# Antisymmetry

For the property of matrices, see Skew-symmetric matrix. For the property of mathematical relations, see Antisymmetric relation.

In linguistics, antisymmetry is a theory of syntactic linearization presented in Richard Kayne's 1994 monograph The Antisymmetry of Syntax.[1] The crux of this theory is that hierarchical structure in natural language maps universally onto a particular surface linearization, namely specifier-head-complement branching order. The theory derives a version of X-bar theory. Kayne hypothesizes that all phrases whose surface order is not specifier-head-complement have undergone movements that disrupt this underlying order. Subsequently, there have also been attempts at deriving specifier-complement-head as the basic word order.[2]

Antisymmetry as a principle of word order is reliant on assumptions that many theories of syntax[which?] dispute, e.g. constituency structure (as opposed to dependency structure), X-bar notions such as specifier and complement, and the existence of ordering altering mechanisms such as movement and/or copying.[citation needed]

## Asymmetric c-command

The theory is based on a notion of asymmetric c-command, c-command being a relation between nodes in a tree originally defined by Tanya Reinhart.[citation needed] 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". A category is a kind of extended node; if two directly connected nodes in a tree have the same label, these two nodes are both segments of a single category. C-command is defined in terms of categories using the notion of "exclusion". A category excludes all categories not dominated by both 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.)

Asymmetric c-command is the relation that holds between two categories, A and B, if A c-commands B but B does not c-command A. This relationship is a primitive in Kayne's theory of linearization, the process that converts a tree structure into a flat (structureless) string of terminal nodes.

## Precedence and asymmetric c-command

Informally, Kayne's theory states that if a nonterminal category A c-commands another nonterminal category B, all the terminal nodes dominated by A must precede all of the terminal nodes dominated by B (this statement is commonly referred to as the "Linear Correspondence Axiom" or LCA). Moreover, this principle must suffice to establish a complete and consistent ordering of all terminal nodes — if it cannot consistently order all of the terminal nodes in a tree, the tree is illicit. Consider the following tree:

(S and S' may either be simplex structures like BP, or complex structures with specifiers and complements like CP.)

In this tree, the set of pairs of nonterminal categories such that the first member of the pair asymmetrically c-commands the second member is as follows: {<BP, A>, <BP, CP>, <A, CP>}. This gives rise to the total ordering: <b, a, c>.

As a result, there is no right adjunction, and hence in practice no rightward movement either.[3] Furthermore, the underlying order must be specifier-head-complement.

## Derivation of X-bar theory

The example tree in the first section of this article is in accordance with X-bar theory (with the exception that [Spec,CP] is treated as an adjunct). It can be seen that removing any of the structure in the tree (e.g. deleting the C dominating the 'c' terminal, so that the complement of A is [CP c]) will destroy the asymmetric c-command relations necessary for linearly ordering the terminals of the tree.

## The universal order

Kayne notes that his theory permits either a universal specifier-head-complement order or a universal complement-head-specifier order, depending on whether asymmetric c-command establishes precedence or subsequence (S-H-C results from precedence) (pp. 35–36)[1] He argues that there are good empirical grounds for preferring S-H-C as the universal underlying order, since the typologically most widely attested order is for specifiers to precede heads and complements (though the order of heads and complements themselves is relatively free). He further argues that a movement approach to deriving non S-H-C orders is appropriate, since it derives asymmetries in typology (such as the fact that "verb second" languages such as German are not mirrored by any known "verb second-from-last" languages).

## Derived orders: the case of Japanese wh-questions

Perhaps the biggest challenge for antisymmetry is to explain the wide variety of different surface orders across languages. Any deviation from Spec-Head-Comp order (which implies overall Subject-Verb-Object order, if objects are complements) must be explained by movement. Kayne argues that in some cases, the need for extra movements (previously unnecessary because different underlying orders were assumed for different languages) can actually explain some mysterious typological generalizations. His explanation for the lack of wh-movement in Japanese is the most striking example of this. From the mid-1980s onwards, the standard analysis of wh-movement involved the wh-phrase moving leftward to a position on the left edge of the clause called [Spec,CP] (i.e., the specifier of the CP phrase). Thus, a derivation of the English question What did John buy? would proceed roughly as follows:

[CP {Spec,CP position} John did buy what]
wh-movement
[CP What did John buy]

The Japanese equivalent of this sentence is as follows[4] (note the lack of wh-movement):

 John-wa nani-o kaimasita ka John-topic_marker what-accusative bought question_particle

Japanese has an overt "question particle" (ka), which appears at the end of the sentence in questions. It is generally assumed that languages such as English have a "covert" (i.e. phonologically null) equivalent of this particle in the 'C' position of the clause — the position just to the right of [Spec,CP]. This particle is overtly realised in English by movement of an auxiliary to C (in the case of the example above, by movement of did to C). Why is it that this particle is on the left edge of the clause in English, but on the right edge in Japanese? Kayne suggests that in Japanese, the whole of the clause (apart from the question particle in C) has moved to the [Spec,CP] position. So, the structure for the Japanese example above is something like the following:

[CP [John-wa nani-o kaimasita] C ka

Now it is clear why Japanese does not have wh-movement — the [Spec,CP] position is already filled, so no wh-phrase can move to it. We therefore predict a seemingly obscure relationship between surface word order and the possibility of wh-movement. A possible alternative to the antisymmetric explanation could be based on the difficulty of parsing languages with rightward movement.[5]

## Dynamic Antisymmetry

A weak version of the theory of antisymmetry (Dynamic antisymmetry) has been proposed by Andrea Moro, which allows the generation of non-LCA compatible structures (points of symmetry) before the hierarchical structure is linearized at Phonetic Form. The unwanted structures are then rescued by movement: deleting the phonetic content of the moved element would neutralize the linearization problem.[6] From this perspective, Dynamic Antisymmetry aims at unifying movement and phrase structure, which otherwise would be two independent properties that characterize all human language grammars.

## Antisymmetry and Ternary Branching

In a recent manuscript, Kayne (2010) has proposed recasting the antisymmetry of natural language as a condition on "Merge", the operation which combines two linguistic elements into one complex linguistic element.[7] Kayne proposes that merging a head H and its complement C yields an ordered pair $$ (rather than the standard symmetric set {H,C}). $$ involves immediate temporal precedence (or immediate linear precedence), so that H immediately precedes (i-precedes) C. Kayne proposes furthermore that when a specifier S merges, it forms an ordered pair with the head directly, $$, or S i-precedes H. Invoking i-precedence prevents more than two elements from merging with H; only one element can i-precede H (the specifier), and H can i-precede only one element (the complement).

Kayne (2010) notes that $,$ is not mappable to a tree structure, since H would have two mothers, and that it has the consequence that $$ and $$ would seem to be constituents. He suggests that $,$ is replaced by $$, "with an ordered triple replacing the two ordered pairs and then being mappable to a ternary-branching tree" (pp. 17). Kayne goes on to say, "This would lead to seeing my [(1981)][8] arguments for binary branching to have two subcomponents, the first being the claim that syntax is n-ary branching with n having a single value, the second being that that value is 2. Mapping [$,$ to $$] would retain the first subcomponent and replace 2 by 3 in the second, arguably with no loss in restrictiveness."

## References and footnotes

1. ^ a b Kayne, Richard S. (1994). The Antisymmetry of Syntax. Linguistic Inquiry Monograph Twenty-Five. MIT Press.
2. ^ Li, Yafei (2005). A Theory of the Morphology-Syntax Interface. MIT Press.
3. ^ Since any rightward movement must also be downward movement if there are no rightward specifiers or right adjunction, and downward movement is generally assumed to be illicit.
4. ^ Jamal Ouhalla (1999). Introducing Transformational Grammar (Second Edition). Arnold/Oxford University Press. (See p. 461 for the Japanese example.)
5. ^ Neeleman, Ad & Peter Ackema (2002). "Effects of Short-Term Storage in Processing Rightward Movement" In S. Nooteboom et al. (eds.) Storage and Computation in the Language Faculty. Dordrecht: Kluwer. Pages 219-256.
6. ^ Moro, A. 2000 Dynamic Antisymmetry, Linguistic Inquiry Monograph Series 38, MIT press, Cambridge, Massachusetts.
7. ^ Kayne, Richard S. (2010). "Why are there no directionality parameters?" In WCCFL XXVIII. Available on http://ling.auf.net/lingBuzz/001100
8. ^ Kayne, Richard S. (1981) “Unambiguous Paths,” in Robert May and Jan Koster (eds.) Levels of Syntactic Representation. Dordrecht: Kluwer. Pages 143-183