@cite{zwicky-pullum-1983}: Cliticization vs. Inflection

@cite{zwicky-pullum-1983}

Empirical data and classification theorems for the argument that English contracted negator -n't is an inflectional affix, not a simple clitic.

Core argument

Six diagnostics (A–F) separate clitics from inflectional affixes. English simple clitics ('s, 've, 'd) score clitic-like on all six. English inflectional affixes (-ed, -s, -est) score affix-like on all six. The contracted negator -n't scores affix-like on all six — a surprising result given the near-universal prior assumption that it is a clitic.

Semantic scope bridge (criterion D)

The scope irregularity of negation with modals provides a bridge to Semantics.Modality: can't means NOT(CAN(P)) but mustn't means MUST(NOT(P)). This non-compositional scope behavior is characteristic of inflectional affixes, not clitics.

Simple clitics: 's (has/is), 've, 'd

Z&P §2 (criteria A–D) and §3 (criteria E–F):

• A. Low selection: attach to prepositions, verbs, adjectives, adverbs
• B. No arbitrary gaps: combine with any phonologically suitable host
• C. No morphophonological idiosyncrasies: regular reduction
• D. No semantic idiosyncrasies: meaning identical to full form
• E. No syntactic rules affect the combination (no SAI on clitic groups)
• F. Can attach to material already containing clitics (I'd've)

def Phenomena.Morphology.ZwickyPullum1983.cliticS : Morphology.Diagnostics.CliticAffixProfile

Equations

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

def Phenomena.Morphology.ZwickyPullum1983.cliticVe : Morphology.Diagnostics.CliticAffixProfile

Equations

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

def Phenomena.Morphology.ZwickyPullum1983.cliticD : Morphology.Diagnostics.CliticAffixProfile

Equations

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

Inflectional affixes: -ed (past), -s (plural), -est (superlative)

Z&P §2 (criteria A–D) and §3 (criteria E–F):

• A. High selection: each attaches to a single major category
• B. Arbitrary gaps: *strided, *goed
• C. Morphophonological idiosyncrasies: slept, went, best
• D. Semantic idiosyncrasies: last (superlative of late, but not "most recent" — rather "final")
• E. Syntactic rules affect affixed words (inflected nouns, verbs, adjectives are regular syntactic units)
• F. Cannot attach to cliticized material

def Phenomena.Morphology.ZwickyPullum1983.affixEd : Morphology.Diagnostics.CliticAffixProfile

Equations

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

def Phenomena.Morphology.ZwickyPullum1983.affixPluralS : Morphology.Diagnostics.CliticAffixProfile

Equations

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

def Phenomena.Morphology.ZwickyPullum1983.affixEst : Morphology.Diagnostics.CliticAffixProfile

Equations

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

The contracted negator -n't

Z&P §4 (the core of the paper):

• A. High selection (closedClass): attaches only to finite auxiliaries (not to main verbs, prepositions, adjectives, adverbs)
• B. Arbitrary gaps: *mayn't, *amn't (Table 1)
• C. Morphophonological idiosyncrasies: won't [wont] ← will, can't [kænt] ← can, don't [dont] ← do, shan't ← shall
• D. Semantic idiosyncrasies: mustn't = MUST(NOT(P)), not NOT(MUST(P)); can't = NOT(CAN(P)), not CAN(NOT(P)). Scope of negation varies.
• E. SAI applies to -n't forms: Isn't he?, Can't you?, Haven't they?. Contracted negator moves with auxiliary under T-to-C.
• F. Cannot attach to cliticized material: *I'd'ven't (cf. I'd've)

def Phenomena.Morphology.ZwickyPullum1983.negNt : Morphology.Diagnostics.CliticAffixProfile

Equations

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

The simple clitics classify as simpleClitic.

theorem Phenomena.Morphology.ZwickyPullum1983.cliticS_is_clitic : cliticS.classify = Core.Morphology.MorphStatus.simpleClitic

theorem Phenomena.Morphology.ZwickyPullum1983.cliticVe_is_clitic : cliticVe.classify = Core.Morphology.MorphStatus.simpleClitic

theorem Phenomena.Morphology.ZwickyPullum1983.cliticD_is_clitic : cliticD.classify = Core.Morphology.MorphStatus.simpleClitic

The inflectional affixes classify as inflAffix.

theorem Phenomena.Morphology.ZwickyPullum1983.affixEd_is_affix : affixEd.classify = Core.Morphology.MorphStatus.inflAffix

theorem Phenomena.Morphology.ZwickyPullum1983.affixPluralS_is_affix : affixPluralS.classify = Core.Morphology.MorphStatus.inflAffix

theorem Phenomena.Morphology.ZwickyPullum1983.affixEst_is_affix : affixEst.classify = Core.Morphology.MorphStatus.inflAffix

The main result: -n't classifies as inflAffix, not simpleClitic.

theorem Phenomena.Morphology.ZwickyPullum1983.nt_is_affix : negNt.classify = Core.Morphology.MorphStatus.inflAffix

-n't scores 6/6 affix-like — unambiguous.

theorem Phenomena.Morphology.ZwickyPullum1983.nt_unambiguous : negNt.isUnambiguousAffix = true

The simple clitics score 0/6 affix-like — unambiguous.

theorem Phenomena.Morphology.ZwickyPullum1983.clitics_unambiguous : cliticS.isUnambiguousClitic = true ∧ cliticVe.isUnambiguousClitic = true ∧ cliticD.isUnambiguousClitic = true

Verify that the paradigm gaps in Table 1 are encoded in the Fragment data.

theorem Phenomena.Morphology.ZwickyPullum1983.may_gap : Fragments.English.FunctionWords.may.negForm = none

may has no contracted negative form (*mayn't is a paradigm gap).

theorem Phenomena.Morphology.ZwickyPullum1983.am_gap : Fragments.English.FunctionWords.am.negForm = none

am has no contracted negative form (*amn't is a paradigm gap).

Verify that the phonologically irregular forms are flagged in Fragment data.

theorem Phenomena.Morphology.ZwickyPullum1983.wont_irregular : Fragments.English.FunctionWords.will.negIrregular = true

won't is phonologically irregular (not willn't).

theorem Phenomena.Morphology.ZwickyPullum1983.cant_irregular : Fragments.English.FunctionWords.can.negIrregular = true

can't is phonologically irregular.

theorem Phenomena.Morphology.ZwickyPullum1983.dont_irregular : Fragments.English.FunctionWords.do_.negIrregular = true

don't is phonologically irregular (not don't [dunt]).

theorem Phenomena.Morphology.ZwickyPullum1983.shant_irregular : Fragments.English.FunctionWords.shall.negIrregular = true

shan't is phonologically irregular (not shalln't).

theorem Phenomena.Morphology.ZwickyPullum1983.mustnt_irregular : Fragments.English.FunctionWords.must.negIrregular = true

mustn't shows [t]-deletion: [mʌsnt] not *[mʌstnt].

theorem Phenomena.Morphology.ZwickyPullum1983.regular_negatives : Fragments.English.FunctionWords.could.negIrregular = false ∧ Fragments.English.FunctionWords.would.negIrregular = false ∧ Fragments.English.FunctionWords.should.negIrregular = false

Regular forms: couldn't, wouldn't, shouldn't show no irregularity.

Scope of negation with contracted modals

Z&P observe that can't and mustn't show opposite scope relations:

• You can't go home = NOT(CAN(P)): negation scopes over possibility
• You mustn't go home = MUST(NOT(P)): necessity scopes over negation

This is an irregularity in the connection between the contracted form and its uncontracted paraphrase. For can, You cannot go home = You can not go home = NOT(CAN(P)). But for must, You must not go home is ambiguous — it can mean MUST(NOT(P)) (the reading that mustn't unambiguously selects).

This scope irregularity is predicted by the inflectional-affix analysis: if -n't is an affix, it forms a lexical unit with the auxiliary, and lexical items can have idiosyncratic scope properties. If -n't were a clitic (a reduced form of not), its scope should always match not.

We formalize this using Semantics.Modality.ModalTheory.

inductive Phenomena.Morphology.ZwickyPullum1983.NegModalScope : Type

Scope of negation relative to a modal operator.

• negOverModal : NegModalScope

  Negation scopes over the modal: NOT(MODAL(P)). You can't go = it's not the case that you can go.

• modalOverNeg : NegModalScope

  Modal scopes over negation: MODAL(NOT(P)). You mustn't go = you must not go.

instance Phenomena.Morphology.ZwickyPullum1983.instDecidableEqNegModalScope : DecidableEq NegModalScope

Equations

• Phenomena.Morphology.ZwickyPullum1983.instDecidableEqNegModalScope x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Morphology.ZwickyPullum1983.instReprNegModalScope : Repr NegModalScope

Equations

• Phenomena.Morphology.ZwickyPullum1983.instReprNegModalScope = { reprPrec := Phenomena.Morphology.ZwickyPullum1983.instReprNegModalScope.repr }

def Phenomena.Morphology.ZwickyPullum1983.instReprNegModalScope.repr : NegModalScope → ℕ → Std.Format

Equations

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

instance Phenomena.Morphology.ZwickyPullum1983.instBEqNegModalScope : BEq NegModalScope

Equations

• Phenomena.Morphology.ZwickyPullum1983.instBEqNegModalScope = { beq := Phenomena.Morphology.ZwickyPullum1983.instBEqNegModalScope.beq }

def Phenomena.Morphology.ZwickyPullum1983.instBEqNegModalScope.beq : NegModalScope → NegModalScope → Bool

Equations

• Phenomena.Morphology.ZwickyPullum1983.instBEqNegModalScope.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

def Phenomena.Morphology.ZwickyPullum1983.evalNegOverModal (T : Semantics.Modality.ModalTheory) (force : Semantics.Modality.ModalForce) (p : Semantics.Modality.Proposition) (w : Semantics.Attitudes.Intensional.World) : Bool

Evaluate NOT(MODAL(P)) at world w.

Equations

• Phenomena.Morphology.ZwickyPullum1983.evalNegOverModal T force p w = !T.eval force p w

def Phenomena.Morphology.ZwickyPullum1983.evalModalOverNeg (T : Semantics.Modality.ModalTheory) (force : Semantics.Modality.ModalForce) (p : Semantics.Modality.Proposition) (w : Semantics.Attitudes.Intensional.World) : Bool

Evaluate MODAL(NOT(P)) at world w.

Equations

• Phenomena.Morphology.ZwickyPullum1983.evalModalOverNeg T force p w = T.eval force (fun (w' : Semantics.Attitudes.Intensional.World) => !p w') w

structure Phenomena.Morphology.ZwickyPullum1983.ContractedNegScope : Type

The scope pattern for a contracted negative auxiliary.

can't: NOT(CAN(P)) — negOverModal with possibility mustn't: MUST(NOT(P)) — modalOverNeg with necessity

That these differ is the semantic idiosyncrasy. If -n't were simply a reduced form of not, both should have the same scope relation.

• auxiliary : String

  The base auxiliary form.

• force : Semantics.Modality.ModalForce

  The modal force of the auxiliary.

• scope : NegModalScope

  Which scope reading the contracted form selects.

instance Phenomena.Morphology.ZwickyPullum1983.instReprContractedNegScope : Repr ContractedNegScope

Equations

• Phenomena.Morphology.ZwickyPullum1983.instReprContractedNegScope = { reprPrec := Phenomena.Morphology.ZwickyPullum1983.instReprContractedNegScope.repr }

def Phenomena.Morphology.ZwickyPullum1983.instReprContractedNegScope.repr : ContractedNegScope → ℕ → Std.Format

Equations

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

def Phenomena.Morphology.ZwickyPullum1983.instBEqContractedNegScope.beq : ContractedNegScope → ContractedNegScope → Bool

Equations

• One or more equations did not get rendered due to their size.
• Phenomena.Morphology.ZwickyPullum1983.instBEqContractedNegScope.beq x✝¹ x✝ = false

instance Phenomena.Morphology.ZwickyPullum1983.instBEqContractedNegScope : BEq ContractedNegScope

Equations

• Phenomena.Morphology.ZwickyPullum1983.instBEqContractedNegScope = { beq := Phenomena.Morphology.ZwickyPullum1983.instBEqContractedNegScope.beq }

def Phenomena.Morphology.ZwickyPullum1983.cantScope : ContractedNegScope

can't selects NOT(CAN(P)): negation over possibility.

Equations

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

def Phenomena.Morphology.ZwickyPullum1983.mustntScope : ContractedNegScope

mustn't selects MUST(NOT(P)): necessity over negation.

Equations

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

theorem Phenomena.Morphology.ZwickyPullum1983.scope_idiosyncrasy : cantScope.scope ≠ mustntScope.scope

The scope patterns differ — this is the semantic idiosyncrasy.

theorem Phenomena.Morphology.ZwickyPullum1983.neg_over_poss_ne_poss_over_neg : ∃ (T : Semantics.Modality.ModalTheory), T.isNormal ∧ ¬∀ (p : Semantics.Modality.Proposition) (w : Semantics.Attitudes.Intensional.World), evalNegOverModal T Core.Modality.ModalForce.possibility p w = evalModalOverNeg T Core.Modality.ModalForce.possibility p w

NOT(CAN(P)) and CAN(NOT(P)) are not equivalent in general.

There exists a normal modal theory where ¬◇P ≠ ◇¬P: when w0 accesses worlds where P differs, ◇P and ◇¬P are both true, so ¬◇P = false but ◇¬P = true.

theorem Phenomena.Morphology.ZwickyPullum1983.neg_over_nec_ne_nec_over_neg : ∃ (T : Semantics.Modality.ModalTheory), T.isNormal ∧ ¬∀ (p : Semantics.Modality.Proposition) (w : Semantics.Attitudes.Intensional.World), evalNegOverModal T Core.Modality.ModalForce.necessity p w = evalModalOverNeg T Core.Modality.ModalForce.necessity p w

NOT(MUST(P)) and MUST(NOT(P)) are not equivalent in general.

There exists a normal modal theory where ¬□P ≠ □¬P: failing to be necessary (¬□P = true when P fails at w2) is weaker than being necessarily false (□¬P = false when P holds at w1).

-n't attaches only to finite auxiliaries. Verify that the host set matches the auxiliary inventory from Fragments/English/FunctionWords.

theorem Phenomena.Morphology.ZwickyPullum1983.aux_hosts_are_closed_class : (Fragments.English.FunctionWords.allAuxiliaries.all fun (a : Fragments.English.FunctionWords.AuxEntry) => a.auxType == Fragments.English.FunctionWords.AuxType.modal || a.auxType == Fragments.English.FunctionWords.AuxType.doSupport || a.auxType == Fragments.English.FunctionWords.AuxType.be || a.auxType == Fragments.English.FunctionWords.AuxType.have) = true

Every auxiliary in the inventory is either a modal, do-support, be, or have.

def Phenomena.Morphology.ZwickyPullum1983.ntHostCount : ℕ

The number of auxiliaries with contracted negative forms (= the productive range of -n't).

Equations

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

def Phenomena.Morphology.ZwickyPullum1983.ntGapCount : ℕ

The number of paradigm gaps (auxiliaries without -n't).

Equations

• Phenomena.Morphology.ZwickyPullum1983.ntGapCount = (List.filter (fun (a : Fragments.English.FunctionWords.AuxEntry) => a.negForm.isNone) Fragments.English.FunctionWords.allAuxiliaries).length

theorem Phenomena.Morphology.ZwickyPullum1983.nt_has_gaps : ntGapCount > 0

Most auxiliaries have a contracted negative form, but there are gaps.

theorem Phenomena.Morphology.ZwickyPullum1983.nt_has_irregulars : (List.filter (fun (a : Fragments.English.FunctionWords.AuxEntry) => a.negIrregular) Fragments.English.FunctionWords.allAuxiliaries).length ≥ 5

At least five auxiliaries show phonological irregularity in their contracted negative form (Z&P criterion C).