Rosetta Stone v20-Annals of the Association of American Geographers

66 Pages·2011·1.67 MB·English

Accepted by: Annals of the Association of American Geographers

Spatial Information Theory Meets Spatial Thinking - Is Topology the Rosetta Stone
of Spatial Cognition?

Alexander Klippel
Abstract. Topology is the most commonly used spatial construct to bridge the gap
between formal spatial information theory and systems on the one side and (human)
spatial cognition and thinking on the other. To this end, we find topological calculi in
virtually all research areas pertinent to spatial information science such as ontological
modeling, geographic information retrieval, image analysis and classification. Manifold
experiments have been conducted to assess the cognitive adequacy of topological calculi
with varying results. Our contribution here is unique for two reasons: on the one hand, we
are addressing, behaviorally, the role of topology in the crucial area of spatio-temporal
information; on the other hand, we are evaluating the role of topology across different
semantic domains. We report five experiments that were conducted in the framework we
developed (Klippel and Li 2009), which combine critical constructs from spatial
information theory and cognitive science. Topologically equivalent movement patterns
were specified across five domains using paths through a conceptual neighborhood graph.
This approach allows us to disentangle the role of topology from the influence of
semantic context. The results show that topology plays an important yet not semantic-
independent role in characterizing the cognitive conceptualization of geographic events.

Keywords: Qualitative spatial reasoning, spatio-temporal information, spatial cognition;
conceptual neighborhood graphs.
Introduction
Spatial information science (SIS) has developed qualitative formalisms to represent and
reason with spatial information. A large number of these research efforts explicitly target
the gap that exists between the requirements of formal symbol processing systems (e.g., a
computer) and those of natural cognitive systems (e.g., humans) for understanding and
interacting with information (Hobbs and Moore 1985; Worboys, Duckham, and Kulik
2005; Kurata and Egenhofer 2009). In a society in which computers are ubiquitous and in
which ambient intelligence is gaining central importance (Gottfried and Aghajan 2009),
the seamless interaction and integration of computational and cognitive systems is a
vision, dream, and challenge at the same time. But how do we cognitively ground
qualitative formalisms?
An important aspect to understand for those seeking to cognitively ground
qualitative formalisms is that humans are embedded in their spatial environments, and
understanding and formally characterizing how humans process spatial information is
essential to improving spatial information theories and systems. An equally important
point is that through embodied interactions with spatial environments, humans develop
fundamental concepts that enable their comprehension of more abstract concepts such as
time. Spatial is special and while SIS and geography are the primary disciplines to
acknowledge this, several disciplines such as the cognitive sciences have given space a
prominent role in their theoretical frameworks (Cohen 1985; Carlson, Hölscher, and
Shipley 2011).
The role that SIS plays is twofold: on the one hand, SIS integrates research on
how humans understand their spatial environments into its theories; on the other hand,
SIS provides theories that help to formally explain what is meant when other disciplines
refer to space and spatial relations. This article addresses formal theories centering on
topology, the most commonly used approach to establish cognitive adequacy for spatial
information theories. It is crucial to note that psychologists, linguists and cognitive
scientists acknowledge the importance of topology as probably the single most important
spatial concept fundamental to cognition in general, not just spatial cognition (Piaget
1955; Klix 1971; Johnson 1987; Lakoff 1987; Jackendoff and Landau 1992; Mandler
1992; Bowerman 2007). Klix (1971) pointed out that one of the reasons contributing to
the centrality of topology is that a topological characterization allows for naming
invariants that can be identified in spatial environments both formally and from the
perspective of cognitive information processing. But, what exactly is meant when
cognitive scientists talk about topology? To unleash the full potential that SIS has in
explaining spatial cognitive processes, novel techniques for experimental designs
(behavioral/cognitive evaluations) and analysis techniques that allow for relating
cognitive and formal perspectives more directly are needed.
It is important to acknowledge and harvest the potential of SIS: On the basis of
formal theories we can render notions of spatial information (such as topology) precise
enough to formulate testable hypotheses. In other words, we can design tailored and
precise experiments that are critical to understanding human spatial cognition. In return,
theories in SIS will be evaluated and the often-used label, cognitively adequate, becomes
more meaningful.
The problem, simply put, is that formal qualitative characterizations of a spatial
environment are by default claimed to be cognitively adequate, that is, they are capturing
spatial aspects important to a cognitive system on the assumption that qualitative =
cognitive. Of course, as part of humans’ common sense knowledge (Hobbs and Moore
1985; Davis 1990; Egenhofer and Mark 1995b, 1995b; Worboys, Duckham, and Kulik
2005), humans think about the world largely qualitatively, not quantitatively. However,
the assumption that, from a formal perspective, everything qualitative equals cognitive is
not scientifically defensible. Hence, the main problem from the perspective of this article
is that for the most part, qualitative formalisms escape the scrutiny of
behavioral/cognitive validation. One of the most often found concluding remarks in
articles that develop qualitative formalisms is that human participant experiments are
needed to validate the proposed formalism. Such follow-up studies almost never happen.
There are a few noteworthy exceptions especially in the area of validating
topological calculi. First and foremost the extensive work by Mark and Egenhofer (Mark
and Egenhofer 1994a, 1994b; Shariff, Egenhofer, and Mark 1998; Mark 1999) that
addressed the validity of Egenhofer’s 9-intersection model as a framework to model the
cognitive understanding of spatial relations. In their research they coined the famous
expression: topology matters and metric refines. In summary, their findings assign
topology the most prominent role in a high-level, conceptual understanding of spatial
relations. The example domain they focused on is a road (statically represented by a line)
and a park. Other studies that come to similar conclusions, that is, that topology is crucial
for modeling the cognitive understanding of spatial relations were conducted by Knauff
and collaborators (1997), Zhan (2002), Riedemann (2005), Xu (2007) and Wang and
collaborators (2008). Additionally, we find related research on Allen’s relations (Allen
1983) that complementarily addresses the role of qualitative temporal characterizations
(Lu, Harter, and Graesser 2009; Matsakis, Wawrzyniak, and Ni 2010).
The following aspects are important to observe in the above mentioned
experimental validations: First, many of them use abstract geometric figures as stimuli
rather than real world scenarios. In case they do use real world scenarios the scope is
limited to one particular scenario. Second, with the exception of Lu and collaborators, the
stimuli used in the above mentioned experiments are static, even though they may be
seen as dynamic phenomena.
Using abstract geometric figures ignores findings from cognitive science that
there is an interplay between bottom-up and top-down information processing (Neisser
1976; Zacks 2004). In other words, taking domain semantics into account may change the
invariants in a spatial environment identified by a cognitive system. The approach to
incorporate both top-down and bottom-up characteristics also corresponds to the rapidly
developing area of assessing and formalizing contextual effects (e.g., Dey 2001; Cai in
press) that we will not further discuss here.

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Figure 1
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To further illustrate this aspect, Figure 1 demonstrates this incongruity by
employing the Rosetta Stone as an example. The Rosetta Stone is seen as one of the most
crucial artifacts in human history for deciphering Egyptian writing. The beauty of the
stone is that it bears three translations of the same passage of “a decree issued at
Memphis, Egypt in 196 BC on behalf of King Ptolemy V.” (Wikipedia, retrieved April
21st 2011): one is the relatively well-known classic Greek, the others (hieroglyphic and
Demotic) were able to be deciphered based on their correspondence to the Greek passage.
Figure 1 shows the Rosetta Stone overlaid with a topology-based conceptual
neighborhood graph (CNG) (Egenhofer and Al-Taha 1992; Freksa 1992). CNGs are
graph structures based on qualitative spatial and temporal formalisms. They were first
proposed for Allen's (1983) temporal intervals by Freksa (1992) and were quickly
adapted to corresponding qualitative spatial calculi (Egenhofer & Al-Taha, 1992; Muller,
1998). Conceptual neighbors are defined as two relations (e.g., disconnected, DC, and
externally connected, EC) that can be directly transformed into one another by
continuous topological transformations such as shortening, lengthening, or moving
(translation). The importance of CNGs come from the fact that virtually all qualitative
calculi that specify jointly exhaustive and pairwise disjoint (JEPD) relations have
conceptual neighborhood graphs (see Cohn and Renz 2008).
In Figure 1, the Rosetta Stone/CNG is surrounded by depictions of trajectories of
moving entities from different semantic domains. This example illustrates what has been
discussed in the preceding section regarding the invariants in spatial cognition and the
importance of topology: each of these trajectories, as different as they may be from the
perspective of Euclidean metric, speed, or background knowledge (semantics), is
identical from a topological perspective. That is, if we apply a topological
characterization (Fernyhough, Cohn, and Hogg 2000; Galton 2000; Muller 2002; Kurata
and Egenhofer 2009), all trajectories are topologically equivalent (identical paths through
the conceptual neighborhood graph)—from a topological perspective they are invariant.
While this approach potentially formalizes the semantics of spatial expressions such as
the verb cross or the preposition across, the critical question is if the trajectories are
indeed all meaningful in the same way (in all semantic domains), and whether they have
the same meaningful, topologically identified subparts. To make the analogy to the
Rosetta Stone, can topology (as the Rosetta Stone) be used to translate between
movement patterns from different semantic domains? That is, are topological relations
equally important and are topologically identified invariants universal across semantic
domains?
If topology were indeed the Rosetta Stone of Spatial Cognition (including the
conceptualization of movement patterns), this paper would end here. However, the
number of formalisms for topology alone is already diverse and debated within SIS and
associated areas of artificial intelligence. For example, the two most often quoted
frameworks for characterizing the relationship between two spatially extended entities,
the region connection calculus (Randell, Cui, and Cohn 1992) and the 4- and 9-
intersection models (4IM / 9IM) (Egenhofer and Franzosa 1991), offer two levels of
granularity distinguishing either eight or five topological relations. It is important to note
that while the fine levels of granularity match and make the same distinctions, the coarse
levels of granularity do not (for details see Discussion Section). In a similar vein,
Clementini et al. (1993) deemed the eight topological relations distinguished in 4IM/9IM
as cognitively inadequate and developed their own model with five topological relations
that they claimed are better suited to user requirements. The model allows for the
incorporation of objects of one or two dimensions. If we follow a recent proposal by
Kurata and Egenhofer (2007; 2009) formalizing the relation between a trajectory and a
region, we have to distinguish 26 primitive relations. The authors discuss approaches to
reduce this number (e.g., Wang, Luo, and Xu 2004, see also Klippel in press).
These are only a few examples of developments of topology-based calculi that
claim (some more, some less) cognitive adequacy. In several of them, the importance of
behavioral user studies is pointed out, but follow up studies are often missing. In this
paper, we discuss five experiments that we designed to shed light on three neglected
questions of how domain semantics influences the role that topology plays as a tool to
model the cognitive conceptualization of movement patterns, whether topological
relations are equally salient in different domains, and what cognitively adequate
topological invariants of movement conceptualization are.

Experiments
Over the past five years we have developed a research framework that allows for the
assessment of the category construction (conceptualization) of geographic (and other)
movement patterns, that is, geographic events. This framework consists of a variety of
tools that allow for conducting behavioral research more efficiently to proof, test, or
augment the cognitive adequacy of formal spatial calculi. Our approach extends work by
Mark and Egenhofer (e.g., Mark and Egenhofer 1994a; Shariff, Egenhofer, and Mark
1998) and Knauff and collaborators (Knauff, Rauh, and Renz 1997) by focusing on
dynamically changing spatial relations—in contrast to static stimuli used in the above
mentioned experiments. The core of our research framework are methods and tools
combining efficient experimental data collection and visual analytics:
 CatScan: A tool to administer category construction experiments.
 KlipArt: A visual analytics environment to explore in depth category construction
as well as linguistic behavior (complementing classic analysis techniques such as
cluster analysis).
 MatrixVisualizer: A tool to visualize raw similarity values and a modification of
the Levenshtein distance to reveal individual differences.
The experiments that are the focus of this paper are a set of five new experiments (re-
running the hurricane experiment Klippel and Li 2009 to match the number of animated
icons) that will allow for the in-depth exploration of the relationship between topology
and domain semantics (see Section Materials and Figures 1 and 2 for details). The five
different domains/scenarios in this series of experiments all have a moving entity and a
reference entity (figure and ground Talmy 2000) that are spatially extended:
 Hurricane / Peninsula (abbreviated as: Hur)
 Tornado / City (Tor)
 Ship / Shallow water (Shi)
 Cannonball / City (Can)