Universals in comparative morphology

[Bob12] surveys comparative and superlative suppletion in some 300 languages and finds three root patterns — AAA, ABB, ABC — with *ABA and *AAB unattested: the Comparative-Superlative Generalization (1)–(2), beside the Synthetic Superlative Generalization (3), the Root Suppletion Generalization (4), and Lesslessness (5). All but the last follow from the Containment Hypothesis (6) — the superlative contains the comparative — under Late Insertion, Elsewhere ordering, and locality (8). A comparative root allomorph is chosen in the superlative too, so ABA needs an accidental homophony that Antihomophony (44) excludes; AAB needs a superlative-conditioned allomorph with no comparative counterpart, which adjacency (190) or the markedness condition (202) excludes; and a root sees CMPR only when Merger has made the comparative synthetic (90), which is the RSG, with the SSG as Merger's downward closure.

Main definitions

• czechBad, englishGood, englishBad, welshGood, latinBonus: the book's vocabularies (39), (203), (194), (198), (204) as SpanRules.
• aabContextual, welshAAB, fakeAba: the vocabularies behind the unattested shapes — (190), (201), and the homophony loophole of (44).
• greekBad: the Modern Greek vocabulary (93).
• latinBonusNS: the Latin entries in nanosyntax form.
• Periphrastic: a two-word grade form.

Main results

• english_patterns, latin_patterns, latin_all_three: the Fragments show the attested patterns of (191) and no others.
• english_ssg, english_rsg: (3) and (4) on the English Fragment.
• czech_bad_abb, latin_realize_abc, welsh_good_abc: the engine derives the book's paradigms.
• aabContextual_not_adjacent, welshAAB_not_grounded, fakeAba_not_antihomophonous: each unattested shape violates exactly one condition.
• latin_sprl_needs_portmanteau: ABC needs a portmanteau ((199)).
• greek_comparative, greek_superlative: pjo kak-ós, not pjo cheir-ós ((94)), and a periphrastic superlative embedding the comparative inherits its root ((106)).
• latin_ns_eq_dm: nanosyntax and DM realize Latin alike.

Implementation notes

Lesslessness (5) — no language has a synthetic comparative of inferiority ((278)–(279)) — is the book's most robust generalization but is not derived here: its account, a polarity-reversing head under the Complexity Condition, is a sketch in the book as well. The generalizations concern relative superlatives only; absolute superlatives lack the comparative component and its structure.

The patterns on the Fragments (ch. 4)

theorem Bobaljik2012.english_patterns (e : English.Modifiers.Adjectives.AdjModifierEntry) : e ∈ English.Modifiers.Adjectives.allEntries → e.suppletion = Morphology.Degree.aaa ∨ e.suppletion = Morphology.Degree.abb

The English Fragment shows only AAA and ABB.

theorem Bobaljik2012.latin_patterns (e : Adjective) : e ∈ Latin.Adjectives.allEntries → e.suppletion = Morphology.Degree.aaa ∨ e.suppletion = Morphology.Degree.abb ∨ e.suppletion = Morphology.Degree.abc

The Latin Fragment shows only the attested patterns of (191).

theorem Bobaljik2012.latin_all_three : (∃ e ∈ Latin.Adjectives.allEntries, e.suppletion = Morphology.Degree.aaa) ∧ (∃ e ∈ Latin.Adjectives.allEntries, e.suppletion = Morphology.Degree.abb) ∧ ∃ e ∈ Latin.Adjectives.allEntries, e.suppletion = Morphology.Degree.abc

Latin shows all three: longus, parvus, bonus.

theorem Bobaljik2012.good_csg1 : English.Modifiers.Adjectives.good.suppletion.SprlSuppletive

CSG1 (1) on good: a suppletive comparative forces a suppletive superlative, by contiguity.

def Bobaljik2012.Periphrastic (f : String) : Prop

A two-word form: periphrastic more X.

Equations

• Bobaljik2012.Periphrastic f = (' ' ∈ f.toList)

@[instance_reducible]

instance Bobaljik2012.instDecidablePeriphrastic (f : String) : Decidable (Periphrastic f)

Equations

• Bobaljik2012.instDecidablePeriphrastic f = Bobaljik2012.instDecidablePeriphrastic._aux_1 f

theorem Bobaljik2012.english_ssg (e : English.Modifiers.Adjectives.AdjModifierEntry) : e ∈ English.Modifiers.Adjectives.allEntries → ∀ s ∈ e.formSuper, ¬Periphrastic s → ∃ c ∈ e.formComp, ¬Periphrastic c

SSG (3) on the Fragment: a synthetic superlative comes with a synthetic comparative — structurally, Synthesis.syntheticAt_of_le.

theorem Bobaljik2012.english_rsg (e : English.Modifiers.Adjectives.AdjModifierEntry) : e ∈ English.Modifiers.Adjectives.allEntries → e.suppletion.CmprSuppletive → ∃ c ∈ e.formComp, ¬Periphrastic c

RSG (4) on the Fragment: a suppletive comparative is synthetic — better, worse, never more bett.

The book's vocabularies (ch. 2, ch. 5)

Each vocabulary is run through the Elsewhere engine of Morphology/Exponence/Containment/Contiguity.lean; degreeShape reads the root pattern off the realized cells.

def Bobaljik2012.czechBad : List (Morphology.Containment.SpanRule 3 String)

Czech BAD (39): hor- under CMPR, elsewhere špatn-.

Equations

• Bobaljik2012.czechBad = [{ exponent := "špatn", spans := 0, context := none }, { exponent := "hor", spans := 0, context := some 1 }]

theorem Bobaljik2012.czech_bad_realize : Morphology.Containment.realize czechBad = ![some "špatn", some "hor", some "hor"]

špatn-ý, hor-ší, nej-hor-ší: the comparative allomorph is chosen in the superlative, since the superlative contains its context.

theorem Bobaljik2012.czech_bad_abb : Morphology.Degree.degreeShape (Morphology.Containment.realize czechBad) = Morphology.Degree.abb

def Bobaljik2012.englishGood : List (Morphology.Containment.SpanRule 3 String)

English GOOD (203): bett- under CMPR, elsewhere good.

Equations

• Bobaljik2012.englishGood = [{ exponent := "good", spans := 0, context := none }, { exponent := "bett", spans := 0, context := some 1 }]

theorem Bobaljik2012.english_good_abb : Morphology.Degree.degreeShape (Morphology.Containment.realize englishGood) = Morphology.Degree.abb

def Bobaljik2012.englishBad : List (Morphology.Containment.SpanRule 3 String)

English BAD (194): worse as a √ROOT+CMPR portmanteau, elsewhere bad.

Equations

• Bobaljik2012.englishBad = [{ exponent := "bad", spans := 0, context := none }, { exponent := "worse", spans := 1, context := none }]

theorem Bobaljik2012.english_bad_abb : Morphology.Degree.degreeShape (Morphology.Containment.realize englishBad) = Morphology.Degree.abb

def Bobaljik2012.welshGood : List (Morphology.Containment.SpanRule 3 String)

Welsh GOOD (198): gor- under SPRL and gwell, both √ROOT+CMPR portmanteaus, elsewhere da.

Equations

• Bobaljik2012.welshGood = [{ exponent := "da", spans := 0, context := none }, { exponent := "gwell", spans := 1, context := none }, { exponent := "gor", spans := 1, context := some 2 }]

theorem Bobaljik2012.welsh_good_abc : Morphology.Degree.degreeShape (Morphology.Containment.realize welshGood) = Morphology.Degree.abc

da, gwell, gor-au: ABC, since the superlative exponent is a portmanteau.

def Bobaljik2012.latinBonus : List (Morphology.Containment.SpanRule 3 String)

Latin GOOD (204): opt- a √ROOT+CMPR portmanteau under SPRL, mel- a root allomorph under CMPR, elsewhere bon. Since opt- expones the CMPR cell, -ior has nothing to realize: opt-imus, not *opt-ior-imus.

Equations

• Bobaljik2012.latinBonus = [{ exponent := "bon", spans := 0, context := none }, { exponent := "mel", spans := 0, context := some 1 }, { exponent := "opt", spans := 1, context := some 2 }]

theorem Bobaljik2012.latin_bonus_realize : Morphology.Containment.realize latinBonus = ![some "bon", some "mel", some "opt"]

theorem Bobaljik2012.latin_realize_abc : Morphology.Degree.degreeShape (Morphology.Containment.realize latinBonus) = Morphology.Degree.abc

theorem Bobaljik2012.latin_wellformed : Morphology.Containment.Adjacent latinBonus ∧ Morphology.Containment.Grounded latinBonus ∧ Morphology.Containment.Antihomophonous latinBonus

Latin satisfies every condition the CSG2 derivation uses.

theorem Bobaljik2012.latin_not_terminal : ¬Morphology.Containment.Terminal latinBonus

Latin is not terminal — it must not be, since terminal adjacent rules plateau at the comparative (realize_const_of_terminal_adjacent), which would exclude ABC.

theorem Bobaljik2012.latin_superlative_portmanteau : Morphology.Containment.winner latinBonus 2 = some { exponent := "opt", spans := 1, context := some 2 }

The superlative winner is the portmanteau opt-.

theorem Bobaljik2012.latin_sprl_needs_portmanteau : ∃ it ∈ latinBonus, Morphology.Containment.winner latinBonus 2 = some it ∧ 0 < ↑it.spans

ABC needs a portmanteau ((199), §5.3.1): under adjacency, distinct comparative and superlative cells force a winner exponing more than the root.

The unattested shapes

AAB has two routes, each closed by one condition: a root allomorph conditioned by a nonadjacent SPRL ((190), (45)), and a portmanteau conditioned by SPRL with no comparative-level counterpart ((201)). Surface ABA has one, accidental homophony, closed by Antihomophony ((44)).

def Bobaljik2012.aabContextual : List (Morphology.Containment.SpanRule 3 String)

(190): be(tt)- conditioned by SPRL across the comparative.

Equations

• Bobaljik2012.aabContextual = [{ exponent := "good", spans := 0, context := none }, { exponent := "bett", spans := 0, context := some 2 }]

theorem Bobaljik2012.aabContextual_realizes_aab : Morphology.Degree.degreeShape (Morphology.Containment.realize aabContextual) = Morphology.Degree.aab

theorem Bobaljik2012.aabContextual_not_adjacent : ¬Morphology.Containment.Adjacent aabContextual

Its context skips the comparative: adjacency excludes it.

def Bobaljik2012.welshAAB : List (Morphology.Containment.SpanRule 3 String)

(201): gor- restricted to the superlative with no comparative-level counterpart — *da – da-ch – gor-au.

Equations

• Bobaljik2012.welshAAB = [{ exponent := "da", spans := 0, context := none }, { exponent := "gor", spans := 1, context := some 2 }]

theorem Bobaljik2012.welshAAB_realizes_aab : Morphology.Degree.degreeShape (Morphology.Containment.realize welshAAB) = Morphology.Degree.aab

theorem Bobaljik2012.welshAAB_not_grounded : ¬Morphology.Containment.Grounded welshAAB

The node [GOOD, CMPR] has a context-sensitive rule and no context-free one: (202) excludes it.

theorem Bobaljik2012.welshAAB_blocked : ¬(Morphology.Containment.Antihomophonous welshAAB ∧ Morphology.Containment.Grounded welshAAB)

realize_const_of_grounded applied: the AAB cells refute Antihomophony and (202) together.

def Bobaljik2012.fakeAba : List (Morphology.Containment.SpanRule 3 String)

The homophony loophole of (44): a superlative allomorph accidentally homophonous with the positive yields surface ABA.

Equations

• Bobaljik2012.fakeAba = [{ exponent := "A", spans := 0, context := none }, { exponent := "B", spans := 0, context := some 1 }, { exponent := "A", spans := 0, context := some 2 }]

theorem Bobaljik2012.fakeAba_realizes_aba : Morphology.Degree.degreeShape (Morphology.Containment.realize fakeAba) = Morphology.Degree.aba

theorem Bobaljik2012.fakeAba_not_antihomophonous : ¬Morphology.Containment.Antihomophonous fakeAba

Periphrasis and locality (§3.3)

def Bobaljik2012.greekBad : List (Morphology.Containment.SpanRule 3 String)

Modern Greek BAD (93): cheiró- under CMPR, elsewhere kak-.

Equations

• Bobaljik2012.greekBad = [{ exponent := "kak", spans := 0, context := none }, { exponent := "cheiró", spans := 0, context := some 1 }]

theorem Bobaljik2012.greek_comparative : DistributedMorphology.realizeIn { wordTop := 1 } greekBad 1 = some "cheiró" ∧ DistributedMorphology.realizeIn { wordTop := 0 } greekBad 1 = some "kak"

(94): with Merger the comparative is cheiró-ter-os; without it the root cannot see CMPR, and the periphrastic comparative is pjo kak-ós, not *pjo cheir-ós — the RSG from locality (90).

theorem Bobaljik2012.greek_rsg : { wordTop := 1 }.SyntheticAt 1

The engine's RSG applied: Greek's distinct root forms certify its comparative as synthetic.

theorem Bobaljik2012.greek_superlative : DistributedMorphology.realizeIn { wordTop := 1 } greekBad 2 = some "cheiró"

(106a): the periphrastic superlative o cheiró-ter-os embeds the comparative word, so it inherits the suppletive root — CSG1 holds of a periphrastic superlative exactly when it embeds the comparative (§3.3.3).

The nanosyntax reading

The book treats opt- and gor- as portmanteaus by Fusion or insertion at a nonterminal node, citing [Cah09] among others (§5.3.1). Caha's lexicon does it with context-free entries storing successively larger constituents, competing under the Superset Principle.

def Bobaljik2012.latinBonusNS : List (Morphology.Containment.SpanRule 3 String)

The Latin entries as a nanosyntax lexicon.

Equations

• Bobaljik2012.latinBonusNS = [{ exponent := "bon", spans := 0, context := none }, { exponent := "mel", spans := 1, context := none }, { exponent := "opt", spans := 2, context := none }]

theorem Bobaljik2012.latin_ns_contextFree : Morphology.Containment.ContextFree latinBonusNS

theorem Bobaljik2012.latin_ns_spellout : Morphology.Containment.spellout latinBonusNS = ![some "bon", some "mel", some "opt"]

Superset spellout derives the same paradigm with no contextual apparatus.

theorem Bobaljik2012.latin_ns_eq_dm : Morphology.Containment.spellout latinBonusNS = Morphology.Containment.realize latinBonus

The two frameworks realize Latin cell for cell — the concrete face of spelloutGenerable_iff_generable.