ARG-ST as a head feature

[Carl Pollard]

I propose the following answer to my own question as to which boolean
algebra Johnson-Bayer would intend to handle the non-acc-gen situation.
It would be (I suggest) the powerset of a seven-element set containing:

  pnom (pure nominative)
  pacc (pure accusative)
  pgen (pure genitive)
  nom_acc (two-way syncretic)
  nom_gen (two-way syncretic)
  acc_gen (two-way syncretic)
  nom_acc_gen (three-way syncretic)

This boolean algebra has a Hasse diagram with bottom, then the seven
elements just mentioned as atoms in a row above bottom, then a row of
21 two-way coordinations, then a row of 35 three-way coordinations,
then a row of 21 4-way coordinations, then a row 7 5-way
coordinations, then top, for a total of 128 (= 2^{7}) elements. The
"basic" values are in the upper row of 21: for example, nom is the
four-way join of pnom, nom_acc, nom_gen, and nom_acc_gen.  (Careful:
the meet of nom and acc is not nom_acc, but rather the join of nom_acc
with nom_acc-gen.)

By contrast, the Levy lattice for three case values has 18 elements,
with the basic elements in the middle row of four (the fourth element
is the three-way coordination of the two-way syncretizations).

If the Pow(7) lattice is indeed the right one for the Johnson-Bayer
analysis of a three-case system, then the following questions arise:

1. What are the extra 110 (128-18) case values for?

2. What evidence is there that coordination/neutralization are booleans?

Carl