SOLUTION -- Case Constraints

To add the case constraints to the SPR and COMPS of verbs, you first must introduce the CASE type into the AGR feature.  To do this simply expand AGR to be

agr-cat := feat-struc &
[ PER per,
  NUM num,
  CASE case ].

and add the two subtypes of case 

case :< *value*.
  nom :< case.
  acc :< case.

Then it's as simple as adding the further restriction that each verb have a nominative specifier and accusative complements.  For example

loves := word &
[ ORTH "loves",
  HEAD verb,
  SPR < [HEAD noun & [ AGR 3sing & [ CASE nom ] ] ] >,
  COMPS < phrase & [HEAD noun & [ AGR [ CASE acc ] ] ] > ].


You should begin to notice that there is a lot of redundancy arising in our lexicon.  For example every verb has  SPR < [HEAD noun & [ CASE nom ] ] >.  Later we'll see how to integrate these redundant constraints (including case) into the lexeme types.



SOLUTION -- 3sing and non-3sing

The textbook's 3sing / non-3sing type hierarchy can be implemented as follows:

3sing := agr-cat &
[ PER 3rd,
  NUM sing,
  GEND gend ].

non-3sing :< agr-cat.

1sing := non-3sing &
[ PER 1st,
  NUM sing ].

non-1sing :< non-3sing.

2sing := non-1sing &
[ PER 2nd,
  NUM sing ].

pl := non-1sing &
[ NUM plur ].


The reason that 3sing will unify with non-3sing is that the type system implemented in the LKB does not require that a feature structure of type t must unify with a subtype of t.  Such a formalism could be constructed, but it's questionable whether the value gained by such a strong notion of well-formedness would be worth the extra computation needed to implement it.

The "Typed feature structures made simple" chapter from the LKB Documentation for suggests that PER and NUM be collapsed into a single feature:

agr-cat := feat-struc &
[ PERNUM pernum,
  CASE case ].

pernum :< *value*.

non-3sing :< pernum.

1sing :< non-3sing.
1plur :< non-3sing.
2sing :< non-3sing.
2plur :< non-3sing.
3sing :< pernum.
3plur :< non-3sing.