We translate the text summarization task into a problem of extracting a set of dependency subtrees in the document cluster.

Let V be the finite set of all valid subtrees in the source documents, where valid subtrees are defined to be the ones that can be regarded as grammatical sentences.

In this paper, we regard subtrees containing the root node of the sentence as valid.

Accordingly, V denotes a set of all rooted subtrees in all sentences.

In this study, we avoid this difficulty by reducing the task to one of extracting dependency subtrees from sentences in the source documents.

The reduction replaces the difficulty of numerous linear constraints with another difficulty wherein two subtrees can share the same word to-

ken when they are selected from the same sentence, and as a result, the cost of the union of the two subtrees is not always the mere sum of their costs.

In effect, since we have hypothesized that the presence of a connective can affect the translation of the two subtrees that it connects, we would like to be able to align each of those subtrees to its translation.

We make the observation that, if two words belong to two different subtrees linked by a connective, so that the path between the two words goes through the connective, then the frontier between the LIS counterparts of those two subtrees should also lie along the path between the signs aligned with those two words.

Then, each pair of words belonging to different subtrees is linked by a path that goes through the connective in the original tree.

Similar to the syntax component, the REG module is implemented as a ranker that selects surface RE subtrees for a given referential slot in a deep or shallow dependency tree.

In the final representation of our data set, we integrate the RE and deep syntax annotation by replacing subtrees corresponding to an RE span.

All RE subtrees for a referent in a text are collected in a candidate list which is initialized with three default RES: (i) a pronoun, (ii) a default nominal (e. g. “the Victim”), (iii) the empty RE.

In contrast to the GREC data sets, our RE candidates are not represented as the original surface strings, but as non-linearized subtrees .

5b): (i) they are equivalent to h1(a) and h2(a), respectively, and (ii) at each node at most two subtrees contain variables.

The variable set of t is the set of all variables that occur in t. The set S(t) of subtree variables of 75 consists of the nonempty variable sets of all subtrees of t. We represent S(t) as a tree v(t), which we call variable tree as follows.

at most two subtrees with variables; and (iii) the terms t1, .

Our hypothesis is a generalization of the original hypothesis since it allows a reducible sequence to form several adjacent subtrees .

Our dependency model contained a submodel which directly prioritized subtrees that form reducible sequences of POS tags.

Or, in terms of dependency structure: A reducible sequence consists of one or more adjacent subtrees .