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Chain

**SYNTAX: **a set of syntactic elements subject to specific conditions.
Formally:

(a^{1},...,a^{n}), 1 =< n, is a chain iff
(i) every a has the same subscript, i.e
(a^{1},...,a^{n}) = (a_{j}^{1},...,a_{j}^{n})
(ii) for every i < n, a^{i} **antecedent-govern**s a^{i+1}

Given this definition a^{1} is called the *head* of the chain, a^{n} the *foot*, and each pair (a^{i},a^{i+1}) is a link. The superscripts only serve to distinguish elements which are otherwise identical; so, superscripts are left out in the notation if the elements are not identical. Different kinds of chains are distinguished. A chain is an A-chain if a^{1} is in an **A-position**, and an A-bar-chain if a^{1} is in an **A-bar position**.
Grammatical properties, such as **theta-role**s and Case visibility (**visibility condition**) are properties of maximal chains. A chain is maximal if it contains a **theta-position**. In general, maximal chains are simply called chains.
** EXAMPLE:** in (i) both (*John*_{i}, t_{i}) and (*the car*_{j}) are A-chains. The chain (*John*_{i}, ti) consists of one link, *John*_{i} being the head and t_{i} being the foot. The chain (*the car*_{j}) has no link, and *the car*_{j} is both its head and its foot.

(i) John_{i} was hit t_{i} by the car_{j}
(ii) Who_{i} t_{i}^{1} seems t_{i}^{2} to have been hit t_{i}^{3} by the car_{j}

In (ii), the chain (*who*_{i}, t_{i}^{1}, t_{i}^{2}, t_{i}^{3}) is an A-bar-chain, since the head *who*_{i} is in an A-bar-position. The foot (i.e. t_{i}^{3}) of this chain is theta-marked (by *hit*). The element t_{1} is case marked (by the matrix INFL).
Hence, the chain satisfies the **case filter** and the **theta criterion**. The A-chain (t_{i}^{1}, t_{i}^{2}) is an example of a non-maximal chain, since this chain, being part of the maximal chain (*who*_{i}, t_{i}^{1}, t_{i}^{2}, t_{i}^{3}) contains no theta-position.
Also see **CHAIN** and **chain composition**.