Haslinger (2025): Pragmatic constraints on imprecision and homogeneity #
Haslinger argues that the availability of imprecise construals is regulated not in the lexicon but by alternatives, through two constraints. No Needless Manner Violations combines two Manner preferences, for lower structural complexity and for less potential for imprecision, as Pareto dominance, and blocks a sentence that a potentially p-equivalent alternative dominates. Inference Preservation blocks an imprecise construal of a subexpression that loses an inference, entailment or incompatibility, that its precise construal licenses about an alternative.
Main results #
lt_complexity_of_lt_potential: an unblocked expression more imprecise than a competitor is strictly simpler, the form–meaning correlation behind the doors and all the doors.forall_not_violates_iff: a bare numeral survives Inference Preservation exactly when its deviation is under half the lcm of the widths of the scales it lies on, so 99 must be exact while 100 tolerates deviations under twenty-five (ninetyNine_hundred); that lcm is the width of the scale Krifka's hearer infers (tolerated_deviation_is_inferred_cell).roundness_depends_on_scales: 180 is rounder than 200 among angles and 200 than 180 among cardinals, (80b,c).conjunction_violates: a conjunction read non-maximally loses the entailment of its conjuncts.
Implementation notes #
The Manner orderings are read off two natural-number measures on an abstract sentence type, with
potential p-equivalence a relation parameter, since the dissertation's (68) quantifies over
contexts that differ only in the issue parameter. Degree expressions are construals over ℚ, the
precise interpretation the exact value and the imprecise one the halo of a contextual deviation
m, (69)–(70). The conventionalized scales of §6.2.1 are sets of expressions; here a scale is the
multiples of its width over the numerals' values, given by the widths salient in a context, so
roundness, (22), is Numerals.Roundness.AtLeastAsRound over Numerals.Roundness.OnScale.
The dissertation's examples are the rows of Data/Examples/Haslinger2025.json; its
Ch. 5 extensions to presupposition and redundancy and the collective exceptions of Ch. 7 are not
modelled.
References #
No Needless Manner Violations #
The Manner profile of a sentence pairs its structural complexity with its potential for imprecision, the two orderings of (58), combined by the product order as in (57).
Equations
- Haslinger2025.manner complexity potential φ = (complexity φ, potential φ)
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A cooperative speaker will not use ψ when a potentially p-equivalent φ is at least as good
on both orderings and better on one, (59): competition among the potentially p-equivalent
sentences along the Manner profile.
Equations
- Haslinger2025.Blocked complexity potential PotEquiv ψ = Competition.Blocked (fun (ψ : S) => {φ : S | PotEquiv φ ψ}) (Haslinger2025.manner complexity potential) ψ
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By the form–meaning correlation, an unblocked sentence with more potential for imprecision than a potentially p-equivalent competitor is strictly simpler than it.
Equations
- Haslinger2025.instDecidableEqPlural x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- Haslinger2025.instReprPlural = { reprPrec := Haslinger2025.instReprPlural.repr }
Equations
- One or more equations did not get rendered due to their size.
- Haslinger2025.instReprPlural.repr Haslinger2025.Plural.the prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Haslinger2025.Plural.the")).group prec✝
- Haslinger2025.instReprPlural.repr Haslinger2025.Plural.all prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Haslinger2025.Plural.all")).group prec✝
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In structural complexity all the doors contains the doors, and the hypothetical (8a) contains all doors.
Equations
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The definites have potential for imprecision and the universal quantifier does not.
Equations
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The doors and all the doors are incomparable, each better on one ordering, so neither blocks the other, (60).
A definite built on the quantifier is dominated by the quantifier, so it is blocked wherever the two are potentially p-equivalent, (8).
Inference Preservation #
[X]^p is the truth set of a predicate for p = true and its falsity set for p = false.
Equations
- Haslinger2025.valued P true = P
- Haslinger2025.valued P false = fun (d : D) => ¬P d
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Equations
- One or more equations did not get rendered due to their size.
Inference Preservation (18), for one alternative ψ of the subexpression φ, blocks the use
when, for some truth value, the precise truth of φ entails that status of ψ, the precise falsity
of φ does not, but the imprecise truth of φ fails to entail the imprecise status of ψ.
Equations
- One or more equations did not get rendered due to their size.
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Degree expressions (Ch. 6) #
A bare numeral is read with deviation at most m, (69a) and (70a).
Equations
- Haslinger2025.numeral n m = { precise := fun (d : ℚ) => d = ↑n, imprecise := fun (d : ℚ) => |d - ↑n| ≤ m }
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More than n is read with deviation at most m, (69b) and (70b).
Equations
- Haslinger2025.moreThan n m = { precise := fun (d : ℚ) => ↑n < d, imprecise := fun (d : ℚ) => ↑n - m < d }
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Two distinct bare numerals whose halos meet violate Inference Preservation, being incompatible precisely and compatible imprecisely.
Distinct bare numerals whose halos are apart preserve every inference.
Roundness and alternatives (§6.2) #
The cardinal scales of (15) have widths fifty, twenty-five, ten, five and one.
Equations
- Haslinger2025.decimal = {50, 25, 10, 5, 1}
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The clock-time scales of (16), over minutes after midnight, count quarter hours, five minutes and minutes.
Equations
- Haslinger2025.clock = {15, 5, 1}
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The angle scales of (17) have widths ninety, ten, five and one degrees.
Equations
- Haslinger2025.angle = {90, 10, 5, 1}
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10:45 is rounder than 10:46 on the clock-time scales, and 150 than 152 on the cardinal ones, (24).
Which of 180 and 200 is rounder depends on the salient scales, 180 among angles and 200 among cardinals, (80b,c).
Roundness is not total, as 25 and 10 lie on different cardinal scales.
A bare numeral read with deviation m survives Inference Preservation against every
alternative at least as round, (79a), exactly when m is under half the lcm of the widths of its
scales.
99 lies only on the scale of units, so its imprecise reading is blocked from half a unit of deviation; 100 lies on every cardinal scale, so its alternatives are the multiples of fifty and it survives deviations under twenty-five.
Under Krifka's hearer model on aligned salient scales, the deviation a bare numeral tolerates under Inference Preservation is half the width of the most probable scale for its report: the dissertation's alternative-based bound is the cell of the scale the hearer infers.
more than n is blocked by its alternative bare n at any positive deviation, (69)–(70), since the imprecise comparative overlaps the exact value it is precisely incompatible with.
Conjunctions (Ch. 7) #
Bert, Claire and Dora were there, (19)–(20), is precisely maximal and imprecisely non-maximal over the worlds recording who was there.
Equations
- Haslinger2025.conjunction = { precise := fun (w : Fin 3 → Bool) => ∀ (i : Fin 3), w i = true, imprecise := fun (w : Fin 3 → Bool) => ∃ (i : Fin 3), w i = true }
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A conjunct alternative, Bert was there, with no potential for imprecision.
Equations
- Haslinger2025.conjunct i = { precise := fun (w : Fin 3 → Bool) => w i = true, imprecise := fun (w : Fin 3 → Bool) => w i = true }
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The non-maximal construal of the conjunction loses the entailment of each conjunct that the precise construal licenses, so only the maximal construal survives Inference Preservation.