In linguistics, antisymmetry is a syntactic theory presented in Richard S. Kayne's 1994 monograph The Antisymmetry of Syntax. It asserts that grammatical hierarchies in natural language follow a universal order, namely specifier-head-complement branching order. The theory is built on the foundation of X-bar theory. Kayne hypothesizes that all phrases whose surface order is not specifier-head-complement have undergone syntactic movements that disrupt this underlying order. Others have posited specifier-complement-head as the basic word order. Antisymmetry as a principle of word order is reliant on X-bar notions such as specifier and complement, the existence of order-altering mechanisms such as movement, and disputed by constituency structure theories (as opposed to dependency structure theories). C-command is a relation between tree nodes, as defined by Tanya Reinhart. Kayne uses a simple definition of c-command based on the "first node up". However, the definition is complicated by his use of a "segment/category" distinction. Two directly connected nodes that have the same label are "segments" of a single "category". A category "excludes" all categories not "dominated" by all its segments. A "c-commands" B if every category that dominates A also dominates B, and A excludes B. The following tree illustrates these concepts: AP1 and AP2 are both segments of a single category. AP does not c-command BP because it does not exclude BP. CP does not c-command BP because both segments of AP do not dominate BP (so it is not the case that every category that dominates CP dominates BP). BP c-commands CP and A. A c-commands C. The definitions above may perhaps be thought to allow BP to c-command AP, but a c-command relation is not usually assumed to hold between two such categories, and for the purposes of antisymmetry, the question of whether BP c-commands AP is in fact moot. (The above is not an exhaustive list of c-command relations in the tree, but covers all of those that are significant in the following exposition.

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