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Monotonicity as an effective theory of morphosyntactic variation

Graf, T. (2019). Journal of Language Modelling, 7(2), 3–47

Graf explains typological gaps in adjectival gradation (*ABA), person-pronoun syncretism and the Person Case Constraint by two components: a fixed base hierarchy of prominence relations, and the requirement that the map from it to surface forms be feasibly monotonic, his definition (6). Over a linear hierarchy feasible monotonicity coincides with contiguity, Elsewhere-generability and Superset-spellability, so the effective theory and the two insertion mechanisms are one constraint. A Person Case Constraint is a monotone map from the reduced dual person hierarchy (27) to the truth values.

Main definitions

FeasiblyMonotone: definition (6), some monotone score identifies the cells the map identifies.

Implementation notes

The person hierarchy is Person.prominence, Zwicky's order 1 > 2 > 3, which on the three persons is the inclusion order of Nevins's privative bundles, as the paper observes (Person.prominence_le_iff_subset). Table 2's paradigms index the persons ascending from the first, the dual order, equivalent for feasible monotonicity by the paper's footnote 1. A combination of indirect and direct object is a scenario (Clause.Scenario), the diagonal excluded as the paper does, so the reduced dual hierarchy (27) is the order on scenarios read on the person hierarchy and the naive one (23) the product order. A constraint is a map from the six combinations to the truth values; Table 4's constraints are those of Pancheva and Zubizarreta's grammars.

TODO

The case-layer hierarchy (13) and the Gender Case Constraint are partial orders whose maps need a partial-order generalization of Paradigm: the ban (14) on multiple cross-level case syncretisms and the nominative stem-allomorphy generalization (16) remain.

References

Graf 2019, Monotonicity as an effective theory of morphosyntactic variation
Bobaljik 2012, Universals in comparative morphology: Suppletion, superlatives, and the structure of words formalized
Bobaljik & Sauerland 2018, *ABA and the combinatorics of morphological features
Harbour 2015, Poor pronoun systems and what they teach us
Zwicky 1977b, Hierarchies of Person
Caha 2009, The Nanosyntax of Case formalized
Nevins 2007, The representation of third person and its consequences for person-case effects
Pancheva & Zubizarreta 2018, The Person Case Constraint: The Syntactic Encoding of Perspective formalized

Feasible monotonicity

L63–66

L68–70

Four characterizations coincide over a linear hierarchy

On a linear containment hierarchy, contiguity, feasible monotonicity (6), Elsewhere generability (Bobaljik 2012) and Superset spellability (Caha 2009) are equivalent.

theorem isContiguous_tfae L74–84

{n : ℕ} {F : Type u_1} (p : Morphology.Paradigm n F) :

[IsContiguous p, FeasiblyMonotone p, Morphology.Containment.ElsewhereGenerable p, Morphology.Containment.SupersetSpellable p].TFAE

Built from

Table 1: adjectival gradation

Every adjectival triple of Bobaljik 2012's Table 4.1 but the Basque doublet is feasibly monotonic, as Table 1's attested rows AAA smart and ABB good are.

theorem feasiblyMonotone_of_ne_basque L88–94

{r : CLDF.Wordlist.RootClasses Bobaljik2012.Wordlist.Cell} (hr : r ∈ Bobaljik2012.Wordlist.rootClasses) (hq : ¬Bobaljik2012.Quantifier r) (hb : r.id ≠ Bobaljik2012.Wordlist.eus_good_on.roots.id) :

FeasiblyMonotone (Bobaljik2012.rootPattern r)

Built from

No order on the forms makes good, better, goodest monotone, whatever the order of the codomain, so the *ABA row is unattested.

theorem aba_not_feasiblyMonotone L96–100

¬FeasiblyMonotone Morphology.Paradigm.aba

Built from

Table 2: person-pronoun syncretism

The attested person partitions are feasibly monotonic over 1 > 2 > 3.

theorem person_attested_feasiblyMonotone L121–126

FeasiblyMonotone personJarawa ∧ FeasiblyMonotone personDamin ∧ FeasiblyMonotone personWinnebago

Built from , , ,

The missing partition is the non-monotonic one.

theorem personGap_not_feasiblyMonotone L128–131

¬FeasiblyMonotone personGap

Built from ,

The AAB division of labor

Monotonicity cannot exclude both ABA and AAB, and the paper welcomes this: AAB is attested in person (Winnebago) though not in adjectival gradation, where its absence has to be stipulated, for instance in terms of syntactic containment.

AAB is feasibly monotonic.

theorem aab_feasiblyMonotone L139–142

FeasiblyMonotone Morphology.Paradigm.aab

Built from

Under antihomophony, Bobaljik 2012's markedness condition and adjacency no vocabulary realizes an AAB pattern, so the gradation-side exclusion is carried by the realization engine, not by monotonicity.

theorem aab_not_realizable L144–155