Documentation

Linglib.Studies.BeaversKoontzGarboden2020

Beavers & Koontz-Garboden (2020): The Roots of Verbal Meaning #

The six representative roots of the book's root typology (ch. 5), and the falsification of the Bifurcation Thesis of Roots ([Emb09]; [Ara05]) and of Manner/Result Complementarity ([RHL10]).

Root	manner	cause	result	state	position
√flat				✓	complement
√blossom			✓	✓	complement
√crack		✓	✓	✓	complement
√jog	✓				adjoined
√hand	✓	✓	✓	✓	adjoined
√drown	✓	✓	✓	✓	complement

The +state cells of √blossom, √crack, √hand, √drown are derived: the book's typology values are the collocational closures (Root.closedKinds) of the base atom kinds, and each closed signature is one of the canonical typology rows (Root.Kinds.pureResult, causativeResult, fullSpec). √blossom falsifies Bifurcation on its own, since change of state is templatic (v_become) content. √hand and √drown additionally falsify Manner/Result Complementarity; they differ only in root position (adjoined vs complement), the contrast carrying the book's account of which root types are attested.

Main declarations #

flat, jog, blossom, crack, hand, drown
exists_violatesBifurcation, bifurcation_thesis_false
exists_hasMannerAndResult, manner_result_complementarity_false

The six representative roots #

def BeaversKoontzGarboden2020.flat :

√flat — pure state.

Equations

BeaversKoontzGarboden2020.flat = { name := "flat", entailments := {Verb.LexEntailment.hasState "flat"} }

Instances For

def BeaversKoontzGarboden2020.jog :

√jog — pure manner of motion.

Equations

BeaversKoontzGarboden2020.jog = { name := "jog", entailments := {Verb.LexEntailment.hasManner "jogging-gait"} }

Instances For

def BeaversKoontzGarboden2020.blossom :

√blossom — result with no specified manner or cause (an internally caused change of state).

Equations

BeaversKoontzGarboden2020.blossom = { name := "blossom", entailments := {Verb.LexEntailment.becomesState "flowering"} }

Instances For

def BeaversKoontzGarboden2020.crack :

√crack — caused result without specified manner.

Equations

BeaversKoontzGarboden2020.crack = { name := "crack", entailments := {Verb.LexEntailment.becomesState "fissured", Verb.LexEntailment.hasCause} }

Instances For

def BeaversKoontzGarboden2020.hand :

√hand — manner + cause + result, adjoined position. The possession result is non-cancelable ("#Mary handed John the book, but he never got it"), so it is root-entailed rather than implicated ([BKG20] ch. 3).

Equations

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

Instances For

def BeaversKoontzGarboden2020.drown :

√drown — manner of killing (Levin 1993's crucify, drown, hang, electrocute class; [BKG20] ch. 4): manner + cause + result, complement position.

Equations

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

Instances For

Kind signatures #

Base signatures record the atom kinds; closed signatures are their collocational closures, and coincide with the canonical rows of the book's typology.

theorem BeaversKoontzGarboden2020.flat_kinds :

flat.kinds = {Verb.LexKind.state}

theorem BeaversKoontzGarboden2020.jog_kinds :

jog.kinds = {Verb.LexKind.manner}

theorem BeaversKoontzGarboden2020.blossom_kinds :

blossom.kinds = {Verb.LexKind.result}

theorem BeaversKoontzGarboden2020.crack_kinds :

crack.kinds = {Verb.LexKind.result, Verb.LexKind.cause}

theorem BeaversKoontzGarboden2020.hand_kinds :

hand.kinds = {Verb.LexKind.manner, Verb.LexKind.result, Verb.LexKind.cause}

theorem BeaversKoontzGarboden2020.drown_kinds :

drown.kinds = {Verb.LexKind.manner, Verb.LexKind.result, Verb.LexKind.cause}

theorem BeaversKoontzGarboden2020.flat_closedKinds :

flat.closedKinds = Verb.Root.Kinds.propertyConcept

theorem BeaversKoontzGarboden2020.jog_closedKinds :

jog.closedKinds = Verb.Root.Kinds.pureManner

theorem BeaversKoontzGarboden2020.blossom_closedKinds :

blossom.closedKinds = Verb.Root.Kinds.pureResult

theorem BeaversKoontzGarboden2020.crack_closedKinds :

crack.closedKinds = Verb.Root.Kinds.causativeResult

theorem BeaversKoontzGarboden2020.hand_closedKinds :

hand.closedKinds = Verb.Root.Kinds.fullSpec

theorem BeaversKoontzGarboden2020.drown_closedKinds :

drown.closedKinds = Verb.Root.Kinds.fullSpec

Falsifying the Bifurcation Thesis #

theorem BeaversKoontzGarboden2020.blossom_violatesBifurcation :

blossom.ViolatesBifurcation

√blossom entails change of state — templatic (v_become) content in the root — falsifying Bifurcation without any manner or cause entailment.

theorem BeaversKoontzGarboden2020.crack_violatesBifurcation :

crack.ViolatesBifurcation

theorem BeaversKoontzGarboden2020.hand_violatesBifurcation :

hand.ViolatesBifurcation

theorem BeaversKoontzGarboden2020.drown_violatesBifurcation :

drown.ViolatesBifurcation

theorem BeaversKoontzGarboden2020.exists_violatesBifurcation :

∃ (r : Verb.Root), r.ViolatesBifurcation

Some root carries templatic content.

theorem BeaversKoontzGarboden2020.bifurcation_thesis_false :

¬∀ (r : Verb.Root), r.RespectsBifurcation

The universal closure of the Bifurcation Thesis is false.

Falsifying Manner/Result Complementarity #

theorem BeaversKoontzGarboden2020.hand_hasMannerAndResult :

hand.HasMannerAndResult

√hand entails both a manner (by-hand transfer) and a result (recipient possession).

theorem BeaversKoontzGarboden2020.drown_hasMannerAndResult :

drown.HasMannerAndResult

√drown entails both a manner (submersion) and a result (death); it differs from √hand in root position.

theorem BeaversKoontzGarboden2020.exists_hasMannerAndResult :

∃ (r : Verb.Root), r.HasMannerAndResult

Some root entails both a manner and a result.

theorem BeaversKoontzGarboden2020.manner_result_complementarity_false :

¬∀ (r : Verb.Root), r.RespectsMannerResultComplementarity

The universal closure of Manner/Result Complementarity is false.

Roots respecting each constraint #

theorem BeaversKoontzGarboden2020.flat_respectsBifurcation :

flat.RespectsBifurcation

√flat (pure state) respects Bifurcation: its signature is bounded by the ontological kinds.

theorem BeaversKoontzGarboden2020.jog_respectsBifurcation :

jog.RespectsBifurcation

√jog (pure manner) respects Bifurcation.

theorem BeaversKoontzGarboden2020.crack_respectsMannerResultComplementarity :

crack.RespectsMannerResultComplementarity

√crack (cause + result, no manner) respects Manner/Result Complementarity.

The roots cash out denotationally ([BKG20] §1.3.2) #

Threading the roots through the change-of-state denotation (Verb.CosModel): a verb's denotation is dispatched on its root's kinds, so the kinds proven above select the event template and the result entailment of (6) follows from the signature. √crack (+cause+result) entails a result state in any model; √jog (pure manner) does not — the break/hit contrast.

def BeaversKoontzGarboden2020.crackV :

crack the change-of-state verb (Mary cracked the vase).

Equations

BeaversKoontzGarboden2020.crackV = { frames := [Frame.np], root := BeaversKoontzGarboden2020.crack, form := "crack" }

Instances For

def BeaversKoontzGarboden2020.jogV :

jog the pure-manner activity verb (Mary jogged).

Equations

BeaversKoontzGarboden2020.jogV = { frames := [], root := BeaversKoontzGarboden2020.jog, form := "jog" }

Instances For

theorem BeaversKoontzGarboden2020.crack_denote_entails_result {Entity : Type u_1} {State : Type u_2} {Time : Type u_3} [LinearOrder Time] (M : Verb.CosModel Entity State Time) (y x : Entity) (e : Event Time) (h : M.denote crackV y x e) :

∃ (e' : Event Time) (s : State), M.become s e' ∧ M.rootState crackV x s

√crack carries .result, so in any model its denotation entails the result state — the non-cancelable result of [BKG20] (6), derived from crack's signature rather than stipulated.

theorem BeaversKoontzGarboden2020.jog_denote_eq_manner {Entity : Type u_1} {State : Type u_2} {Time : Type u_3} [LinearOrder Time] (M : Verb.CosModel Entity State Time) (y x : Entity) :

M.denote jogV y x = M.manner jogV

√jog has no .result (nor .cause), so its denotation is the bare manner core — no become, no result state. Only the change-of-state root entails a result.

The same contrast at the template level ([RHL98]) #

Verb.Root.template reads the event-structure template off a root's collocational closure; the kinds proven above fix it, and HasResultState reduces to carrying result (Verb.Root.template_hasResultState_iff). So the denotational result entailment (√crack) and the template result diagnostic are one fact seen through kinds.

theorem BeaversKoontzGarboden2020.flat_template :

flat.template = Semantics.Lexical.EventStructure.Template.state

theorem BeaversKoontzGarboden2020.jog_template :

jog.template = Semantics.Lexical.EventStructure.Template.activity

theorem BeaversKoontzGarboden2020.blossom_template :

blossom.template = Semantics.Lexical.EventStructure.Template.achievement

theorem BeaversKoontzGarboden2020.crack_template :

crack.template = Semantics.Lexical.EventStructure.Template.accomplishment

theorem BeaversKoontzGarboden2020.crack_template_hasResultState :

crack.template.HasResultState

√crack's template embeds a result state (it carries result); √jog's does not — the break/hit contrast, now at the template layer and provably the same signature fact as crack_denote_entails_result.

theorem BeaversKoontzGarboden2020.jog_template_no_resultState :

¬jog.template.HasResultState

theorem BeaversKoontzGarboden2020.crack_template_forces_denote_result {Entity : Type u_1} {State : Type u_2} {Time : Type u_3} [LinearOrder Time] (M : Verb.CosModel Entity State Time) (y x : Entity) (e : Event Time) (h : M.denote crackV y x e) :

∃ (e' : Event Time) (s : State), M.become s e' ∧ M.rootState crackV x s

√crack's template embeds a result state, so by denote_result_from_template its denotation entails the result state in any model — the template diagnostic and the denotational entailment are one fact through crack's kinds.