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<Paper uid="W01-0805">
  <Title>A Meta-Algorithm for the Generation of Referring Expressions</Title>
  <Section position="6" start_page="0" end_page="0" type="concl">
    <SectionTitle>
5 Concluding remarks
</SectionTitle>
    <Paragraph position="0"> In this paper, we have presented a general graph-theoretical approach to content-determination for referring expressions. The basic algorithm has clear computational properties: it is NP complete, but there exist various modifications (a ban on non-looping edges, planar graphs, upper bound to the number of edges in a distinguishing graph) which make the algorithm polynomial. The algorithm is fully implemented. The graph perspective has a number of attractive properties. The generation of relational descriptions is straightforward; the problems which plague some other algorithms for the generation of relational descriptions do not arise. The use of cost functions allows us to model different search methods, each restricting the search space in its own way. By defining cost functions in different ways, we can model and extend various well-known algorithms from the literature such as the Full Brevity Algorithm and the Incremental Algorithm. In addition, the use of cost functions paves the way for integrating statistical information directly in the generation process.a30 Various important ingredients of other generation algorithms can be captured in the algorithm proposed here as well. For instance, Horacek (1997) points out that an algorithm should not collect a set of properties which cannot be realized given the constraints of the grammar. This problem can be solved, following Horacek's suggestion, by slightly modifying the algorithm in such a way that for each potential edge it is immediately investigated whether it can expressed by the realizer. Van Deemter's (2000) proposal to generate (distributional) distinguishing plural descripa39 null A final advantage of the graph model certainly deserves further investigation is the following. We can look at a graph such as that in Figure 2 as a Kripke model. The advantage of this way of looking at it, is that we can use tools from modal logic to reason about these structures. For example, we can reformulate the problem of determining the content of a distinguishing description in terms of hybrid logic (see e.g., Blackburn 2000) as follows:  In words: when we want to refer to node a235 , we are looking for that distinguishing formula a230 which is true of (&amp;quot;at&amp;quot;) a235 but not of any a233 different from a235 . One advantage of this perspective is that logical properties which are usually considered problematic from a generation perspective (such as not having a certain property), fit in very well with the logical perspective. tions (such as the dogs) can also be modelled quite easily. Van Deemter's algorithm takes as input a set of objects, which in our case, translates into a set of nodes from the scene graph. The algorithm should be reformulated in such a way that it tries to generate a subgraph which can refer to each of the nodes in the set, but not to any of the nodes in the scene graph outside this set. Krahmer &amp; Theune (1999) present an extension of the Incremental Algorithm which takes context into account. They argue that an object which has been mentioned in the recent context is somehow salient, and hence can be referred to using fewer properties. This is modelled by assigning salience weights to objects (basically using a version of Centering Theory (Grosz et al. 1995) augmented with a recency effect), and by defining the set of distractors as the set of objects with a salience weight higher or equal than that of the target object. In terms of the graph-theoretical framework, one can easily imagine assigning salience weights to the nodes in the scene graph, and restricting the distractor set essentially as Krahmer &amp; Theune do. In this way, distinguishing graphs for salient objects will generally be smaller than those of non-salient objects.</Paragraph>
  </Section>
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