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Universals in comparative morphology: Suppletion, superlatives, and the structure of words

Bobaljik, J. D. (2012). MIT Press

Bobaljik surveys comparative and superlative suppletion in some 300 languages and finds three root patterns — AAA, ABB, ABC — with *AAB unattested and *ABA attested only in a Basque doublet that the book leaves open (section 4.1.2): 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, either a root allomorph conditioned across the comparative (190), which meets the markedness condition (202) and which adjacency excludes, or a portmanteau with no context-free counterpart (201), which (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. The same locality condition limits CSG1 to periphrastic superlatives that embed the comparative (§3.3.3), so Russian plox-oj – xuž-e – samyj plox-oj, whose superlative embeds the positive, is ABA without any homophony.

The derivation of CSG1 here uses containment and antihomophony but no property of the Elsewhere ordering: under any ranking of an antihomophonous vocabulary the comparative's allomorph blocks the positive's in the superlative, and the ordering decides only which contiguous pattern a vocabulary yields. Antihomophony (44) bars only contextual allomorphs homophonous with a default, while the engine assumes that all exponents are distinct; the difference matters from four grades on, where two homophonous contextual allomorphs yield ABCB.

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).
Antihomophony, abcb: Antihomophony (44), and a four-grade vocabulary meeting it that is not contiguous.
greekBad, russianBad: the Modern Greek vocabulary (93) and its Russian counterpart.
positiveEmbedding: the word extents of a superlative embedding the positive.
latinBonusNS: the Latin entries in nanosyntax form.
Synthetic, Periphrastic: a grade form of one word, and one of several.
rootPattern, Quantifier: the root classes of a triple over the grades, and the triples of quantifiers.
BearsOnCSG: a language of the broad sample with suppletion and a morphological superlative.
MorphComparative, MorphSuperlative, Records: a table row's M columns, and the synthetic extents of a language's adjectives they record.

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 book gives no Russian vocabulary. russianBad is built in the format of the Greek (93), with the comparative root xud- that §6.4.4 identifies in xuž-e.

References

Bobaljik 2012, Universals in comparative morphology: Suppletion, superlatives, and the structure of words
Caha 2009, The Nanosyntax of Case formalized

Merger as successive-cyclic head bundling

The synthetic extent

Word-internal realization

CSG1

L255–257

CSG1 under any ranking

Selecting the applicable rule of greatest score realizes a contiguous pattern whatever the score, since applicability grows with the grade. The Elsewhere ordering is one score among others: it decides which contiguous pattern a vocabulary yields, not that the pattern is contiguous.

CSG1 holds of an antihomophonous vocabulary over the containment structure however its rules are ranked.

theorem csg1_of_any_ranking L265–271

{F : Type u_1} {α : Type u_2} [LinearOrder α] (f : Morphology.Containment.SpanRule 3 F → α) {v : Morphology.Exponence.RuleSet (Morphology.Containment.SpanRule 3 F)} (hv : v.Antihomophonous) (h : v.realize f 1 ≠ v.realize f 0) :

v.realize f 2 ≠ v.realize f 0

The suppletive triples (Tables 4.1 and 4.2)

The 73 adjectival cognate triples of Table 4.1, each with the root classes the book assigns its grades: ABC for the triples (31) names and the Greek pair counted on p. 112, ABA for the Basque doublet (143), and ABB for the rest, by the summary on p. 109. The quantifier triples of Table 4.2 follow in their own section. A triple counts once however many languages share it (section 1.3).

Every adjectival triple but the Basque doublet (143b) is contiguous.

theorem isContiguous_iff_ne_basque L300–305

(r : CLDF.Wordlist.RootClasses Wordlist.Cell) :

r ∈ Wordlist.rootClasses → ¬Quantifier r → (IsContiguous (rootPattern r) ↔ r.id ≠ Wordlist.eus_good_on.roots.id)

Built from ,

No triple, adjectival or quantifier, is AAB.

theorem ne_aab L307–311

(r : CLDF.Wordlist.RootClasses Wordlist.Cell) :

r ∈ Wordlist.rootClasses → Setoid.ker (rootPattern r) ≠ Setoid.ker Morphology.Paradigm.aab

Built from

The ABC triples are the four of (31) and the Greek pair counted on p. 112; no quantifier triple is ABC.

theorem abc_iff L313–320

(r : CLDF.Wordlist.RootClasses Wordlist.Cell) :

r ∈ Wordlist.rootClasses → (Setoid.ker (rootPattern r) = Setoid.ker Morphology.Paradigm.abc ↔ r.id ∈ [Wordlist.lat_good.roots.id, Wordlist.cym_good.roots.id, Wordlist.sga_good.roots.id, Wordlist.pal_good.roots.id, Wordlist.grc_good_amein.roots.id])

Built from

CSG1 holds of every adjectival triple but the Basque doublet.

theorem csg1_of_ne_basque L322–326

{r : CLDF.Wordlist.RootClasses Wordlist.Cell} (hr : r ∈ Wordlist.rootClasses) (hq : ¬Quantifier r) (h : r.id ≠ Wordlist.eus_good_on.roots.id) :

rootPattern r 2 ≠ rootPattern r 0

Built from ,

No antihomophonous vocabulary realizes the Basque triple on – hobe – on-en (143b), whose homophony Antihomophony (44) excludes, as section 4.1.2 leaves open.

theorem basque_not_realized L328–334

{v : Morphology.Exponence.RuleSet (Morphology.Containment.SpanRule 3 ℕ)} (hv : v.Antihomophonous) :

Morphology.Containment.realize v ≠ some ∘ rootPattern Wordlist.eus_good_on.roots

Built from

The broad sample (Appendix A)

The 148 languages of Table A.1, chosen on a quasi-random basis (section 1.3). Most languages satisfy the generalizations for trivial reasons, lacking suppletion, superlatives or adjectives (p. 16): a language bears on the CSG only with suppletion and a morphological superlative.

L342–345

L347–348

Four of the 148 languages bear on the CSG.

theorem bearsOnCSG_names L350–354

List.map (fun (x : StructureDataset.Row) => x.language.name) (List.filter (fun (x : StructureDataset.Row) => decide (BearsOnCSG x)) StructureDataset.broadSample) = ["Persian (Farsi)", "Czech", "Finnish", "Basque"]

Built from

Every language of the sample with suppletion is in Eurasia: comparative suppletion with morphological superlatives is confined to a Greater European area (p. 17).

theorem eurasia_of_suppletion L356–360

(r : StructureDataset.Row) :

r ∈ StructureDataset.broadSample → (∃ v ∈ r.suppl, v.code = StructureDataset.Suppl.yes) → ∃ v ∈ r.region, v.code = StructureDataset.Region.eurasia

Each language of the sample that bears on the CSG has a cognate triple in Table 4.1.

theorem exists_rootClasses_of_bearsOnCSG L362–366

(r : StructureDataset.Row) :

r ∈ StructureDataset.broadSample → BearsOnCSG r → ∃ t ∈ Wordlist.rootClasses, ¬Quantifier t ∧ some t.lexeme.languageId = r.language.glottocode

Built from ,

The English Fragment

On the English Fragment a synthetic superlative comes with a synthetic comparative. This is the SSG (3), which Synthesis.syntheticAt_of_le derives structurally.

theorem english_ssg L380–384

(e : Degree.GradableAdjective) :

e ∈ English.Adjectives.allEntries → Synthetic e.comparison.superlative → Synthetic e.comparison.comparative

Built from

On the English Fragment a comparative not on the positive's root is synthetic (better, worse, never more bett). This is the RSG (4).

theorem english_rsg L386–391

(e : Degree.GradableAdjective) :

e ∈ English.Adjectives.allEntries → e.comparison.comparative ≠ [] → Morphology.Morph.root e.form ∉ e.comparison.comparative → Synthetic e.comparison.comparative

Built from

The Synthetic Superlative Generalization over both samples (§3.4)

The focused survey of Table B.1 adds 174 languages with morphological comparison or comparative suppletion and their relatives (section 1.3). A table row records the synthetic extents of the language's adjectives, so Merger's downward closure predicts the SSG (89) of every row. Over both tables four rows fail it, the apparent counterexamples of §3.4.2 and §3.4.3: Western and Eastern Armenian, whose superlative amen-a- may be a compound or sit on a null comparative affix; Zulu, whose questionable -kazi may form absolute superlatives; and Alutor, whose brief description omits the comparative suffix that the longer description of its sister Koryak records.

A row records some synthetic extents exactly when it satisfies the SSG.

theorem exists_records_iff L427–436

{r : StructureDataset.Row} :

(∃ (S : Set (Synthesis 3)), Records r S) ↔ MorphSuperlative r → MorphComparative r

Built from , , ,

L438–439

The rows of the two samples that record no synthetic extents are the four of §3.4.2 and §3.4.3.

theorem ssg_exceptions L441–447

List.map (fun (x : StructureDataset.Row) => x.language.name) (List.filter (fun (r : StructureDataset.Row) => decide ¬∃ (S : Set (Synthesis 3)), Records r S) (StructureDataset.broadSample ++ StructureDataset.focusedSurvey)) = ["Zulu", "Armenian (Western)", "Armenian (Eastern)", "Alutor"]

Built from ,

L450–452

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

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

L460–461

L463–464

The engine derives the book's paradigms.

theorem czech_bad_abb L466–467

Setoid.ker (Morphology.Containment.realize czechBad) = Setoid.ker Morphology.Paradigm.abb

Built from

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

theorem welsh_good_abc L490–491

Setoid.ker (Morphology.Containment.realize welshGood) = Setoid.ker Morphology.Paradigm.abc

Built from

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

theorem latin_sprl_needs_portmanteau L513–518

∃ it ∈ latinBonus, latinBonus.selectBy Morphology.Containment.SpanRule.threshold 2 = some it ∧ 0 < ↑it.spans

Built from

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)).

L527–528

L530–531

Its context skips the comparative, so adjacency excludes it.

theorem aabContextual_not_adjacent L533–534

¬Morphology.Containment.Adjacent aabContextual

Built from

L537–538

L540–542

L544

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

theorem welshAAB_not_markedness L546–548

¬Morphology.Containment.Markedness welshAAB

Built from

Periphrasis and locality (§3.3)

L589–590

With Merger the comparative is cheiró-ter-os, and without it pjo kak-ós, not *pjo cheir-ós (94), the RSG from locality (90).

theorem greek_comparative L592–597

realizeIn { wordTop := 1 } greekBad 1 = some "cheiró" ∧ realizeIn { wordTop := 0 } greekBad 1 = some "kak"

Built from ,

L599–600

Periphrastic superlatives (§3.3.3)

A periphrastic superlative may embed the comparative word, as Greek o cheiró-ter-os does, or the positive, as Russian samyj plox-oj does. By locality (90) only the first inherits a suppletive comparative root, so CSG1 holds of the first type and fails for the second.

With a suppletive comparative, CSG1 holds of the superlative exactly when the superlative's adjective word contains the comparative head (§3.3.3).

theorem csg1_iff_one_le L609–625

{F : Type u_1} {e : Fin 3 → Fin 3} (he : ∀ (g : Fin 3), e g ≤ g) {v : Morphology.Exponence.RuleSet (Morphology.Containment.SpanRule 3 F)} (hAH : v.Antihomophonous) (h : Morphology.Containment.realize v (e 1) ≠ Morphology.Containment.realize v (e 0)) :

Morphology.Containment.realize v (e 2) ≠ Morphology.Containment.realize v (e 0) ↔ 1 ≤ e 2

The periphrastic superlative o cheiró-ter-os (106a) embeds the comparative word, so it inherits the suppletive root.

theorem greek_superlative L627–630

realizeIn { wordTop := 1 } greekBad 2 = some "cheiró"

Built from ,

L632–633

L635

L637–639

Plox-oj, xuž-e, samyj plox-oj (106d) is ABA under an antihomophonous vocabulary, since its periphrastic superlative lacks CMPR.

theorem russian_bad_eq_ploxoj L641–648

Built from , ,

L650–652

L654–655

In the English, Latin and Russian Fragments a superlative on the positive's root after a comparative on another is periphrastic, embedding the positive, so every morphological superlative satisfies CSG1.

theorem periphrastic_of_aba L657–666

(e : Adjective) :

e ∈ List.map (fun (x : Degree.GradableAdjective) => x.toAdjective) English.Adjectives.allEntries ++ Latin.Adjectives.allEntries ++ Russian.Adjectives.allEntries → e.comparison.comparative ≠ [] → Morphology.Morph.root e.form ∉ e.comparison.comparative → Morphology.Morph.root e.form ∈ e.comparison.superlative → Periphrastic e.comparison.superlative

Built from

The quantifier triples (Table 4.2)

Of the quantifier triples, all but three are ABB; the three apparent ABA triples are Karelian, Armenian and Bulgarian (165). Bulgarian naj is a freestanding particle (pp. 127-128) and Armenian amena- a compound with amen 'all' (pp. 128-129), so their superlatives embed the positive, as Russian samyj plox-oj does. The Karelian ABA comes from Zajkov's dictionary; the online dictionary gives the ABB triple (170), which a questionnaire of seven speakers bears out (pp. 129-131), none of whom gave or recognized Zajkov's superlative.

Every quantifier triple but the three of (165) is contiguous.

theorem quantifier_isContiguous_iff L677–683

(r : CLDF.Wordlist.RootClasses Wordlist.Cell) :

r ∈ Wordlist.rootClasses → Quantifier r → (IsContiguous (rootPattern r) ↔ r.id ∉ [Wordlist.krl_many.roots.id, Wordlist.hye_many.roots.id, Wordlist.bul_many.roots.id])

Built from ,

The Bulgarian and Armenian triples are ABB seen through a superlative that embeds the positive, as (168) and (169) analyse them.

theorem bulgarian_armenian_eq_abb_comp L685–690

(r : CLDF.Wordlist.RootClasses Wordlist.Cell) :

r ∈ [Wordlist.bul_many.roots, Wordlist.hye_many.roots] → Setoid.ker (rootPattern r) = Setoid.ker (Morphology.Paradigm.abb ∘ positiveEmbedding)

Built from ,

The two Karelian sources disagree: Zajkov's triple (165a) is ABA, the triple (170) ABB.

theorem karelian_sources L692–696

Setoid.ker (rootPattern Wordlist.krl_many.roots) = Setoid.ker Morphology.Paradigm.aba ∧ Setoid.ker (rootPattern Wordlist.krl_many_onego.roots) = Setoid.ker Morphology.Paradigm.abb

Built from

Zajkov's Karelian (165a), the one non-contiguous quantifier triple no parse makes ABB, has a form no questionnaire respondent gave or recognized (p. 130).

theorem exists_ungrammatical_of_not_isContiguous L698–706

(r : CLDF.Wordlist.RootClasses Wordlist.Cell) :

r ∈ Wordlist.rootClasses → Quantifier r → ¬IsContiguous (rootPattern r) → r.id ∉ [Wordlist.hye_many.roots.id, Wordlist.bul_many.roots.id] → ∃ f ∈ r.forms, ∃ g ∈ Wordlist.marked, g.judgment = Judgment.ungrammatical ∧ g.cell = f.cell ∧ g.form = f.form ∧ g.lexeme.id = r.lexeme.id

Built from ,

The nanosyntax reading

The book treats opt- and gor- as portmanteaus by Fusion or insertion at a nonterminal node, citing Caha 2009 among others (§5.3.1). Caha's lexicon does it with context-free entries storing successively larger constituents, competing under the Superset Principle.

L715–716

L718–719

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

theorem latin_ns_eq_dm L721–724

Morphology.Containment.spellout latinBonusNS = Morphology.Containment.realize latinBonus

Built from ,