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4.3.1 Structuring links

The hyperlinks that nowadays proliferate on the World Wide Web provide a conduit for easy navigation between hypernodes. However, they do not supply any information about the relation between the nodes. In the modular model, links not only establish a `physical' connection between modules, but they also make explicit different types of relations between the information units represented in the modules.

The idea of characterising links has already been brought up in the early work of e.g. Trigg [Trigg, 1983], who proposed a concrete, fine-grained classification of hyperlinks for `normal links' connecting the nodes of scientific articles and `commentary links' connecting statements about a node to the node itself. His approach is rather phenomenological. In another early work, De Rose has given an abstract taxonomy of a wide range of explicit and implicit types of links, that ``differ not only in purpose, but in structure, function and preferred means of implementation" [De Rose, 1989, p.250]. His taxonomy is rather coarse-grained.

In this work, we try to establish a systematic, fine-grained typology for links between the different types of modules defined in the previous, in which the classes of relation we identified the corpus articles are taken into account. An appropriate characterisation of the links enables readers to make a well-considered choice as to whether or not to follow the link, and also enables them to take the links into account in the process of locating and retrieving relevant information. Links are, firstly, characterised by the relations they express. According to the modular model, each link can simultaneously represent one or more different types of relations, and therefore each link can carry a full characterisation including of one or more different labels. Secondly, a link has a particular source and target. Thirdly, each link is also characterised by well-defined meta-information, such as the name of its author and the date it was created. Consequently, both modules and links are uniquely characterised `information objects' that can be manipulated using database management and retrieval techniques. This ensures the authenticity and priority of each `information object' when new links or modules are added to published work. In our analysis, we have only considered links created by the authors when they write the article, so that the bibliographic data about the link coincide with the data about the modules they connect. Therefore we have left the characterisation of the links by the meta-information implicit. In the following, we shall consider the sources and targets of links, and their characterisation by the relations they express.

A link is a directed connection leading from a source to a target, where the source and the target can consist of: 

The source and target of a link do not have to be of the same type.        
Figure 4.5: A link, between two segments of modules, representing three relations:
a) an elucidation relation between those segments,
b) a range-based relation between the entire modules and
c) a problem-solving dependency relation between the information units underlying the entire modules

The link types we distinguish are reversible: the links can be followed in the opposite direction by way of the explicit reverse of the link. In the case of symmetric links, the type of the link itself coincides with the type of its reverse. For instance, a link expressing the fact that two connected modules are part of the same article has the same meaning when followed in both directions. Asymmetric link types have the opposite meaning when followed in the opposite direction. An example of an asymmetric link is a link expressing the fact that the source module is a constituent module part of a complex target module; the reverse link then expresses the fact that the target contains the source.4.24

A single link can represent more than one relation. In figure 4.5, we illustrate this with an example of a source (a particular figure in a microscopic Treated results module) and a target (a particular paragraph in a mesoscopic module Theoretical methods dealing with the techniques for data analysis and treatment) that are connected by means of a link, in which the following relations are expressed. In the first place, the link expresses the fact that in the target of the link an elucidation is given of the source. In the second place, the fact is expressed that the results presented in the figure depend on the methods described in that Theoretical methods module. And in the third place, the link expresses the fact that the mesoscopic module has a wider range than the microscopic module.4.25

A relation is identified between `relata'.  Each relatum of such a relation can be:4.26

The relata of a particular relation each are either `real world' entities, conceptual representations, or symbolic representations. One of the relata can be (or be represented in) a module as a whole, whereas the other one is (or represents) only a segment of a module. The relata can also be different types of representation, e.g. a text and a figure.

[To the full figure] Figure 4.6: How can the source of a link correspond to the `source relatum' of a relation represented in that link: a) the source coincides with the relatum, b) the source is part of the relatum, c) the source represents the relatum, d) the source is a part of the representation of the relatum. However, e) the source cannot contain the relatum, and f) the source cannot contain a representation of the relatum either.

Now, let us examine how the source and target of a particular link can be associated to the various relata of the relations represented in that link. For simplicity, we concentrate our discussion on one end of the link, namely the source of the link and the corresponding source relata of the particular relations represented in that link. The following situations can arise (an overview is given in figure 4.6).

Both the source of the link and the source relatum are the same module (or the same segment of a module). In that case, the source coincides with a relatum, as is illustrated in figure 4.6a.

For example, as the information represented in a particular microscopic  module differs in range from the information in a mesoscopic  module, a range-based relation can be identified between the entire modules (as the relata). A link is created between the modules (as a whole) to express this relation. In this case, the source and the target of the link coincide with the relata of the expressed relation.

The source of the link is a particular segment of a module and the source relatum is the entire module. In that case the source is a part of the relatum (figure 4.6b).

Consider, for instance, a link created between a particular sentence in one module (source of the link) and a paragraph in another (target) to provide the required elucidation of that source sentence. Suppose that the module containing the source sentence is a microscopic module and the one containing the target paragraph a mesoscopic one. Then the link should also express the range-based relation between those modules. As the source relatum for the range-based relation is the entire module, the source of the link is part of the source relatum of the range-based relation.

The source of the link is an entire module (or a segment of a module), and the relatum is 1) the information unit underlying that module (or segment of a module; see figure 4.6c1), or 2) an entity addressed in that module (or segment of a module; see figure 4.6c2). In these cases, the source represents the relatum.

Suppose that the microscopic and mesoscopic module in our example represent respectively results and the experimental methods used to generate them. A link between the two modules expresses the problem-solving dependency relation between the results and the methods as `real world' entities. In that case, the source of the link is a representation of the source relatum of the dependency relation.

The source is a particular segment of a module, and the relatum is 1) the information unit underlying that module as a whole (figure 4.6d1) , or 2) an entity addressed in that module as a whole (figure 4.6d2). In these cases, the source is a part of a representation of the relatum.

An example of such a case is a link connecting at one end the error bars in a particular figure, and at the other end, the specific paragraph about the restrictions of the experimental results. This link expresses a problem-solving dependency relation between the entire results and the entire experimental methods. Thus the source of the link (the error bars in the particular figure) is a part of the representation of the source relatum (the results).

The source cannot contain the relatum (figure 4.6e) or a representation of the relatum (figure 4.6f), because then the anchor of the link would be underspecified. For instance, a link connecting two modules cannot express a relation between two particular sentences in those modules. If a relation is identified between more specific relata, that relation has to be expressed in a (new) link connecting a more specific source and target.

Figure 4.6: Labelling a link S $\to $ T and its reverse T $\to $ S: the target module T is a constituent module of the source module S, that provides more details and is the next step in the sequential route

As we characterise the links from different angles, corresponding to the different relations that can be identified, the typology for the links is multidimensional, like the typology for the modules. Visualising the geometry of such a characterisation space, the relation can be associated with a `label' along the positive axis, the reverse along the negative axis, and the origin would provide a default for `neutral' type of relations, for example expressing the fact that neither one of two connected modules contains the other. A relation can be of only one type, but a link between modules can represent different, complementary relations and thus carry labels that correspond to different, complementary characterisation dimensions . As in the case of the characterisation of the information, a multidimensional characterisation space can be visualised, in which the complete type of a link is determined by its position in the characterisation space, or in other words, by the values of the co-ordinates corresponding to the characterisation dimensions. An example of the characterisation of a link is given in figure 4.7.

We restrict ourselves to links that are made explicit in the article, in particular, the links put in place by authors of modular articles. De Rose calls these links `extensional', as opposed to `intensional' links that only implicitly connect a source to a target, e.g. by invoking a search. A valuable asset of an electronic, modular publishing environment for instance, would be a `dictionary' or `encyclopaedia' with standard definitions, providing a background for less informed readers. The links to such a dictionary do not have to be hardwired in the modules: the reader can extract the term he is unfamiliar with and feed it into a dictionary search engine, by means of an (in De Rose's terminology intensional vocative) implicit link or an (intensional) retrieval link. The intensional link types can play a role in actual modular articles. These links, however, are not part of the model for the writing of modular articles, because they are reader-driven and are generated on demand. Trigg's `commentary links' [Trigg, 1983], which are related to De Rose's annotational links, are not taken into account either, because the model concentrates on articles and not on comments on articles,. Taking into account such other categories of links can lead to additional components of the modular model

Our modular model distinguishes two basic kinds of relations that are represented in links.  Firstly, organisational relations refer to the organisation of the article. The relata of an organisational relation are (in all cases but one) entire modules, without reference to their content. A link representing such a relation can express, for example, the fact that the connected modules are part of the same article. Different kinds of organisational relations are introduced in section 4.3.2.  Secondly, links representing scientific discourse relations express how the elements of the scientific  discourse in the modules, the information units underlying them, and the entities they refer to are related. Different kinds of these relations are presented in section

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