Antisymmetry
Encyclopedia
In linguistics
, antisymmetry is a theory of syntactic
linearization presented in Richard Kayne
's 1994 monograph The Antisymmetry of Syntax. 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.
, c-command being a relation between nodes in a tree
originally 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". 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.
(S and S' may either be simplex structures like BP, or complex structures with specifers 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: {, , }. 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. Furthermore, the underlying order must be specifier-head-complement.
(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.
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).
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:
The Japanese equivalent of this sentence is as follows (note the lack of wh-movement):
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:
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.
) 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. 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.
(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)] 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."
Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....
, antisymmetry is a theory of syntactic
Syntax
In linguistics, syntax is the study of the principles and rules for constructing phrases and sentences in natural languages....
linearization presented in Richard Kayne
Richard Kayne
Richard Stanley Kayne is Professor of Linguistics in the Linguistics Department at New York University.After receiving an A.B. in mathematics from Columbia College, New York in 1964, he studied linguistics at the Massachusetts Institute of Technology, receiving his Ph.D. in 1969...
's 1994 monograph The Antisymmetry of Syntax. 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
Branching (linguistics)
In linguistics, branching is the general tendency towards a given order of words within sentences and smaller grammatical units within sentences...
. The theory derives a version of X-bar theory
X-bar theory
X-bar theory is a component of linguistic theory which attempts to identify syntactic features presumably common to all those human languages that fit in a presupposed framework...
. 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.
Asymmetric c-command
The theory is based on a notion of asymmetric c-commandC-command
In syntax, c-command is a relationship between nodes in parse trees. Originally defined by Tanya Reinhart ,it corresponds to the idea of "siblings and all their descendants" in family trees.-Definition and Example:...
, c-command being a relation between nodes in a tree
Tree (graph theory)
In mathematics, more specifically graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one simple path. In other words, any connected graph without cycles is a tree...
originally defined by Tanya Reinhart
Tanya Reinhart
Tanya Reinhart was an Israeli linguist who wrote frequently on the Israeli-Palestinian conflict. She contributed columns to the Israeli newspaper Yediot Aharonot and longer articles to the CounterPunch, Znet, and Israeli Indymedia websites....
. 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 specifers 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: {
As a result, there is no right adjunction, and hence in practice no rightward movement either. 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 theoryX-bar theory
X-bar theory is a component of linguistic theory which attempts to identify syntactic features presumably common to all those human languages that fit in a presupposed framework...
(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) He argues that there are good empirical grounds for preferring S-H-C as the universal underlying order, since the typologicallyLinguistic typology
Linguistic typology is a subfield of linguistics that studies and classifies languages according to their structural features. Its aim is to describe and explain the common properties and the structural diversity of the world's languages...
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
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
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-movementWh-movement
Wh-movement is a syntactic phenomenon found in many languages around the world, in which interrogative words or phrases show a special word order. Unlike ordinary phrases, such wh-words appear at the beginning of an interrogative clause...
in Japanese
Japanese language
is a language spoken by over 130 million people in Japan and in Japanese emigrant communities. It is a member of the Japonic language family, which has a number of proposed relationships with other languages, none of which has gained wide acceptance among historical linguists .Japanese is an...
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 (note the lack of wh-movement):
-
John-wa nani-o kaimasita ka John-topic_marker what-accusative Accusative caseThe accusative case of a noun is the grammatical case used to mark the direct object of a transitive verb. The same case is used in many languages for the objects of prepositions...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
Auxiliary verb
In linguistics, an auxiliary verb is a verb that gives further semantic or syntactic information about a main or full verb. In English, the extra meaning provided by an auxiliary verb alters the basic meaning of the main verb to make it have one or more of the following functions: passive voice,...
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.
Dynamic Antisymmetry
A weak version of the theory of antisymmetry (Dynamic antisymmetryDynamic antisymmetry
Antisymmetry is a theory of syntactic linearization presented in Richard Kayne's 1994 monograph The Antisymmetry of Syntax. The crux of this theory is that hierarchical structure in natural language maps universally onto a particular surface linearization, namely specifier-head-complement branching...
) has been proposed by Andrea Moro
Andrea Moro
Andrea Moro is an Italian linguist.Moro is currently full professor of general linguistics at the Institute for Advanced Study IUSS Pavia, Italy...
, 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. 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. 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)] 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."