Getting beyond the link primitive:
Expressing textual structures
in terms of link structures
Paul Rohr
Nov. 13, 1991
Chunk Models [me... M85]
"Chunky" models of hypertext can be ranked by their structural
complexity.
| The simplest "chunky" model of hypertext allows only node-to-node
links. All you get are chunks of text and links between them.
Thus the tendency is to fragment your information as much as possible,
using links to represent all structural relationships.
Example: HyperCard
| 
|
| A slightly more complex model allows for point-to-node links.
Here, specific spans of text within nodes are allowed as source-points
for links.
This allows for somewhat larger nodes, and for a partial ordering of
information. (Each point expands to a larger chunk.)
Example: Storyspace
| 
|
| The next most complex model allows for point-to-point links. Here,
the destination as well as the source can be a point.
By implication, this model can derive a reduction to the first one,
since there is an implicit (albeit far less detailed) relationship
between chunks which are the site of linked points.
Example: InterMedia
| 
|
Linearity [me... L2]
Hypertext is often touted for its ability to work against the
"linearity" of text. In other words, there is a preconceptual notion
that text is a linear sequence (or string) of words.
"Chunky" theorists represent the conceptual complexity of the discrete
ideas woven into that "sequence" by chopping it up into smaller, more
manageable chunks of text, and then explicitly re-linking them. The
chunks all remain (locally) linear, but they're each folded up into a
separate node and linked together.
Thus, for "chunky" theorists, the chief problem is to decide how to
divide up long strings of text into shorter ones whose linearity is not
a problem. This is known as the "fragmentation problem".
For large amounts of text, this choice of element granularity can
become very important, since it becomes increasingly difficult to find
one's way around in larger and larger spaces of such locally-linked
chunks. This is known as the "disorientation problem", and is endemic
to collections of data whose mass of detail greatly outstrips the
amount of general information available for structuring, arranging, and
locating specific instances -- whether in relation to one another or to
those larger referential structures.
Unfortunately, at this (low) level of theoretical complexity there's
simply not that much structure around to use as a lever. Basically, you
have three structural elements to work with: nodes, links, and
node-link interactions. The first two can be named and/or assigned to
known classes of types, information which can then be used (via
querying) to group similar nodes, and filter out unwanted ones. On the
other hand, node-link interactions can be used to either generate maps
and overviews (both locally and more generally) or to calculate
proximity measures of the clustering of and distance between nodes.
Finally, any text affiliated with any such structures can also be the
subject of free-text searches for occurrences of various words or
phrases (another kind of filtering).
However, even in combination, these structures just don't provide all
that much leverage for navigating large populations of chunked
information.
Creamy Models [DeRose, Durand 87]
In contrast, "creamy" theorists insist that the problem is that there's
simply too much "chunking" going on. Instead, they tend to focus on how
to retain the structural power of large expanses of text --
particularly as presented in the highly-evolved formats of printed
books and scholarly articles.
In other words, "creamy" models assert that the "largest natural unit"
of text is the document, and it must be represented at that level
directly, as well as being broken down into smaller substructures.
OHCO [DeRose, Durand, Mylonas, Renear 90]
Although these substructures could be though of as also occurring in
sequence -- thus forming a "chunkier" sort of "linearity" -- a typical
"creamy" theorist instead emphasizes the presence of other sorts of
structures, and especially hierarchies.
In the terminology of the two papers cited, a document is an Ordered
Hierarchy of Content Objects (OHCO), a term which is intended to
suggest how the linear sequence of textual exposition (at the bottom)
is an ordered traversal of the hierarchy (above it).
Note the reciprocal relationship between segmentation and aggregation
here.
Implicit in the notion of a hierarchy is the ability to "roll up"
smaller substructures to higher levels of aggregation, thus affecting
the level of granularity of segmentation.
Likewise, an equivalent transformation yields:
Note, however, that these transformations can be derived as an
algorithmic result of the overall structure, and thus need not be
explicitly stored.
As always, the storage-vs-recalculate tradeoff will depend on the
particular speed and cost of available resources.
Beyond Creamy [me... M83]
The "creamy" doctrine that texts should be represented as full documents
can be extended in a number of ways. After all, the composition or
aggregation links used to indicate internal hierarchical structure
within texts are not the only sorts of links possible.
Indeed, the most hypertextual of these are the external links between
documents, in the forms of citation and allusion (among others).
Once again, there is an implicit ability to aggregate here, reducing the
detail of numerous point-to-point links to a composite text-to-text
link.
Knots [Harpold 91]
However, contemporary theorists of textuality understand these
intertextual (or transtextual, depending on the theorist) relationships
in a somewhat different -- and perhaps more radically hypertextual --
way. Instead of thinking of individual texts as distantly separate
chunks which are connected by thin links, they might choose to think of
each text as a winding thread of discourse which is only locally linear
(in its exposition) and which crosses other textual threads from time
to time.
Harpold refers to the (potentially tangled) site of this crossing as a
"knot".
Threads [me... L2]
In the very simplest class of texts, there may be only one such crossing
of any two textual threads, although any single text probably crosses a
number of others. For example, conventional scholarly articles often
include an initial section which reviews and summarizes prior results
on a given problem, with a brief gloss for each citation.
When the author is only interested in the main results of an article,
she may choose to cite the entire thing, or she may refer to a specific
aspect of that work, localizing the citation to a particular portion of
the article.
However, the supposedly rigid "linearity" of these threads comes into
question as soon as multiple citations of the same work are allowed.
In such a case, there is no way to think of both threads (that of the
text and that of the subtext) as being simultaneously linear. Depending
on the reader's perspective, one of the threads may be thought of as
linear, but this necessarily implies that all other threads entangled
with it are not.
Note that in this example, the order of the cited spans is the same in
both texts. While this assumption simplifies the picture, in the more
general case we often find the order of exposition varying greatly
between text and subtext -- even in the most faithful of close
readings! (Indeed, this variation is one of the chief advantages of
such readings.)
Imagine, then, the complex "geometry" of any text in which a number of
such threads are interwoven, and the conclusion becomes obvious: only
within the immediate locale of a particular interaction can any two
threads be considered simultaneously linear.
Zones [me... M33]
Of course, there are many other sorts of links besides citations and
allusions. For example, anything which might be indexed can be treated
as a link, since there is both a source (the index entry) and a
destination (the occurrence of the indexed feature within the text).
Each individual link points to a specific span of text, and it's
important to specify such links and spans at the smallest applicable
level of granularity. Still, the usefulness of any individual link,
considered in isolation, is confined to the simple operation of
following it. In contrast, if we consider the more complex structures
which can be built up out of links, then far more powerful operations
become possible.
As the diagram indicates, link structures can divided into two general
classes, "threads" of occurrences and schemes of "zones", depending on
how they cover the text. Generalizing the notion introduced in previous
pages, we define a thread as a sparse set of discrete occurrences --
specified in terms of textual spans -- which have something in common.
From another perspective, a thread can be seen as a set of links from a
shared feature (in the analogy above, the indexed term) to its various
occurrences. Note that aggregate collections of threads (for example,
all terms in a domain) also form threads, albeit less sparse ones.
Alternatively, we can obtain a different sort of link structure by
dividing a text up into a series of contiguous zones which completely
cover it. Here, each zone is a span of text, labeled according to some
classification scheme.
Zone Schemes [me... K41]
Threads and zone-schemes can both be thought of as ordered aggregations
of a set of linked spans. However, there the resemblance ends. Whereas
each occurrence on a single thread points to the same shared
description (at some level), zone-schemes are more complex. Of course,
each zone is a span of text with a label linked to it, but it would be
senseless for all zones in a scheme to point to the same label. (A
zone-scheme covers the entire text, which implies that the entire text
would be covered with spans all pointing to the same label. In other
words, there would only be one zone, spanning the length of the text,
which in no way discriminates particular locations within the text.)
Thus, we can further classify zone-schemes by the systematicity of
their zone-labelling.
On the one hand, we can have a consistent set of alternating zones which
cover the text in an intermittent fashion. Within such a zone-scheme,
recurrences of any single zone could also be thought of as an isolated
thread. Still, in the aggregate structure formed by merging the entire
set of related zones, this thread-like nature disappears into the
mosaic of the overall pattern.
On the other hand, if zones don't recur, but follow one after another
in continuous sequence, then we get a quite different kind of
zone-scheme. Here we find that a number of continuous zone-schemes can
be specified at different levels of granularity, and synchronized to
form a hierarchy. Unlike the intermittent case, continuous zone-schemes
thus decompose directly into either links or other continuous
zone-schemes, rather than threads.
That having been said, we should also note that arbitrary sets of (less
organized) zones can, in principle, be treated as (dense) threads.
Algebra [me... M86]
As the partial taxonomy on the previous page indicates, there are a
wide range of embedded and interpretive textual structures which can be
expressed in terms of the "thread" and "zone" link-structures. With
those distinctions and examples in mind, we can now proceed to briefly
examine the structural interactions supported by such a system.
Insofar as threads are sets of occurrences of textual features, they
are amenable to common set operations (union, intersection). However,
the applicability of these operations is restricted by the fact that
they presuppose an ability to discretely identify equivalent
occurrences when deciding whether to include them in the resulting set.
Since the occurrences in question are actually spans of arbitrary
length, then in most cases the less strict -- and equally less familiar
-- segment operations (overlap, containment) will need to be
substituted for the usual equality condition. In other words, strict
set operations can only be reliably used to add and remove occurrences
from related threads, since otherwise, there is no simple guarantee
that spans on the two threads will be either exactly equivalent or
completely disjoint.
Likewise, these less strict forms of intersection can be applied to
zone-schemes, as well as threads. While overlap operations on pairs of
threads, zone-schemes, or any combination thereof always result in
either an empty set or a thread (as per the note at the bottom of page
8), it is necessary to specify the desired level of granularity of that
resulting thread. The analogous requirement for containment operations
is even stricter, since that operation -- no matter how it's defined --
is implicitly *not* symmetric.
Finally, the directed operations (expansion, refinement) can be used to
translate any thread in terms of any zone-scheme, thus changing the
density of the thread.
[me... K42]
Since a full formal presentation of all of this material still remains
to be worked out, the following assertions are offered without
proof:
According to the presentation above, the following assertions are false,
but they suggest that another operation may be needed:
[Raymond, Tompa 88]
When compared with current "chunky" link-based hypertexts, the full-scale texts
that scholars work with every day provide a much richer mix of structural cues
and hooks for manipulating them. Anyone who hopes to supplement -- or, indeed,
eventually supplant -- paper texts with electronic versions and variants thereof
should, of course, plan to provide additional functionality in the new medium
(such as active links) which current media and methods cannot easily supply. Yet
first these same designers must ensure that in the process of enhancing existing
texts and textual methods their current level of functionality is not destroyed
or degraded. Clearly the radical expedient of chunking and re-linking texts will
have trouble satisfying this standard.
[me ... BA paper, section 3, a lot fuzzier]
My argument here and elsewhere has been that (1) the link primitive
itself can only go so far to ameliorate this problem, (2) direct
segmentation of the text in any form is equally problematic, and (3)
the abstract link structures described here can be implemented
externally, by means of the span abstraction, in a sufficiently
non-destructive and flexible way ...
... provided a suitable index structure [cf. Bentley, McCreight, and
Chazelle] can be found to support that abstraction.
In addition, this approach has the decided advantage of maintaining the
"smoothness" of any "locale" in the text, while constantly allowing the
reader to expand, explore, and refine the inter-related details of any
number of threaded contexts....
[me... M83]
As the partial taxonomy on the previous page indicates, there are a
wide range of embedded and interpretive textual structures which can be
expressed in terms of the "thread" and "zone" link-structures. It is
important to remember that these structures are built up out of links,
because this allows them to be completely removed from the body of the
text, yet re-applied as needed. Once a canonical span abstraction has
been defined (such as the one described in my BA paper), the link
anchors no longer need to be embedded in the text. Thus, an arbitrary
number and variety of link structures can be separately defined in
relation to a given text or set of texts, with specific structures then
"layered over" various locales of the text(s) as needed.
The rich interaction of such structures is what makes the TextBase
environment so powerful.
In the simplest case,
Although there is quite a bit of coordination within an individual instance
of either class of zone-schemes, the same is not true for the interaction
of different zone-schemes. The requirement of consistency no longer applies
(dominates) outside these structures. Overlaps, rather than strict
containments, are the rule.
In principle, any two intermittent zone-schemes will clash, as will any two
hierarchies of continuous zones. However, this is a good thing.
The actual interaction of a number of different structures, classifications,
etc. is what forms the detailed context of any given region in the text.
...