Decision-Theoretic Semantics: "Even" ([Mer99a] §5) #

Merin's DTS account of the scalar particle "even". The felicity of "A CONJ even(B)" requires B to be more relevant than A, resolving the dispute between Anscombre (argumentative value), [Kay90] (contextual entailment), and [Fra95] (surprise) under a single relevance ordering.

Key Definitions #

evenFelicitous (Hypothesis 5): felicity conditions for "A CONJ even(B)"

Main Results #

Prediction 3 (but_even_incompatible): "but" and "even" are incompatible — "A but even(B)" is always infelicitous.

Note on the Dispute #

Merin shows that relevance subsumes all three prior analyses:

Anscombre's "argumentative value" = Bayes factor ordering
Kay's "contextual entailment" ≈ BF(B) > BF(A) in strong form
Francescotti's "surprise" ≈ low prior probability ≈ high BF

The DTS account derives all three as special cases of "B is more relevant than A to the current issue."

Felicity conditions for "even" #

source

def DTS.Even.evenFelicitous {W : Type u_1} [MeasurableSpace W] (ctx : Context W) (a b : Set W) :

Prop

Hypothesis 5: Felicity conditions for "A CONJ even(B)" with VP-focus.

"A and even B" is felicitous iff: (i) A is positively relevant to some issue H, (ii) B is positively relevant to H, (iii) B is more relevant than A (BF(B) > BF(A)), (iv) H ≠ B (the issue is not B itself — that would collapse to "also").

The key innovation: "even" marks B as the more informative conjunct, not merely "surprising" or "unexpected."

Equations

DTS.Even.evenFelicitous ctx a b = (DTS.posRelevant ctx a ∧ DTS.posRelevant ctx b ∧ DTS.bayesFactor ctx a < DTS.bayesFactor ctx b ∧ ctx.topic ≠ b)

Instances For

Predictions #

source

theorem DTS.Even.but_even_incompatible {W : Type u_1} [MeasurableSpace W] (ctx : Context W) (a b : Set W) :

But.butFelicitous ctx a b → ¬evenFelicitous ctx a b

Prediction 3: "But" and "even" are incompatible.

"A but even(B)" is never felicitous: butFelicitous requires B to be negatively relevant (BF < 1), while evenFelicitous requires B to be positively relevant (BF > 1). These are contradictory.