Spalek & McNally (2026): The Anatomy of a Verb

This file formalizes the contrastive analysis of English tear and Spanish rasgar of [SMcN26]. The two verbs are counterparts in comparative lexical databases and share an event structure: both are simple result verbs of the break class ([Lev93]) describing a minimal, binary-scale change, the partly uncontrolled loss of integrity of a whole, with a causative alternation and no agentive intransitive use. They differ in root content, the fine within-class half of a root's meaning beside its templatic kinds ([BKG20]): rasgar requires a flimsy or insubstantial patient and implies a linear, gash-like separation without much force, where tear takes patients of any robustness, implies separation in contrary directions, often with force, and is compatible with careful action. Figurative extensions follow the root content, the case complementary to the event-structural contrasts of [McNS22]: rasgar disturbs fragile states, silence and darkness, and describes linear movement through an insubstantial medium; tear rends with force and describes fast motion along a path. In the bidirectional parallel corpus the verbs are asymmetric translation equivalents: rasgar is one of the rarer renderings of tear, whose most frequent counterpart is arrancar, while tear is the usual rendering of rasgar.

The root contents are the fragment entries' Verb.rootContent, regions of the substrate's Root.Content space. A Situation is a point of that space, a described event's value on every dimension, and Admits says a root's regions contain it; overlaps_iff_exists_admits identifies the substrate's Overlaps with the existence of a situation both roots admit, the zone in which the verbs are intertranslatable. The paper's contrasts are situations one root admits and the other rejects: the chunk of bread (14), the engraved cement (16b), the carefully torn foil (17), the rooster and the silence (18), and the ball tearing through the rough (23); the soft contact lenses (16a) are admitted by both.

Implementation notes

The translation counts of the paper's Tables 1 and 2 are reported in prose. Each contrast situation is fixed on the dimension the paper names for it and agrees with the contact lenses elsewhere, inside both roots' regions, so that each verdict turns on the named dimension alone: robustness for the bread, result geometry for the cement, agent control for the foil, robustness and force for the silence, force for the rough.

References

• [SMcN26]
• [McNS22]
• [BKG20]
• [Lev93]

Situations and admission

structure SpalekMcNally2026.Situation : Type

A described situation: a value on every dimension of root content.

• force : Semantics.Root.Content.ForceLevel
• forceDirection : Semantics.Root.Content.ForceDirection
• instrument : Semantics.Root.Content.InstrumentType
• agentControl : Semantics.Root.Content.AgentControl
• resultGeometry : Semantics.Root.Content.ResultGeometry
• patientRobustness : Semantics.Root.Content.Robustness
• patientDimensionality : Semantics.Root.Content.ObjectDimensionality

@[instance_reducible]

instance SpalekMcNally2026.instDecidableEqSituation : DecidableEq Situation

Equations

• SpalekMcNally2026.instDecidableEqSituation = SpalekMcNally2026.instDecidableEqSituation.decEq

def SpalekMcNally2026.instDecidableEqSituation.decEq (x✝ x✝¹ : Situation) : Decidable (x✝ = x✝¹)

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@[instance_reducible]

instance SpalekMcNally2026.instReprSituation : Repr Situation

Equations

• SpalekMcNally2026.instReprSituation = { reprPrec := SpalekMcNally2026.instReprSituation.repr }

def SpalekMcNally2026.instReprSituation.repr : Situation → ℕ → Std.Format

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

def SpalekMcNally2026.Admits (c : Semantics.Root.Content) (s : Situation) : Prop

A root's content admits a situation when its region on every dimension contains the situation's value.

Equations

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

@[instance_reducible]

instance SpalekMcNally2026.instDecidableAdmits (c : Semantics.Root.Content) (s : Situation) : Decidable (Admits c s)

Equations

• SpalekMcNally2026.instDecidableAdmits c s = id inferInstance

theorem SpalekMcNally2026.overlaps_iff_exists_admits (p q : Semantics.Root.Content) : p.Overlaps q ↔ ∃ (s : Situation), Admits p s ∧ Admits q s

Two roots overlap exactly when some situation is admitted by both: the overlap of the regions is the zone of intertranslatability.

The paper's situations

def SpalekMcNally2026.lenses : Situation

Tearing soft contact lenses with one's nails (16a): a flimsy patient separated by a moderate, linear force.

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def SpalekMcNally2026.bread : Situation

Tearing a chunk off a slice of bread (14): a robust patient.

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

def SpalekMcNally2026.cement : Situation

An awl engraving cement (16b): a gash on a surface, with no separation in contrary directions.

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

def SpalekMcNally2026.foil : Situation

Children carefully tearing tin foil (17): controlled action.

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

def SpalekMcNally2026.silence : Situation

A rooster tearing the silence of the dawn (18): a fragile state, disturbed by the least force.

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def SpalekMcNally2026.rough : Situation

A ball tearing through the rough (23): movement with considerable energy.

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theorem SpalekMcNally2026.lenses_admitted : Admits English.Verbs.tear_.rootContent lenses ∧ Admits Spanish.Verbs.rasgar.rootContent lenses

The contact lenses lie in both roots' regions.

theorem SpalekMcNally2026.roots_overlap : English.Verbs.tear_.rootContent.Overlaps Spanish.Verbs.rasgar.rootContent

The two roots overlap: the contact lenses witness the zone where the verbs translate each other.

theorem SpalekMcNally2026.bread_contrast : Admits English.Verbs.tear_.rootContent bread ∧ ¬Admits Spanish.Verbs.rasgar.rootContent bread

The bread: tear takes a robust patient, rasgar does not.

theorem SpalekMcNally2026.cement_contrast : ¬Admits English.Verbs.tear_.rootContent cement ∧ Admits Spanish.Verbs.rasgar.rootContent cement

The cement: a gash without contrary separation is a rasgar result, not a tear.

theorem SpalekMcNally2026.foil_contrast : Admits English.Verbs.tear_.rootContent foil ∧ ¬Admits Spanish.Verbs.rasgar.rootContent foil

The foil: careful action is compatible with tear and not with rasgar.

theorem SpalekMcNally2026.silence_contrast : ¬Admits English.Verbs.tear_.rootContent silence ∧ Admits Spanish.Verbs.rasgar.rootContent silence

The silence: a fragile state disturbed without force is torn by rasgar, while tear wants force and contrary motion.

theorem SpalekMcNally2026.rough_contrast : Admits English.Verbs.tear_.rootContent rough ∧ ¬Admits Spanish.Verbs.rasgar.rootContent rough

The rough: energetic motion is a tear extension and not a rasgar one, whose flimsy patients call for no such force.