Minimal domain

Notion in checking theory. The minimal domain of X is the smallest subset K of the domain(X) S, such that for any element A of S, some element B of K reflexively dominates A.

Example

In (i), the minimal domain of X is {UP, ZP, WP, YP, H}. The minimal domain of H is {UP, ZP, WP, YP}.

(i)    XP1
       /\
      /  \
     UP  XP2
        /\
       /  \
     ZP1    X'
    /\      /\
   /  \    /  \
  WP  ZP2  X1  YP
          /\
         /  \
        H   X2

Links

Utrecht Lexicon of Linguistics

References

• Chomsky, N. 1993. A Minimalist Program for Linguistic Theory, MIT occasional papers in linguistics, 1-67. Reprinted in: Chomsky (1995).