@cite{potts-levy-2015}: Negotiating Lexical Uncertainty and Speaker Expertise with Disjunction #

@cite{potts-levy-2015}

"Negotiating Lexical Uncertainty and Speaker Expertise with Disjunction." Proceedings of the 41st Annual Meeting of the Berkeley Linguistics Society, 417–445.

The Puzzle #

Hurford-violating disjunctions like "X or A" (where A ⊆ X semantically) are predicted to be redundant, yet they are felicitous and carry ignorance implicatures: the listener infers that the speaker is uncertain which disjunct holds.

@cite{potts-levy-2015} show that an RSA model with lexical uncertainty derives this: L1 infers that the speaker might be using a lexicon under which the disjuncts are non-overlapping, and the disjunction signals the speaker's uncertainty about the world.

The Model #

Three worlds:

w₁: only A-worlds (speaker knows A)
w₂: only B-worlds (speaker knows B, where B ⊆ X \ A)
w₁₂: both A- and B-worlds possible (speaker uncertain)

Three lexica for X:

base: X = A ∪ B (unrefined, overlapping with A)
excl: X = B only (exhaustified, disjoint from A)
syn: X = A (synonymous with A)

Five utterances: A, B, X, AorX, null.

Key insight: under syn, "A or X" and "A" are equivalent (Hurford violation). Under excl, "A or X" partitions {w₁, w₂} cleanly. L1 marginalizes over lexica, and excl dominates for "A or X" — deriving the prediction that disjunction implies speaker uncertainty (w₁₂ > w₁ > w₂).

Join Closure #

The join state w₁₂ represents speaker uncertainty. Following the paper's convention, an utterance m is true at w₁₂ iff m is true at BOTH w₁ and w₂ (the "must" reading: the speaker can assert m only if m holds across all worlds compatible with their knowledge).

Expertise Model (S2) #

The paper's key contribution is the expertise parameter β: a level-2 speaker who cares not only about informativity (L1 inferring the correct world) but also about lexicon signaling (L1 inferring the correct lexicon). The S2 utility:

U_S2(m, w, L; β) = ln L₁(w|m) + β · ln L₁(L|m)

When β > 0, the speaker has extra incentive to use utterances that signal the excl lexicon — precisely the Hurford-violating disjunction "A or X". Following the @cite{yoon-etal-2020} pattern, we define S2 utility directly from L1 marginals and prove comparative predictions.

Verification Against Paper #

Our model operates in the Hurfordian parameter regime (α > β) with α = 2, β = 0, C = 0. The paper's Hurfordian worked example (Figure 10) uses α = 2, β = 1, C(or) = 1. All 10 qualitative predictions match the paper:

L1 world inference (§6): w₁₂ > w₁ > w₂ given "A or X" (paper Figure 10 L2: .91 > .09 > 0)
L1 lexicon inference (§7): excl > base > syn given "A or X" (paper Figure 10 L2: .49 > .34 > .17)
S1 speaker (§8): prefers AorX at w₁₂, prefers A at w₁ (under excl) (paper Figure 7(b), p. 436)
S2 endorsement (§10): prefers AorX at w₁₂, A at w₁ (paper p. 436: "S₂'s preferred message given observed state w₁∨w₂ and lexicon L₁ is A or X")
Lexicon signaling (§10): AorX signals excl more than A (paper Section 5.2)

Two Implementations #

RSAConfig (§4–§10): L₁-level predictions via rsa_predict, zero costs, structural correspondence with linglib's RSA infrastructure.
Full ℚ model (§12): L₂-level predictions via native_decide, with the paper's Hurfordian parameters (α = 2, β = 1, C(or) ≈ 1).

The paper's definitional reading (where syn dominates, e.g., "wine lover or oenophile") requires β > α (paper Section 5.4, Figures 13–14) and is not modeled here.

Connection to @cite{potts-etal-2016} #

Both papers use lexical uncertainty (Latent := Lexicon). @cite{potts-etal-2016} applies it to embedded scalar implicatures; this paper applies it to Hurford-violating disjunctions and speaker expertise. The mechanism is identical — only the domain and lexica differ.