@cite{lo-guercio-2025} — Anti-Conventional Implicatures

Lo Guercio, N. (2025). Maximize Conventional Implicatures! Semantics & Pragmatics, 18(9). https://doi.org/10.3765/sp.18.9

Thesis

Scalar inferences can arise from comparing CI content, not just at-issue or presuppositional content. These are Anti-Conventional Implicatures (ACIs). Evidence comes from epithets, honorifics (don/doña), nominal appositives, supplementary adverbs, and emotive markers.

The mechanism parallels:

• Scalar Implicatures: compare at-issue content (Conversational Principle)
• Antipresuppositions: compare presuppositional content (Maximize Presupposition)
• ACIs: compare CI content (Maximize Conventional Implicatures!)

All three are instances of violatesMaximize from Theories/Semantics/Alternatives/Structural.lean, applied to different content dimensions; violatesMCIs is the CI-content instantiation.

The MCIs! Principle (@cite{lo-guercio-2025} def 15)

Do not use φ if there's a formal alternative φ' ∈ F(φ) such that: a. ⟦φ'⟧ᵘ ⊂ ⟦φ⟧ᵘ (CI-stronger) b. φ' ∈ C (contextually relevant) c. ¬⟦φ'⟧ᵘ doesn't contradict C given φ (innocently excludable)

Properties of ACIs (vs SIs and Antipresuppositions)

1. Don't require same assertive content (unlike antipresuppositions)
2. Not affected by DE contexts (unlike SIs)
3. Cancellable
4. Reinforceable
5. Pattern with CI expressions on embeddability

This file is self-contained: it bundles the theoretical analysis (property comparison, polarity-insensitivity, structural-alternative epithet example, grounding theorem) with the empirical judgment data.

structure Phenomena.Expressives.Studies.LoGuercio2025.ScalarInferenceComparison : Type

Summary of how ACIs differ from their "scalar cousins".

Property	SI	Antipresup	ACI
Same assertive content req	No	Yes	No
Affected by DE context	Yes	Varies	No
Cancellable	Yes	Yes	Yes
Reinforceable	Yes	No*	Yes

• Reinforcing a presupposition is redundant

• inferenceType : String
• requiresSameAssertion : Bool
• affectedByDE : Bool
• cancellable : Bool
• reinforceable : Bool

@[implicit_reducible]

instance Phenomena.Expressives.Studies.LoGuercio2025.instReprScalarInferenceComparison : Repr ScalarInferenceComparison

Equations

• Phenomena.Expressives.Studies.LoGuercio2025.instReprScalarInferenceComparison = { reprPrec := Phenomena.Expressives.Studies.LoGuercio2025.instReprScalarInferenceComparison.repr }

def Phenomena.Expressives.Studies.LoGuercio2025.instReprScalarInferenceComparison.repr : ScalarInferenceComparison → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Expressives.Studies.LoGuercio2025.siProperties : ScalarInferenceComparison

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Expressives.Studies.LoGuercio2025.antipresupProperties : ScalarInferenceComparison

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Expressives.Studies.LoGuercio2025.aciProperties : ScalarInferenceComparison

Equations

• One or more equations did not get rendered due to their size.

inductive Phenomena.Expressives.Studies.LoGuercio2025.ACIJudgment : Type

Judgment status for whether an ACI arises.

• arises : ACIJudgment
• doesNotArise : ACIJudgment
• marginal : ACIJudgment

@[implicit_reducible]

instance Phenomena.Expressives.Studies.LoGuercio2025.instDecidableEqACIJudgment : DecidableEq ACIJudgment

Equations

• Phenomena.Expressives.Studies.LoGuercio2025.instDecidableEqACIJudgment x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Phenomena.Expressives.Studies.LoGuercio2025.instReprACIJudgment : Repr ACIJudgment

Equations

• Phenomena.Expressives.Studies.LoGuercio2025.instReprACIJudgment = { reprPrec := Phenomena.Expressives.Studies.LoGuercio2025.instReprACIJudgment.repr }

def Phenomena.Expressives.Studies.LoGuercio2025.instReprACIJudgment.repr : ACIJudgment → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

structure Phenomena.Expressives.Studies.LoGuercio2025.EmpiricalItem : Type

A single empirical item from the paper.

• description : String

  Description of the example context

• sentence : String

  The sentence tested

• potentialACI : String

  The potential ACI content

• judgment : ACIJudgment

  Whether the ACI arises empirically

• priorContext : Option String

  Prior context (if any)

def Phenomena.Expressives.Studies.LoGuercio2025.instReprEmpiricalItem.repr : EmpiricalItem → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[implicit_reducible]

instance Phenomena.Expressives.Studies.LoGuercio2025.instReprEmpiricalItem : Repr EmpiricalItem

Equations

• Phenomena.Expressives.Studies.LoGuercio2025.instReprEmpiricalItem = { reprPrec := Phenomena.Expressives.Studies.LoGuercio2025.instReprEmpiricalItem.repr }

def Phenomena.Expressives.Studies.LoGuercio2025.outOfBlue_epithet_noACI : EmpiricalItem

Out of the blue, no epithet ACI arises.

"John arrived late." ⇝̸ ¬(John is a bastard)

The epithet alternative "that bastard John arrived late" is more complex (requires NP structure not in the substitution source), so it is not a formal alternative. MCIs! correctly predicts no ACI.

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Expressives.Studies.LoGuercio2025.priorMention_epithet_ACI : EmpiricalItem

With prior mention of epithet for another individual, ACI arises.

Context: "John arrived first, then that bastard Pedro arrived." The bare "John" in the first clause triggers the ACI: ¬(John is a bastard).

Because "that bastard" is now contextually relevant (mentioned in the second clause), it enters the substitution source for the first clause. "That bastard John arrived first" is then a formal alternative of equal complexity. MCIs! predicts the ACI.

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Expressives.Studies.LoGuercio2025.subconstituent_epithet_ACI : EmpiricalItem

Subconstituent context also licenses epithet ACI.

"Yesterday, John met with that bastard Pedro." ⇝ ¬(John is a bastard)

"That bastard" occurs as a subconstituent, making the epithet alternative for John available as a formal alternative.

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Expressives.Studies.LoGuercio2025.outOfBlue_honorific_noACI : EmpiricalItem

Out of the blue, no honorific ACI arises for Spanish don/doña.

"Diego entró." (Diego entered.) ⇝̸ ¬(speaker respects Diego)

Unlike Japanese ADTs, the mere absence of don/doña does not license an ACI. Honorific alternatives are not systematically contextually relevant in Spanish conversations.

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Expressives.Studies.LoGuercio2025.contrastive_honorific_ACI : EmpiricalItem

With contrastive honorification, ACI arises.

"Primero entró Donato. Después entró Don Pedro." (First Donato entered. Then HON Pedro entered.) ⇝ ¬(speaker respects Donato)

Using Don for Pedro but not Donato triggers the ACI: the speaker could have used the CI-stronger "Don Donato" but chose not to.

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Expressives.Studies.LoGuercio2025.japanese_systematic_vs_spanish_contextual : Bool

Systematic licensing in Japanese vs contextual in Spanish.

Key cross-linguistic contrast: Japanese ADTs (san, kun, chan) and polite forms (desu/masu) systematically license ACIs because there is a default shared expectation that all referents and the addressee be properly honorified. Omitting the ADT (yobisute) systematically conveys closeness or disrespect.

In Spanish, don/doña only licenses ACIs when the honorific alternative becomes contextually relevant due to concrete features of the conversational context.

Equations

• Phenomena.Expressives.Studies.LoGuercio2025.japanese_systematic_vs_spanish_contextual = true

def Phenomena.Expressives.Studies.LoGuercio2025.outOfBlue_appositive_noACI : EmpiricalItem

Out of the blue, no appositive ACI arises.

"Diego recommended an aspirin." ⇝̸ ¬(Diego is a doctor)

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Expressives.Studies.LoGuercio2025.priorMention_appositive_ACI : EmpiricalItem

With prior appositive mention, ACI arises.

"Diego recommended an aspirin. Laura, a doctor, recommended an antibiotic." ⇝ ¬(Diego is a doctor)

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Expressives.Studies.LoGuercio2025.outOfBlue_suppAdverb_noACI : EmpiricalItem

Out of the blue, no supplementary adverb ACI.

"Juan signed up for the tournament." ⇝̸ ¬luckily/amazingly(Juan signed up)

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Expressives.Studies.LoGuercio2025.priorMention_suppAdverb_ACI : EmpiricalItem

With prior use, supplementary adverb ACI arises.

"Juan signed up for the tournament and luckily/amazingly, Pedro signed up for the tournament." ⇝ ¬luckily/amazingly(Juan signed up for the tournament)

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Expressives.Studies.LoGuercio2025.priorMention_emotiveMarker_ACI : EmpiricalItem

Emotive markers: same pattern.

"Juan signed up for the tournament, and Alas/Wow!, Pedro signed up too." ⇝ ¬(speaker is disappointed/surprised about Juan signing up)

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Expressives.Studies.LoGuercio2025.aciIndependentOfAssertion : Bool

Property test: ACIs do not require same assertive content.

"Juan called María or that bastard Pedro." ⇝ ¬(María is a bastard)

The CI-stronger alternative "Juan called María and that bastard Pedro" has different assertive content (conjunction vs disjunction), yet the ACI still arises. This distinguishes ACIs from antipresuppositions, which require same assertive content.

Equations

• Phenomena.Expressives.Studies.LoGuercio2025.aciIndependentOfAssertion = true

def Phenomena.Expressives.Studies.LoGuercio2025.aciUnaffectedByDE : Bool

Property test: ACIs not affected by DE contexts.

"I doubt that Juan or that bastard Pedro passed the exam."

• SI blocked (DE reverses entailment: no implicature ¬(both passed))
• ACI not blocked: ⇝ ¬(Juan is a bastard)

CI content is independent of truth-conditional entailment, so DE environments have no effect on ACIs.

Equations

• Phenomena.Expressives.Studies.LoGuercio2025.aciUnaffectedByDE = true

def Phenomena.Expressives.Studies.LoGuercio2025.aciCancellable : Bool

Property test: ACIs are cancellable.

"Juan arrived first. Then that bastard Pedro arrived. (By the way, Juan is also a bastard.)"

The parenthetical cancels the ACI. This parallels scalar implicature cancellation and distinguishes ACIs from presuppositions (which are redundant when reinforced).

Equations

• Phenomena.Expressives.Studies.LoGuercio2025.aciCancellable = true

def Phenomena.Expressives.Studies.LoGuercio2025.aciReinforceable : Bool

Property test: ACIs are reinforceable.

"Juan arrived first. That bastard Pedro arrived second. (By the way, Juan is not a bastard.)"

The reinforcement is informative, not redundant. This contrasts with presupposition reinforcement, which sounds redundant.

Equations

• Phenomena.Expressives.Studies.LoGuercio2025.aciReinforceable = true

theorem Phenomena.Expressives.Studies.LoGuercio2025.si_affected_by_de : siProperties.affectedByDE = true

Scalar implicatures are affected by DE contexts.

theorem Phenomena.Expressives.Studies.LoGuercio2025.antipresup_requires_same_assertion : antipresupProperties.requiresSameAssertion = true

Antipresuppositions require same assertive content.

theorem Phenomena.Expressives.Studies.LoGuercio2025.aci_no_same_assertion : aciProperties.requiresSameAssertion = false

ACIs do not require same assertive content.

theorem Phenomena.Expressives.Studies.LoGuercio2025.aci_not_affected_by_de : aciProperties.affectedByDE = false

ACIs are not affected by DE contexts.

theorem Phenomena.Expressives.Studies.LoGuercio2025.aci_reinforceable : aciProperties.reinforceable = true

ACIs are reinforceable (unlike presuppositions).

def Phenomena.Expressives.Studies.LoGuercio2025.registerBlocking_noACI : EmpiricalItem

Register differences block ACIs even when one alternative is CI-stronger.

"That bastard John is late." ⇝̸ ¬(John is a motherfucker)

Even though motherfucker is CI-stronger than bastard (both are lexical items, hence both in the substitution source), the ACI does not arise because the two expressions differ in register — motherfucker is coarser than bastard.

Scalar reasoning requires alternatives to be "in the same dialect or register" (@cite{levinson-2000}). Register mismatch provides the hearer with an alternative explanation for why the speaker didn't use the stronger form: not that the speaker doesn't believe the CI content, but that the alternative was inappropriate due to register.

Equations

• One or more equations did not get rendered due to their size.

inductive Phenomena.Expressives.Studies.LoGuercio2025.ArgExtensionPattern : Type

Argument extension patterns for expressive adjectives (§3.2.4).

EAs behave erratically regarding ACIs because they can scope over different constituents (@cite{potts-2005}, @cite{gutzmann-2019}, @cite{frazier-dillon-clifton-2015}). Lo Guercio notes that this makes "the identification of potential ACIs very complicated" and confines himself to "merely presenting the problem and pointing to a plausible line of analysis."

Three competing accounts:

1. @cite{potts-2005}: semantic polymorphism (EA is type-flexible)
2. @cite{gutzmann-2019}: syntactic iEx feature (Agree-based)
3. @cite{lo-guercio-orlando-2022}: isolated CIs (late merge at PF)

The third account is most promising for ACIs: if EAs are late-merged at PF, they are invisible at LF and thus not formal alternatives in the relevant sense, predicting no ACI computation for EAs.

• local : ArgExtensionPattern

  EA targets its syntactic sister

• argumentLowering : ArgExtensionPattern

  EA targets a higher constituent (e.g., whole VP or S)

• argumentHopping : ArgExtensionPattern

  EA inside DP targets a non-local argument

@[implicit_reducible]

instance Phenomena.Expressives.Studies.LoGuercio2025.instDecidableEqArgExtensionPattern : DecidableEq ArgExtensionPattern

Equations

• Phenomena.Expressives.Studies.LoGuercio2025.instDecidableEqArgExtensionPattern x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Expressives.Studies.LoGuercio2025.instReprArgExtensionPattern.repr : ArgExtensionPattern → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[implicit_reducible]

instance Phenomena.Expressives.Studies.LoGuercio2025.instReprArgExtensionPattern : Repr ArgExtensionPattern

Equations

• Phenomena.Expressives.Studies.LoGuercio2025.instReprArgExtensionPattern = { reprPrec := Phenomena.Expressives.Studies.LoGuercio2025.instReprArgExtensionPattern.repr }

theorem Phenomena.Expressives.Studies.LoGuercio2025.aci_polarity_insensitive {C W World : Type} (src : Alternatives.AlternativeSource (Core.Tree.Tree C W)) (ciContentFn : Core.Tree.Tree C W → World → Bool) (φ : Core.Tree.Tree C W) (weaklyAssertable : Core.Tree.Tree C W → Bool) (_ctx1 _ctx2 : Core.NaturalLogic.ContextPolarity) : Alternatives.Structural.violatesMCIs src ciContentFn φ weaklyAssertable = Alternatives.Structural.violatesMCIs src ciContentFn φ weaklyAssertable

ACIs are polarity-insensitive: the definition of violatesMCIs is structurally independent of context polarity.

Unlike scalar implicatures (which compare at-issue entailment, reversed in DE contexts), MCIs! compares CI content via ciContentFn, which is a function of trees and worlds — not of truth-conditional entailment. Therefore the same violatesMCIs applies regardless of whether the embedding context is UE or DE.

"I doubt that Juan or that bastard Pedro passed"

• SI blocked (DE reverses entailment)
• ACI survives: ⇝ ¬(Juan is a bastard)

This is not a separate definition — it is a structural observation about violatesMCIs: there is no polarity parameter in its type signature, so polarity cannot affect it.

inductive Phenomena.Expressives.Studies.LoGuercio2025.EWord : Type

Vocabulary for epithet examples.

• john : EWord
• pedro : EWord
• arrived : EWord
• first : EWord
• then : EWord
• that_ : EWord
• bastard : EWord

@[implicit_reducible]

instance Phenomena.Expressives.Studies.LoGuercio2025.instDecidableEqEWord : DecidableEq EWord

Equations

• Phenomena.Expressives.Studies.LoGuercio2025.instDecidableEqEWord x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Phenomena.Expressives.Studies.LoGuercio2025.instReprEWord : Repr EWord

Equations

• Phenomena.Expressives.Studies.LoGuercio2025.instReprEWord = { reprPrec := Phenomena.Expressives.Studies.LoGuercio2025.instReprEWord.repr }

def Phenomena.Expressives.Studies.LoGuercio2025.instReprEWord.repr : EWord → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Expressives.Studies.LoGuercio2025.epithetLex : List (Core.Tree.Tree Core.Tree.Cat EWord)

Lexicon including "bastard" as a lexical item.

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Expressives.Studies.LoGuercio2025.johnArrived : Core.Tree.Tree Core.Tree.Cat EWord

φ = "[DP John] arrived first" — bare DP subject.

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Expressives.Studies.LoGuercio2025.bastardJohnArrived : Core.Tree.Tree Core.Tree.Cat EWord

φ' = "[DP that bastard John] arrived first" — epithet DP subject.

This tree is MORE complex than johnArrived because it replaces the terminal N(john) with a node DP[Det(that), N(bastard), N(john)].

Out of the blue, this is NOT reachable from johnArrived by structural operations, because constructing the DP node requires structure not in the substitution source. Hence no ACI arises (matching @cite{lo-guercio-2025}'s prediction for the out-of-the-blue case).

Equations

• One or more equations did not get rendered due to their size.

theorem Phenomena.Expressives.Studies.LoGuercio2025.epithet_has_dp : Core.Tree.Tree.containsCat Core.Tree.Cat.DP bastardJohnArrived = true

The epithet DP contains a DP category node.

theorem Phenomena.Expressives.Studies.LoGuercio2025.bare_lacks_dp : Core.Tree.Tree.containsCat Core.Tree.Cat.DP johnArrived = false

The bare sentence does NOT contain a DP category node.

theorem Phenomena.Expressives.Studies.LoGuercio2025.source_lacks_dp : ((Alternatives.Structural.substitutionSource epithetLex johnArrived).all fun (t : Core.Tree.Tree Core.Tree.Cat EWord) => !Core.Tree.Tree.containsCat Core.Tree.Cat.DP t) = true

The substitution source (out of the blue) lacks DP.

theorem Phenomena.Expressives.Studies.LoGuercio2025.epithet_not_alternative_outOfBlue : bastardJohnArrived ∉ Alternatives.Structural.structuralAlternatives epithetLex johnArrived

Out of the blue, the epithet sentence is NOT a structural alternative.

Proof by category_preservation: no item in L(φ) has DP, φ has no DP, so no reachable tree has DP. But the epithet sentence has DP. QED.

This formalizes @cite{lo-guercio-2025}'s prediction: out of the blue, "that bastard John arrived first" is not a formal alternative to "John arrived first", so no ACI arises.

theorem Phenomena.Expressives.Studies.LoGuercio2025.aci_grounded_in_mcis {W : Type u_1} (φ ψ : Pragmatics.Expressives.TwoDimProp W) (h_ci_stronger : Pragmatics.Expressives.ciStrongerThan ψ φ) : ∃ (w : W), φ.ci w ∧ ¬ψ.ci w

The ACI mechanism is grounded in:

1. @cite{potts-2005}: CI content is independent of at-issue content
2. @cite{fox-katzir-2011}: Formal alternatives are structurally constrained
3. Gricean reasoning: Cooperative speakers maximize informativeness

Given these, MCIs! derives ACIs compositionally: if the speaker used φ when a CI-stronger formal alternative ψ was available and relevant, the hearer infers the speaker believes the CI of ψ does not hold.