt (t.denote R P)

def RobertsSimons2024.cosPrecondition {ι : Type u_1} (t : Aspect.Phasal) (R : SetRel ι ι) (P : ι → Prop) : Set ι

The ontological precondition of a change of state is its prior state at an earlier index, as being on the ladder is for falling off it (5). It is what the phasal verb presupposes.

Equations

• RobertsSimons2024.cosPrecondition t R P = Function.support (t.denote R P)

theorem RobertsSimons2024.cosOccurs_subset_cosPrecondition {ι : Type u_1} {t : Aspect.Phasal} {R : SetRel ι ι} {P : ι → Prop} : cosOccurs t R P ⊆ cosPrecondition t R P

A sentence describing a change of state entails its precondition (§2.1).

Why preconditions project (§3.1)

theorem RobertsSimons2024.mem_cosPrecondition_diff_cosOccurs {ι : Type u_1} {t : Aspect.Phasal} {R : SetRel ι ι} {P : ι → Prop} {i i' : ι} (hr : (i, i') ∈ R) (hp : t.Prior (P i')) (hn : ¬t.Result (P i)) : i ∈ cosPrecondition t R P \ cosOccurs t R P

The precondition of a change of state can hold without the change, as when John smoked and still smokes, so accommodating it is consistent with John didn't stop smoking (§3.1).

theorem RobertsSimons2024.inter_compl_cosOccurs_eq_empty {ι : Type u_1} {t : Aspect.Phasal} {R : SetRel ι ι} {P : ι → Prop} {F : Set ι} (hF : F ⊆ cosOccurs t R P) : F ∩ (cosOccurs t R P)ᶜ = ∅

An entailment that holds only where the change occurs, as a consequence or concomitant of it does, is inconsistent with the negated trigger, which makes the precondition the safer thing to accommodate (§3.1).

theorem RobertsSimons2024.stop_mem_cosPrecondition_diff_cosOccurs {ι : Type u_1} {R : SetRel ι ι} {P : ι → Prop} {i i' : ι} (hr : (i, i') ∈ R) (h' : P i') (h : P i) : ∃ (t : Aspect.Phasal), English.Verbs.stop.phasal = some t ∧ i ∈ cosPrecondition t R P \ cosOccurs t R P

In John didn't stop smoking (§3.1), with stop the English Fragment's entry, John having smoked is consistent with the negated trigger, since he may still smoke.

inductive RobertsSimons2024.Cell : Type

The cells of the question "Does Jane know that it's raining?" in the §3.1 diagram are raining and Jane knows it, raining and she doesn't, and not raining.

• rainKnown : Cell
• rainUnknown : Cell
• noRain : Cell

@[instance_reducible]

instance RobertsSimons2024.instDecidableEqCell : DecidableEq Cell

Equations

• RobertsSimons2024.instDecidableEqCell x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance RobertsSimons2024.instFintypeCell : Fintype Cell

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance RobertsSimons2024.instMeasurableSpaceCell : MeasurableSpace Cell

Equations

• RobertsSimons2024.instMeasurableSpaceCell = ⊤

instance RobertsSimons2024.instDiscreteMeasurableSpaceCell : DiscreteMeasurableSpace Cell

def RobertsSimons2024.raining : Set Cell

R, that it's raining.

Equations

• RobertsSimons2024.raining = {RobertsSimons2024.Cell.rainKnown, RobertsSimons2024.Cell.rainUnknown}

def RobertsSimons2024.knows : Set Cell

K(j,r), that Jane knows that it's raining.

Equations

• RobertsSimons2024.knows = {RobertsSimons2024.Cell.rainKnown}

theorem RobertsSimons2024.uniformOn_raining_compl_knows : (ProbabilityTheory.uniformOn raining).real knowsᶜ < (ProbabilityTheory.uniformOn Set.univ).real knowsᶜ ∧ (ProbabilityTheory.uniformOn raining).real knowsᶜ = (ProbabilityTheory.uniformOn raining).real knows

Relative to a context restricted to raining, the negative answer Jane doesn't know that it's raining is less probable than relative to one that leaves the rain open, so asserting it is more informative, and the two answers become equiprobable (§3.1).

theorem RobertsSimons2024.uniformOn_knows_lt_one : (ProbabilityTheory.uniformOn Set.univ).real knows < 1 ∧ (ProbabilityTheory.uniformOn raining).real knows < 1

The affirmative Jane knows that it's raining is informative relative to either context (§3.1).

Suppression (§3.2)

On the projective reading the speaker presumes a context C entailing the precondition pre of the event they raise, C ⊆ pre (§3.1); suppression is the case in which that presumption cannot be attributed to them.

theorem RobertsSimons2024.not_presumes_of_doubt {ι : Type u_1} {C S pre : Set ι} (hS : S ⊆ C) (h : ¬S ⊆ pre) : ¬C ⊆ pre

In cases 1 and 2 of §3.2.1 projection is suppressed where someone who must accept the presumed context does not take the precondition to hold, the hearer in (23), whom the speaker knows to reject it, or the doubting speaker in (24). In (23) the context itself is agnostic, so the suppression does not come from a contradiction in the context.

theorem RobertsSimons2024.resolves_of_presumes {ι : Type u_1} {C pre : Set ι} {Q : Question ι} (h : pre ∈ Q.alt) (hp : C ⊆ pre) : C ∈ Q

In case 3 of §3.2.1 projection is suppressed where the precondition is at issue, since presuming a precondition that is an alternative of the question under discussion resolves it, which the speaker in (25) signals she cannot do.

theorem RobertsSimons2024.not_subset_of_presumes_ignorance {ι : Type u_1} {Dox : ι → Set ι} {C P : Set ι} {w : ι} (hw : w ∈ C) (hbel : Dox w ⊆ C) (hign : C ⊆ {v : ι | ¬Dox v ⊆ P}) : ¬C ⊆ P

In (28c), If I discover later that I have not told the truth, discover has the agent's prior ignorance among its preconditions, and a speaker who presumes that she is ignorant whether P, where Dox gives her beliefs, cannot also presume P, since she believes what she presumes ([Sta74]'s explanation, sharpened by the ignorance precondition (29)).

Filtering (§4)

The filtering constructions (41), (42), (43) place the trigger in the second conjunct, in the consequent, or in a disjunct. The paper shares with the satisfaction theory the assumption that the trigger is evaluated in the context updated with the other clause, the local context of [Kar74a]'s table (Presupposition.Connective.localContext), but not the requirement that the local context entail the precondition.

theorem RobertsSimons2024.localContext_subset {ι : Type u_1} {C A pre : Set ι} : (A ⊆ pre → Presupposition.Connective.localContext C A Presupposition.Connective.conj ⊆ pre ∧ Presupposition.Connective.localContext C A Presupposition.Connective.cond ⊆ pre) ∧ (Aᶜ ⊆ pre → Presupposition.Connective.localContext C A Presupposition.Connective.disj ⊆ pre)

Filtering arises where the first clause asserts or supposes the precondition, or the other disjunct is its negation. The trigger is then evaluated in a context entailing the precondition, so no global presumption is attributable to the speaker; in disjunction the condition concerns the other disjunct whichever comes first (§4).

theorem RobertsSimons2024.disjunctive_antecedent_filters {ι : Type u_1} {C pre : Set ι} (hopen : ¬C ⊆ pre) : Presupposition.Connective.localContext C preᶜ Presupposition.Connective.disj ⊆ pre ∧ ¬Presupposition.Connective.localContext C Set.univ Presupposition.Connective.cond ⊆ pre

The contrast in (44) is that, in a context that leaves the precondition open, a disjunctive antecedent whose other disjunct negates the precondition filters it, whereas a simple antecedent leaves the precondition to be presumed globally, which the open context forbids.