Decision-Theoretic Semantics: "Even" (@cite{merin-1999} §5)

@cite{francescotti-1995} @cite{kay-1990} @cite{merin-1999}

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), Kay (contextual entailment), and Francescotti (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."

def DTS.Even.evenFelicitous {W : Type u_1} [Fintype W] (ctx : DTSContext W) (a b : Set W) [DecidablePred fun (x : W) => x ∈ a] [DecidablePred fun (x : W) => x ∈ b] : 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 b > DTS.bayesFactor ctx a ∧ ctx.topic ≠ b)

theorem DTS.Even.but_even_incompatible {W : Type u_1} [Fintype W] (ctx : DTSContext W) (a b : Set W) [DecidablePred fun (x : W) => x ∈ a] [DecidablePred fun (x : W) => x ∈ b] : 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.

def DTS.Even.dtsLikelihood {W : Type} [Fintype W] (ctx : DTSContext W) : Semantics.FocusParticles.LikelihoodOrder W

DTS Bayes factor ordering as a likelihood ordering for focus particles.

Higher BF = more informative about the issue = less likely a priori = more surprising. This connects Merin's relevance ordering to the traditional EVEN presupposition framework in Semantics.FocusParticles.

@cite{merin-1999} subsumes @cite{francescotti-1995}'s "surprise" and @cite{kay-1990}'s "informativeness" as special cases of signed relevance.

Note: LikelihoodOrder operates on World → Bool functions (the upstream Focus.Particles interface). We embed each Bool predicate into a Prop predicate via · = true to apply bayesFactor.

Equations

• DTS.Even.dtsLikelihood ctx a b = (DTS.bayesFactor ctx {w : W | a w = true} > DTS.bayesFactor ctx {w : W | b w = true})