Argument-building "too" from COCA (ex. 1a/14a). ANT = Ernie took Iree in on her own; π = it was a good thing she did. Both jointly support the conclusion that Ernie helped Iree a great deal.
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Argument-building "too" from COCA (ex. 1b/14b). ANT = I know a couple people who have gotten tickets; π = the fine is a hefty one. Both jointly support the conclusion: you should worry about traffic enforcement.
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Argument-building "too" from COCA (ex. 1c/14c/65). ANT = A room just opened up at this hotel; π = It looks kind of fancy. Both jointly support the conclusion: this hotel would be a good place to stay. Primary worked example in §5.3.
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All argument-building examples from @cite{thomas-2026}.
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Standard focus-alternative "too" (ex. 5a/10/21). ANT = "I like pizza", π = "I like spaghetti". Both are partial answers to "What do you like?"
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Standard additive presupposition example (ex. 2). Q: Who did Avery invite? ANT = Avery invited Bailey. π = She invited Cameron.
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Standard focus-alternative examples.
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Infelicitous: π entails the resolution — violates non-triviality (ex. 11/29a/73). ANT = "Sam is happy", π = "He's ecstatic". Since "ecstatic" entails "happy", ⟦π⟧ ⊆ RQ|_{ANT∩⟦π⟧} = |Sam is ecstatic|, violating Def. 64c.i.
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Infelicitous: reversed argumentative orientation — no suitable RQ (ex. 15a/19a). In the context of (14a) where Ernie's actions are evaluated positively, replacing "good thing" with "bad thing" reverses the argumentative direction. No RQ satisfies both the Antecedent and Conjunction Conditions.
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Infelicitous: conjunction provides no additional evidence — fails Conjunction Condition (ex. 72B). ANT = "She invited Bailey and Cameron", π = "Dogs are mammals". π provides no information about who Avery invited.
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Infelicitous: weaker alternative works just as well — violates maximality (ex. 30/74). ANT = "Avery plays an instrument", π = "Bailey plays the cello". "Bailey plays an instrument" (weaker than π) gives the same evidential boost to the resolution.
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Infelicitous: cross-product question — no single RQ satisfies both conditions (ex. 13/40/75). Q: Who ate what? ANT = "Avery ate pizza", π = "Bailey ate spaghetti". Every resolution to "Who ate what?" specifies what BOTH Avery and Bailey ate, so ANT alone provides no information about Bailey's food.
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Infelicitous: reversed argumentative orientation in hotel context (ex. 66). ANT = "A room just opened up at this hotel", π = "It looks kind of dingy". The discourse goal is finding a GOOD hotel, but "dingy" argues AGAINST the hotel being good. No RQ relevant to the discourse goals has its felicity conditions satisfied.
Contrast with hotelRoom (ex. 65): same ANT but π = "fancy" supports
the "good hotel" conclusion. @cite{thomas-2026} notes that replacing
"fancy" with "dingy" makes "too" unacceptable because ANT ∩ ⟦π⟧ does
not raise the probability of any resolution desirable to the interlocutors.
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Infelicitous examples from @cite{thomas-2026}.
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All examples.
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End-to-End Verification #
Concrete Fin 4 instantiations of the felicity conditions (Def. 64) from
@cite{thomas-2026}. Five verified scenarios cover the three use types and
all four felicity conditions:
- Hotel room (felicitous, argument-building): all four conditions pass
- Pizza/spaghetti (felicitous, standard): mention-all partition question
- Happy/ecstatic (infelicitous): Def. 64c.i non-triviality failure
- Instrument/cello (infelicitous): Def. 64c.ii maximality failure
- Cross-product (infelicitous): Def. 64b Conjunction Condition failure
4-world model for the hotel room scenario (@cite{thomas-2026}, ex. 65).
| World | Room Available | Fancy | Good Hotel |
|---|---|---|---|
| w₀ | ✓ | ✓ | ✓ |
| w₁ | ✓ | ||
| w₂ | ✓ | ||
| w₃ |
Prior: w₀ = 3/8, w₁ = 1/8, w₂ = 2/8, w₃ = 2/8 (room availability more likely).
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- Phenomena.Focus.AdditiveParticles.Studies.Thomas2026.roomAvail w = (↑w == 0 || ↑w == 1)
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- Phenomena.Focus.AdditiveParticles.Studies.Thomas2026.fancyH w = (↑w == 0 || ↑w == 2)
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Non-uniform prior: room availability (w₀, w₁) more likely.
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Hotel room "too" is felicitous: all four conditions of Def. 64 hold.
- Antecedent Condition: P(good | room) = 3/4 ≠ P(good) = 3/8
- Conjunction Condition: P(good | room ∧ fancy) = 1 > P(good | room) = 3/4
- Non-triviality: fancy includes w₂ which is not a good hotel
- Maximality: every ANT ∧ good world is also a fancy world
4-world model for the happy/ecstatic scenario.
| World | Ecstatic | Happy (not ecstatic) | Not Happy |
|---|---|---|---|
| w₀ | ✓ | ||
| w₁ | ✓ | ||
| w₂ | ✓ | ||
| w₃ | ✓ |
Prior: uniform 1/4.
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- Phenomena.Focus.AdditiveParticles.Studies.Thomas2026.happyE w = (↑w == 0 || ↑w == 1)
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"What is Sam's emotional state?" — three-way partition.
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"Sam is happy. #He's ecstatic, too." is infelicitous. Def. 64c.i (non-triviality) fails: the strengthened resolution is {w₀} = "ecstatic", and ⟦π⟧ = "ecstatic" = {w₀} entails it, making the conjunction informationally redundant with respect to RQ.
4-world model for the standard focus-alternative scenario.
| World | Like Pizza | Like Spaghetti | Partition Cell |
|---|---|---|---|
| w₀ | ✓ | ✓ | both |
| w₁ | ✓ | pizza only | |
| w₂ | ✓ | spaghetti only | |
| w₃ | neither |
Prior: uniform 1/4. ANT = "I like pizza", π = "I like spaghetti". RQ = "What do you like?" as a mention-all question with 4-cell partition.
The strengthened resolution under ANT ∧ π is "both" = {w₀}, which π (= {w₀,w₂}) does NOT entail. This is why standard use passes non-triviality: the partition cell "both" is strictly stronger than π.
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- Phenomena.Focus.AdditiveParticles.Studies.Thomas2026.likePizza w = (↑w == 0 || ↑w == 1)
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"What do you like?" — mention-all partition.
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Standard "too" is felicitous: "I like pizza. I like spaghetti, too."
- Antecedent Condition: P("both" | pizza) = 1/2 > P("both") = 1/4
- Conjunction Condition: P("both" | pizza ∧ spaghetti) = 1 > P("both" | pizza) = 1/2
- Non-triviality: spaghetti = {w₀,w₂} ⊄ "both" = {w₀}
- Maximality: every pizza ∧ "both" world (= {w₀}) has spaghetti true
4-world model for the maximality failure scenario.
| World | Avery Plays | Bailey Plays Cello | Bailey Plays (any) |
|---|---|---|---|
| w₀ | ✓ | ✓ | ✓ |
| w₁ | ✓ | ✓ (non-cello) | |
| w₂ | ✓ | ||
| w₃ |
Prior: uniform 1/4. ANT = "Avery plays an instrument". π = "Bailey plays the cello". RQ = "Who plays an instrument?" (polar: does Bailey play?).
Maximality fails: "Bailey plays an instrument" (S ⊃ π) gives the same evidential boost as "Bailey plays the cello" (π), since both make P(Bailey plays | ANT ∧ ·) = 1. The specific instrument is irrelevant to RQ.
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- Phenomena.Focus.AdditiveParticles.Studies.Thomas2026.baileyPlays w = (↑w == 0 || ↑w == 1)
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"Avery plays an instrument. #Bailey plays the cello, too." is infelicitous. Def. 64c.ii (maximality) fails: w₁ is an ANT ∧ baileyPlays world but not a baileyPlaysCello world, so a weaker proposition (baileyPlays) gives the same evidential boost to RQ.
4-world model for the cross-product question scenario.
| World | Avery Eats | Bailey Eats |
|---|---|---|
| w₀ | pizza | pizza |
| w₁ | pizza | spaghetti |
| w₂ | spaghetti | pizza |
| w₃ | spaghetti | spaghetti |
Prior: uniform 1/4. ANT = "Avery ate pizza", π = "Bailey ate spaghetti".
@cite{thomas-2026} §5.5.1 (pp. 40-41) argues that for "Who ate what?", no single RQ simultaneously satisfies both the Antecedent and Conjunction Conditions. We verify this for RQ = "What did Avery eat?" ((76a)): ANT already determines the resolution (P(Avery pizza | ANT) = 1), so learning π = "Bailey ate spaghetti" adds nothing about Avery — the Conjunction Condition fails because no alternative is strengthened.
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- Phenomena.Focus.AdditiveParticles.Studies.Thomas2026.averyPizzaCP w = (↑w == 0 || ↑w == 1)
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RQ = "What did Avery eat?" (polar: did Avery eat pizza?).
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"Avery ate pizza. #Bailey ate spaghetti, too." is infelicitous when RQ = "What did Avery eat?" Conjunction Condition fails: P(Avery pizza | ANT∩π) = 1 = P(Avery pizza | ANT), so π provides no additional evidence about what Avery ate.