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Linglib.Core.Case.Hierarchy

Blake's Case Hierarchy @cite{blake-1994} #

@cite{iggesen-2013} @cite{moravcsik-1974}

The case hierarchy (@cite{blake-1994}, §5.8, example 68) is an implicational tendency over case inventories:

NOM ACC/ERG GEN DAT LOC ABL/INST others

If a language has a case at position n, it usually has at least one case from each position to the left. Blake hedges this as holding "with overwhelmingly greater than chance frequency" (borrowing @cite{greenberg-1963}). Gaps occur when higher grammatical relations are marked by bound pronouns or word order (p. 89).

Ranks 6–2 directly encode Blake's hierarchy. Ranks 1 (COM, ALL, PERL, BEN) and 0 (VOC, PART, CAUS) are our assignment within Blake's undifferentiated "others" — he notes "it is doubtful whether the hierarchy can be developed much further" beyond ABL/INST (p. 160).

Contiguity #

validInventory formalizes the hierarchy as a strict no-gaps predicate: an idealization of Blake's tendency. Real languages occasionally violate it (e.g., Nanai has NOM ACC DAT LOC ABL INST ALL but no GEN — Blake's example 76, p. 160). The predicate is useful for checking well-formedness of idealized inventories.

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def Core.Case.hierarchyRank :
Case → Nat

Position on Blake's case hierarchy (@cite{blake-1994}, §5.8, ex. 68).

Higher rank = more likely to exist in a language's case inventory.

Ranks are grouped into tiers:

  • 6: core grammatical (NOM, ACC, ERG, ABS) — alternatives, not all required
  • 5: genitive
  • 4: dative
  • 3: locative
  • 2: ablative, instrumental
  • 1: comitative, allative, perlative, benefactive (our ranking within Blake's undifferentiated "others")
  • 0: vocative, partitive, causal (sporadic, outside the main hierarchy)
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    def Core.validInventory (inv : List Case) :
    Bool

    A case inventory is contiguous (no rank gaps) on the hierarchy.

    For every pair of cases in the inventory, each intermediate rank must have at least one representative in the inventory. This matches Blake's implicational tendency (1994, §5.8): if a language has cases at ranks N and M (N < M), it usually has at least one case at each rank between them.

    The predicate does NOT require all cases at a given rank to be present — Blake's slash notation (ACC/ERG, ABL/INST) signals alternatives, not conjunctions, and a language may have COM without PERL.

    Real languages occasionally violate even this weaker check (e.g., Nanai: @cite{blake-1994}, ex. 76, p. 160).

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    • One or more equations did not get rendered due to their size.
    Instances For
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      theorem Core.core_highest :
      Case.nom.hierarchyRank = 6

      Core cases are at the top of the hierarchy.

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      theorem Core.gen_above_dat :
      Case.gen.hierarchyRank > Case.dat.hierarchyRank

      GEN outranks DAT on the hierarchy.

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      theorem Core.dat_above_loc :
      Case.dat.hierarchyRank > Case.loc.hierarchyRank

      DAT outranks LOC on the hierarchy.

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      theorem Core.loc_above_abl :
      Case.loc.hierarchyRank > Case.abl.hierarchyRank

      LOC outranks ABL/INST on the hierarchy.

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      theorem Core.loc_above_inst :
      Case.loc.hierarchyRank > Case.inst.hierarchyRank
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      theorem Core.abl_inst_same_rank :
      Case.abl.hierarchyRank = Case.inst.hierarchyRank

      ABL and INST occupy the same tier.

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      theorem Core.two_case_valid :
      validInventory [Case.nom, Case.acc] = true

      A two-case system {NOM, ACC} is valid.

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      theorem Core.three_case_with_gen_valid :
      validInventory [Case.nom, Case.acc, Case.gen] = true

      {NOM, ACC, GEN} is valid.

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      theorem Core.four_case_valid :
      validInventory [Case.nom, Case.acc, Case.gen, Case.dat] = true

      {NOM, ACC, GEN, DAT} is valid.

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      theorem Core.five_case_valid :
      validInventory [Case.nom, Case.acc, Case.gen, Case.dat, Case.loc] = true

      {NOM, ACC, GEN, DAT, LOC} is valid.

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      theorem Core.seven_case_valid :
      validInventory [Case.nom, Case.acc, Case.gen, Case.dat, Case.loc, Case.abl, Case.inst] = true

      {NOM, ACC, GEN, DAT, LOC, ABL, INST} is valid.

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      theorem Core.ergative_four_case_valid :
      validInventory [Case.erg, Case.abs, Case.gen, Case.dat] = true

      An ergative core {ERG, ABS, GEN, DAT} is also valid.

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      theorem Core.split_ergative_valid :
      validInventory [Case.nom, Case.erg, Case.abs, Case.gen] = true

      Mixed core {NOM, ERG, ABS, GEN} — split-ergative system.

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      theorem Core.skip_gen_invalid :
      validInventory [Case.nom, Case.acc, Case.dat] = false

      {NOM, ACC, DAT} skips GEN — invalid by contiguity.

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      theorem Core.skip_gen_dat_invalid :
      validInventory [Case.nom, Case.acc, Case.loc] = false

      {NOM, ACC, LOC} skips GEN and DAT — invalid.

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      theorem Core.skip_to_abl_invalid :
      validInventory [Case.nom, Case.acc, Case.abl] = false

      {NOM, ACC, ABL} skips GEN, DAT, LOC — invalid.

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      theorem Core.skip_dat_invalid :
      validInventory [Case.nom, Case.acc, Case.gen, Case.loc] = false

      {NOM, ACC, GEN, LOC} skips DAT — invalid.