Evcen, Bale and Barner (2026): Conditional Inference and Access to Alternatives #

This file formalizes [EBB26]'s account of conditional perfection as a quantity implicature over the alternatives a context makes available, and the three experiments that test it. A conditional if p then q is perfected to only if p when the conditionals with the alternative antecedents are excluded ([GZ71], [vF01]); under [Sta68]'s semantics the negation of if r then q is if r then not q. The alternatives are the answers to the Question Under Discussion ([Rob96]) that the speaker is competent about, so that the exhaustification operator negates only the non-weaker alternatives in ALT(p) ⊆ ANS(QUD) ∩ {q : K(q) ∨ K(¬q)}, and from the speaker's not having asserted an alternative she knows the truth of, the hearer infers its falsity (§1). In the paradigm Mary tests buttons that each play an animal sound only she hears and answers a question with If you press the blue button, it will play a dog barking; the participant is asked whether the orange button plays that sound, No being the perfected reading. Experiment 1 varies the question: an antecedent-focused one, which button plays the dog sound, makes the other buttons' conditionals the alternatives and yields perfection, a consequent-focused one, what the blue button plays, makes the other sounds the alternatives and yields none, and a neutral one, what happens with the buttons, makes every button–sound pair an alternative, whose exclusion would say that Mary heard nothing from the other buttons, against the context, so strengthening is blocked; the perfection rates were 0.65, 0.22 and 0.29 (N = 98). Experiment 2 finds that an overly informative answer, naming one square where the question asked which shape, is perfected within its shape like an optimally informative one (0.84 against 0.92, N = 55), so that such answers count as relevant or the question is accommodated to their grain. Experiment 3 finds perfection only when Mary has tested all three buttons (0.72 against 0.21, N = 72): untested, the orange button's conditional is not among the alternatives and cannot be excluded, the competence gate that governs scalar implicature ([BNRB25], [BG12]). [Hor00]'s alternative, the unconditional q no matter what, is too weak: its negation leaves open which other button fails, while participants answered No about a specific button.

Implementation notes #

A world assigns each button a sound; every button plays one, the context Mary's listening establishes. With buttons deterministic, the Stalnaker conditional if you press b, it plays s holds at a world exactly when b plays s there, so perfection about a button is the negation of its conditional.
The operator is the paper's Exh of its seventh footnote, the prejacent with every non-weaker alternative negated, and strengthening is blocked when the result is contextually inconsistent (§2.3); on the licensed case it coincides with [vF01]'s exhaustive answer by innocent exclusion, exh_eq_exhaustifiedAnswer.
Mary knows what a button plays exactly when she tested it.
Experiment 2's shapes are modelled separately, a world recording which of the four buttons play the dog sound, with a cell-level answer read as the dog button being among the shape's, which the paper treats as weaker than the specific answer.
The rows carry each condition's modal response; the rates stay in the prose above.

Evcen, Bale and Barner (2026): Conditional Inference and Access to Alternatives #

Implementation notes #

References #

Alternatives #

Experiments 1 and 3 #

Von Fintel's exhaustive answer #

Horn's unconditional alternative #

Experiment 2: optimally and overly informative answers #