[LG25] — Anti-Conventional Implicatures

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

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, [Kat07])
• Antipresuppositions: compare presuppositional content (Maximize Presupposition, [Sch12b])
• ACIs: compare CI content (Maximize Conventional Implicatures!)

All three are instances of violatesMaximize from Semantics/Alternatives/Competition.lean, applied to different content dimensions; violatesMCIs is the CI-content instantiation. The two structural-parallel theorems violatesMaximize_of_violatesMP and violatesMP_of_violatesMaximize_sameAssertion (in Competition.lean) discharge Lo Guercio's §4 diagnostic that "ACIs do not require same assertive content, unlike antipresuppositions" — MP is literally Maximize-on-presupposition plus a same-assertion clause.

The CI content function used in the §3 worked example follows the [Gut15] / [Kap99] felicity-set semantics adopted by Lo Guercio (paper def 12, p. 9): ⟦φ⟧ᵘ is the set of contexts where φ is felicitously usable. The bare sentence is felicitous everywhere (trivial CI); the epithet construction is felicitous only at worlds where the speaker holds the relevant CI-belief.

Main declarations

• Examples — the paper's 15 empirical items, sourced from Linglib/Data/Examples/LoGuercio2025.json.
• EWord, epithetLex, johnArrived, bastardJohnArrived, bastardPedroDP, priorContextLex — vocabulary, lexicons, and trees for the §3 worked example.
• expressiveCI — concrete CI content function modeling Lo Guercio's felicity-set semantics for the epithet construction.
• outOfBlue_no_ACI — out-of-the-blue (paper (18)): no formal alternative supplies stronger epithet-CI than the bare sentence, so violatesMCIs does NOT fire.
• priorMention_yes_ACI — prior-mention configuration (paper (20a)): with the epithet construction contextually relevant (added to the substitution source), violatesMCIs DOES fire.
• outOfBlue_vs_priorMention_contrast — the paper's central diagnosis packaged as a single theorem: same content function, same host, two substitution sources, opposite outcomes.

Implementation notes

Empirical items live as typed LinguisticExample rows in Linglib/Data/Examples/LoGuercio2025.json and are inserted between -- BEGIN/END GENERATED EXAMPLES markers by scripts/gen_examples.py. The paperFeatures field records paper-internal classifications (aciStatus, expressionType, licensingMechanism); downstream theorems project these as needed.

The §3 worked example uses a STRUCTURAL PROXY for the felicity-set CI semantics: expressiveCI φ w is true iff φ lacks the structural marker of the epithet construction (containsCat .DP here — the bare-name subject is intentionally modeled as a bare [N john] terminal, while the epithet variant introduces the [DP that bastard john] node) OR the speaker holds the CI belief at w. The structural proxy is faithful to the paper's mechanism for this fragment — the CI is triggered by the epithet DP construction — and lets category_preservation discharge the out-of-the-blue case constructively. A full compositional interpretation through Pragmatics.Expressives.TwoDimProp.ci would require a Pottsian lexical entry for bastard and a tree-interpretation function; see the Todo bullet below.

The contrastive-honorific ACI in (22a) is read in Lo Guercio (around (24), paper p. 14) as a Horn-style upper-bounding inference — at most the lower honorific attitude toward the bare-name referent — not as a literal contrastive denial. The JSON comment field for that example records this distinction.

The Japanese vs Spanish honorific systematicity contrast (paper §3.2.2, JSON outOfBlue_honorific and contrastive_honorific comments) is the paper's key cross-linguistic argument and is grounded in [McC19b] (plain vs desu/masu polite-form competition) and [Osh23] (san/kun/chan affixal designation terms). In Japanese, ADTs and polite forms are systematically contextually relevant by virtue of a default expectation of honorification; their omission systematically triggers an ACI. Spanish don/doña lacks this default expectation, so omission triggers an ACI only when honorification is locally relevant.

Todo

• Replace expressiveCI with a compositional interpretation through Pragmatics.Expressives.TwoDimProp.ci: define a Pottsian lexical entry bastardLex : TwoDimProp World and an interpretation function interpret : Tree Cat EWord → TwoDimProp World, then derive expressiveCI as (interpret φ).ci. Substrate-level change; defer.
• §3.2.4 expressive-adjective argument extension (paper p. 25-27): Lo Guercio is explicit (p. 26) that he merely points to a tentative line of analysis (late-merge at PF following [LGO22]); not formalized.
• §4 embeddability data (paper (55)-(60)) — paper devotes 3 pages; promote to a shared embeddability generalisation (Data/Generalizations/) once a second study (Kratzer 1999 or Potts 2007) contributes parallel stimuli.
• §4 Magri-style oddness puzzles (paper (64)-(68)) — paper itself declares this unresolved/erratic; defer.
• The priorMention_yes_ACI reachability hypothesis is currently supplied by the caller. A constructive proof requires either modeling the bare-name subject as [DP [N john]] (paper (24) notation) and a stronger structural-preservation lemma than category_preservation (one that tracks 1-child vs multi-child DP nodes), or a separate worked tree for the priorMention case. Substrate refactor; defer.

§3 worked example: epithet as structural alternative

The §3 mechanism in two stages:

1. Out of the blue: the epithet construction [DP that bastard John] requires more structural complexity than the bare-name sentence provides. category_preservation (Structural.lean) closes the "no DP reachable" lemma constructively.
2. Prior mention: when the epithet construction occurs elsewhere in the discourse (paper's [DP that bastard Pedro] in (20a)), the substitution source clause (a) admits it as "contextually relevant" ([FK11] def 41). We model this by adding bastardPedroDP to priorContextLex. Now two Katzir substitutions reach bastardJohnArrived: outer DP → bastardPedroDP, then inner Pedro → John.

inductive LoGuercio2025.EWord : Type

Vocabulary for the epithet worked example.

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

@[implicit_reducible]

instance LoGuercio2025.instDecidableEqEWord : DecidableEq EWord

Equations

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

def LoGuercio2025.instReprEWord.repr : EWord → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.
• LoGuercio2025.instReprEWord.repr LoGuercio2025.EWord.john prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "LoGuercio2025.EWord.john")).group prec✝
• LoGuercio2025.instReprEWord.repr LoGuercio2025.EWord.pedro prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "LoGuercio2025.EWord.pedro")).group prec✝
• LoGuercio2025.instReprEWord.repr LoGuercio2025.EWord.first prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "LoGuercio2025.EWord.first")).group prec✝
• LoGuercio2025.instReprEWord.repr LoGuercio2025.EWord.that_ prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "LoGuercio2025.EWord.that_")).group prec✝

@[implicit_reducible]

instance LoGuercio2025.instReprEWord : Repr EWord

Equations

• LoGuercio2025.instReprEWord = { reprPrec := LoGuercio2025.instReprEWord.repr }

@[implicit_reducible]

instance LoGuercio2025.instBEqEWord : BEq EWord

Equations

• LoGuercio2025.instBEqEWord = { beq := fun (a b : LoGuercio2025.EWord) => decide (a = b) }

instance LoGuercio2025.instLawfulBEqEWord : LawfulBEq EWord

def LoGuercio2025.epithetLex : List (Syntax.Tree Syntax.Cat EWord)

Out-of-the-blue lexicon: terminals only, no DP-shaped items.

Equations

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

def LoGuercio2025.johnArrived : Syntax.Tree Syntax.Cat EWord

φ = "John arrived first" — bare-name subject, NO DP node.

The bare-name N-terminal modeling is the structural proxy that lets category_preservation close the OOTB no-ACI direction (the source has no DP, so no reachable tree does). The paper's actual modeling of John as a DP ([DP John], paper (24)) would require a richer subtree-tracking lemma.

Equations

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

def LoGuercio2025.bastardJohnArrived : Syntax.Tree Syntax.Cat EWord

φ' = "[DP that bastard John] arrived first" — epithet DP subject. Strictly more complex than johnArrived: replaces the terminal [N John] with a 3-child DP [DP that bastard John].

Equations

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

def LoGuercio2025.bastardPedroDP : Syntax.Tree Syntax.Cat EWord

The epithet DP for Pedro: [DP that bastard Pedro]. In the paper's prior-mention configuration (20a), this constituent is introduced by the second conjunct ("then that bastard Pedro arrived") and becomes contextually relevant — by Fox-Katzir's substitution-source clause (a) it then enters the source for the first conjunct's alternatives.

Equations

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

def LoGuercio2025.priorContextLex : List (Syntax.Tree Syntax.Cat EWord)

Prior-mention lexicon: out-of-the-blue lexicon augmented by the contextually-relevant bastardPedroDP constituent. This is the substitution-source clause (a) in [FK11] def 41 made concrete: "α is contextually relevant in c (e.g., by virtue of having been mentioned)" → α enters the substitution source.

Equations

• LoGuercio2025.priorContextLex = LoGuercio2025.epithetLex ++ [LoGuercio2025.bastardPedroDP]

Structural lemmas (OOTB case via category_preservation)

theorem LoGuercio2025.epithet_has_dp : Syntax.Tree.ContainsCat Syntax.Cat.DP bastardJohnArrived

The epithet sentence contains a DP node.

theorem LoGuercio2025.bare_lacks_dp : ¬Syntax.Tree.ContainsCat Syntax.Cat.DP johnArrived

The bare sentence has no DP node.

theorem LoGuercio2025.source_lacks_dp (t : Syntax.Tree Syntax.Cat EWord) : t ∈ Alternatives.Structural.substitutionSource epithetLex johnArrived → ¬Syntax.Tree.ContainsCat Syntax.Cat.DP t

The OOTB substitution source contains no DP.

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

The OOTB epithet sentence is NOT a structural alternative. Discharged by category_preservation: no source item has a DP, the host has no DP, so no reachable tree has a DP — but the epithet variant does.

CI content via felicity-set semantics

expressiveCI is the operative content function fed to violatesMCIs. It models Lo Guercio's def-12 felicity-set semantics (Gutzmann 2015 / Kaplan 1999): the bare sentence is felicitous everywhere (trivial CI); the epithet construction is felicitous only at worlds where the speaker holds the negative-attitude CI toward John.

@[reducible, inline]

abbrev LoGuercio2025.World : Type

World type for the §3 example: a Bool flag for whether the speaker believes John is a bastard at this world.

Equations

• LoGuercio2025.World = Bool

def LoGuercio2025.speakerBelievesJohnBastard : World → Prop

The speaker-belief predicate (just w under the Bool world model).

Equations

• LoGuercio2025.speakerBelievesJohnBastard w = (w = true)

@[reducible, inline]

abbrev LoGuercio2025.hasEpithetStructure (φ : Syntax.Tree Syntax.Cat EWord) : Prop

A tree carries the epithet CI iff it contains a DP node (structural proxy for "the epithet construction is present"; see Implementation notes).

Equations

• LoGuercio2025.hasEpithetStructure φ = Syntax.Tree.ContainsCat Syntax.Cat.DP φ

def LoGuercio2025.expressiveCI : Syntax.Tree Syntax.Cat EWord → World → Prop

Felicity-set CI content ([Gut15] / [Kap99]; adopted by Lo Guercio (paper def 12, p. 9)).

expressiveCI φ w holds iff φ is felicitous at world w on the CI dimension: either it doesn't carry the epithet CI (true vacuously for non-epithet sentences) or the speaker actually believes the CI content at w (the felicity condition for using the epithet).

Equations

• LoGuercio2025.expressiveCI φ w = (¬LoGuercio2025.hasEpithetStructure φ ∨ LoGuercio2025.speakerBelievesJohnBastard w)

theorem LoGuercio2025.epithet_ciStronger_than_bare : (∀ (w : World), expressiveCI bastardJohnArrived w → expressiveCI johnArrived w) ∧ ∃ (w : World), expressiveCI johnArrived w ∧ ¬expressiveCI bastardJohnArrived w

The epithet variant is CI-stronger than the bare sentence: the bare sentence is felicitous at every world; the epithet variant only at worlds where the speaker believes.

Thesis discharge — the OOTB / priorMention contrast

theorem LoGuercio2025.outOfBlue_no_ACI : ¬Alternatives.violatesMCIs (Alternatives.Structural.katzirSource epithetLex) expressiveCI johnArrived fun (x : Syntax.Tree Syntax.Cat EWord) => True

Out of the blue, the bare sentence "John arrived first" does NOT violate MCIs!: no formal alternative in the substitution source supplies stronger epithet-CI content than the bare sentence itself.

The proof works by contradiction. Any φ' witnessing violatesMCIs must have ¬ expressiveCI φ' w at some world — which by the felicity-set definition forces hasEpithetStructure φ' = True, i.e. φ' contains a DP. But category_preservation says no Katzir-reachable tree from the DP-free source has a DP. Contradiction.

theorem LoGuercio2025.priorMention_yes_ACI (priorSrc : Alternatives.Source (Syntax.Tree Syntax.Cat EWord)) (h_reach : bastardJohnArrived ∈ priorSrc johnArrived) : Alternatives.violatesMCIs priorSrc expressiveCI johnArrived fun (x : Syntax.Tree Syntax.Cat EWord) => True

Prior mention (paper (20a)): when an alternative source makes the epithet variant bastardJohnArrived reachable (by Fox-Katzir def 41 clause (a): "α is contextually relevant in c (e.g., by virtue of having been mentioned)" — the second conjunct's [DP that bastard Pedro] enters the substitution source for the first conjunct's alternatives), the bare sentence violates MCIs!.

The reachability is supplied as a hypothesis (h_reach) rather than proved constructively. The paper's substitution-source clause (a) IS what provides this hypothesis: the constructive proof would require either modeling the bare-name subject as [DP [N john]] (paper (24) notation) — which breaks the category_preservation route used by outOfBlue_no_ACI — or a stronger structural-preservation lemma distinguishing 1-child from multi-child DPs. Either route is a substrate refactor and is flagged in the Todo bullet for expressiveCI's compositional-interpretation upgrade.

theorem LoGuercio2025.outOfBlue_vs_priorMention_contrast (priorSrc : Alternatives.Source (Syntax.Tree Syntax.Cat EWord)) (h_reach : bastardJohnArrived ∈ priorSrc johnArrived) : (¬Alternatives.violatesMCIs (Alternatives.Structural.katzirSource epithetLex) expressiveCI johnArrived fun (x : Syntax.Tree Syntax.Cat EWord) => True) ∧ Alternatives.violatesMCIs priorSrc expressiveCI johnArrived fun (x : Syntax.Tree Syntax.Cat EWord) => True

The paper's central contrast (paper §3.2.1, contrasting (18)-(19) with (20)-(23)): same content function, same host sentence, two substitution sources — opposite violatesMCIs outcomes. The contrast turns purely on whether the CI-stronger formal alternative is in the source (the second hypothesis); under expressiveCI the epithet IS CI-stronger in both cases.

This is the operational content of Lo Guercio's claim that ACI licensing depends on whether the CI alternative is a formal alternative, NOT on whether it is theoretically CI-stronger.