Dominance

Dominance is a dominance is a binary relation between nodes in a tree structure which can be defined as follows:

(i) Node A dominates node B iff A is higher up the tree than B such that you
    can trace a line from A to B going only downwards

The Dominance relation has the following logical properties:

 - irreflexivity:	a node does not dominate itself
 - asymmetry:		if A dominates B, B does not
                        dominate A
 - transitivity:	if A dominates B, and B dominates C,
                        then A dominates C

A relation which has these three properties is called a partial order.

Example

node A dominates all other nodes in (ii). C dominates F and G, but F and G do not dominate C.

(ii)		 A
	        / \
	       /   \
	      B	    C
	     / \   / \
            D  E   F G

Also, node C in (ii) does not dominate the nodes B, D, or E, nor is it dominated by either of these nodes. Furthermore, node A immediately dominates the nodes B and C: there is no intervening node between A on the one hand and B and C on the other hand, i.e. there is no node N such that N dominates B and C and is dominated by A. Analogously, D and E are immediately dominated by B; F and G by C. Nodes D and E are called sisternodes. The same holds for F and G, and B and C. The nodes B and C are daughters of A; D and E are daughters of B; F and G daughters of C. In recent literature (May 1985, Chomsky 1986b), the dominance relation has been redefined in terms of the notion segment:

	(iii) A is dominated by B iff A is dominated by
              every segment of B

In (iv), there are two nodes XP¹ and XP², the result of movement by adjunction, which are each taken to be a segment of the maximal projection XP (= {XP², XP¹}) of X.

(iv)		XP2
	       /|
	      /	|
	  ZPi	XP1
		|
		X'
		|\
		| \
		X  YP
		   |
		   Y'
		   |\
		   | \
		   Y  ZP
		      |
		      ti

XP¹ is the original maximal projection. It is called the minimal maximal projection or the base maximal projection. The adjoined ZP is dominated in the original sense of (i) by the topmost maximal projection segment XP² but it is not dominated in the sense of (i) by the minimal maximal projection segment XP¹. Thus, by the definition in (iii), ZP is not dominated by XP. ZP is not fully part of the projection of X: it is not dominated by every segment of the maximal projection of X. YP, in contrast, is dominated both by XP¹ and by XP². YP, then, is completely inside the projection of X, i.e. YP is dominated by XP in the sense of (iii). Even though ZP is not dominated by the maximal projection of X, it is not entirely outside the maximal projection of X, being dominated by the topmost node XP². It is said then, that ZP is not excluded from XP. Exclusion is defined in (v).

(v) Exclusion
    B excludes A if no segment of B dominates A

Chomsky (1992) distinguishes s(egment)-domination from c(ategory)-domination. A c-dominates B if every segment of A dominates B. A s-dominates B if some segment of A dominates B.

Link

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).
• Chomsky, N. 1986b. Barriers, MIT Press, Cambridge, Mass.
• Haegeman, L. 1991. Introduction to Government and Binding Theory, Oxford, Blackwell.
• May, R.C. 1977. The Grammar of Quantification, unp. PhD diss., MIT.
• Radford, A. 1988. Transformational grammar: a first course, Cambridge University Press, Cambridge UK.

Other languages

• German Dominanz