Spatial Dimensionality as a Classification
Criterion for Qualities
Florian PROBST 1, Martin ESPETER
Institute for Geoinformatics, University of Münster, Germany.
Abstract. We discuss how the spatial extent of physical endurants influences the
conceptualization of their spatial qualities. Comparing the spatial dimensionality
of a physical endurant with the spatial dimensionality of its qualities leads to an
interesting formal ontological question. Should a spatial quality be conceptualized
as having a value range instead of a single value when its bearer has a higher
spatial dimensionality? For example, the one-dimensional depth quality can be
conceptualized as having a value range when it is assigned to the threedimensional water body of a lake. In terms of the foundational ontology DOLCE,
the “value” of a quality, sometimes called quale, is located at an atomic region at a
certain time. Allowing a value range at a time is to model qualities as being
located at non-atomic regions at a time. That might be philosophically debatable,
yet, this modeling approach enables the development of information discovery
systems that can cope with ontologically imprecise user queries and can assist the
user in defining ontologically precise quality specifications. This brings formal
ontology closer to practical applications.
The investigation is based on the foundational ontology DOLCE and introduces a
classification for spatial qualities based on their spatial dimensionality.
Keywords. formal ontology, spatial feature, geospatial ontology engineering
Introduction
In the context of open and distributed information sources, successful discovery of an
information source requires a precise description of the offered information and a
precise formulation of a query. Formal ontology has proven a useful basis to enable
precise descriptions. One can expect that professional ontology engineers take the
burden of providing semantic annotations for information sources offered via the web
that are consistent with a foundational ontology2. But can one expect an information
requester to be able to formulate queries that are consistent with a foundational
ontology? Natural language leaves a substantial range of ambiguity in the meanings of
words denoting qualities. This has proven to be efficient and powerful in direct human
communication but turned out to be the central drawback when no direct dialog for
1
2
Corresponding Author: Florian Probst, Robert-Koch-Str. 26-28, 48149 Münster, Germany; Email: f.probst@uni-muenster.de
We employed DOLCE as foundational ontology for the investigations presented here.
http://www.loa-cnr.it/DOLCE.html
agreeing on the meaning of the used symbols is possible. One can observe that
(geospatial) questions which appear valid when stated in natural language cannot be
aligned consistently to the foundational ontology DOLCE [1]. For example, "What is
the depth of Lake Constance?" The emerging problem with quality specification is as
follows.
According to DOLCE, a quality can have only one quale (value) at a certain time.
In this sense, stating that a lake has a depth quality implies that the lake has only one
depth “value” at a time. This is problematic since one can conceptualize the water body
as having a single depth quality whose depth values increase from zero (at the lake
shore) to a maximum depth value. In other words, the depth quality’s quale changes in
time as well as in space. Yet, the change in space is limited to the space region
occupied by the lake’s water body.
We present an approach that takes spatial dimensionality as central criterion for
classifying qualities of physical endurants. In this context, two contradicting modeling
possibilities arise.
1. A quality can be conceptualized as having a quale located at a non-atomic
quality region when the quality is inherent in an entity with a higher spatial
dimensionality. In other words, the quality has a “value range”. For example,
the depth of a lake.
2. An entity with spatial dimensionality n is modeled with an infinite number of
qualities with dimensionality < n, each quality having a single value. For
example, a lake (3D) has infinitely many depth qualities (1D), each with a
single quale (value).
In this paper, we make a case for possibility 1). Allowing a quality to be located at a
non-atomic quality region may be debatable from a philosophical point of view, but it
allows the user in the process of discovering suitable information sources to enter the
discovery process with a rather imprecise question. It is important that systems are able
to accept such imprecise queries and assist to turn them into precise queries. We
assume that users tend to take the context of their query as obvious or even as the only
possible context, thus they tend to neglect the need for a precise quality specification.
While driving a truck, the question, "What is the height of the tunnel?" seems to refer
obviously to the minimum height quality.
We show that dimensionality plays a crucial role in the way we assign spatial
qualities to physical objects. The results contribute to the development of semantic
reference systems as introduced in [2].
The remainder of the paper is organized as follows. The background section
introduces the notions of physical endurant, feature, quality, quality space and quale as
well as our assumptions about physical space and spatial dimensionality.
We introduce our view on how endurants extend in physical space and emphasize in
this context the importance of spatial features and their spatial dimensionality. We
provide an axiomatization of spatial qualities and their extent in space. We then discuss
the consequences, when a spatial feature and its spatial extent quality have a different
dimensionality, thus are located at non-identical space regions. We conclude by
discussing the benefits of this quality specification approach for the discovery process
of information sources.
Background
Our work is based on the foundational ontology DOLCE [1]. The following section
introduces the categories relevant for our purposes. Furthermore, we briefly introduce
our assumptions regarding physical space.
Physical Endurants
The main characteristics of a physical endurant are its location in space, its complete
presence at a certain time and its participation in some perdurant, which is sometimes
called temporal entity. Any physical endurant has some direct physical quality apart
from having a spatial location. It can be a part of some other physical endurant as well
as having other physical endurants as part. DOLCE provides three subcategories of
physical endurant: Amount of Matter, Physical Objects and Features. Since features are
relevant for our purposes here, they are briefly introduced.
The main characteristic of a feature is its one-sided generic dependence ([1] axiom
Ad 70) on its host, which means that the host can exist without the feature but not vice
versa. For some spatial features however, we assume that even mutual generic
dependence applies. Examples for such features are body or surface. They are essential
parts of their hosts. For example, an apple has a feature apple surface and the apple
cannot exist without it. The feature’s constituting amount of matter can be changed,
e.g. the apple can shrivel, yet there is still a surface.
The most important distinction between feature and quality is that qualities are the
only entities that can be directly observed or measured. A feature does have physical
qualities. The surface feature has an area quality. The area quality can be measured in
contrast to the surface which cannot be measured. It is important to note that the
qualities of a feature indirectly characterize the feature’s host. Fore example, the
volume quality of an apple’s body characterizes the apple.
A feature can be part of another physical endurant as well as having another
feature as part. In contrast, qualities inhere in other entities, they can be neither part of
an entity nor have parts.
Quality, Quality Space and Quale
Qualities are seen as the basic entities we can perceive or measure, for example shapes,
colours, weights or lengths [1]. Every physical endurant comes with certain qualities,
which exist as long as the endurant exists. DOLCE defines a strict distinction between
a quality (e.g., the colour of a specific rose), and its “value” (e.g., a particular shade of
red).
The “value” of a quality is understood as atomic quality region and is called a quale.
Quality regions are abstract entities. Currently, DOLCE requires that a quality can be
located at exactly one quale at a time. Over time however, the quale can change.
Together, the regions at which the qualities of a certain quality type are located form
the quality space of that quality type. As described in [3], the general idea is that for
each perceivable or conceivable quality a region in at least one associated quality space
exists.
Assumptions about Physical Space
Since we aim to provide a classification of qualities based on their extent in physical
space, we briefly introduce our assumptions about physical space. Several ontology
projects that attempt to account for physical space are summarized in [4].
We assume that a three dimensional physical space exists. We assume all physical
endurants to be in this physical space. In DOLCE, the spatial location quality is the
central spatial quality accounting for being located in physical space. We understand
this quality in a Newtonian sense as identifying the region in physical space that a
physical object occupies. In this sense, the spatial location quality identifies its
absolute position in space.
In this investigation, we take physical space to be a quality space with three
orthogonal location dimensions. This has the side effect that physical space as such is
understood as an abstract entity. We assume that within this three dimensional physical
space, regions with lower dimensions can exist. See definitions (1-3) below.
A potential misunderstanding is that the quality space for spatial location accounts
directly for the volume, shape, area or length qualities of an entity. This holds only
indirectly. An entity which has a volume or an area quality does necessarily have a
spatial location quality, yet volume and location qualities are distinct qualities.
More generally, a quality space for spatial location requires a spatial reference
system in order to turn the absolute locations in space into comparable and measurable
space regions. This is inline with Kuhn and Raubal [5], proposing that spatial reference
systems are special kinds of semantic reference systems.
Physical Endurants and Their Spatial Qualities
After introducing physical endurants, qualities, their associated quality spaces and the
assumptions about physical space, we now discuss the spatial qualities of physical
endurants.
Being in Space versus Extending in Space
Being in space and being extended in space are often understood as synonym. In our
approach, it is important to distinguish between both. In DOLCE, being in space is
reflected in the spatial location quality that any physical endurant necessarily
entertains. The quality space of the spatial location quality directly refers to physical
space; physical space is the quality space of the spatial location quality. In other words,
any physical endurant has a spatial location quality that has as “value” the space region
it occupies. We assume this quality to be the most central spatial quality since it is a
prerequisite for an entity to be in space. But how to describe being in space more
precisely? Here, the spatial qualities extent and figure (shape) come into play. The
distinction between being in space and being extended becomes apparent when taking
physical endurants into account whose spatial location qualities are located at atomic
regions in space. Casati et al. [6] indicate that a theory of spatial representation should
account for the fact that the different types of spatial entities bear different types of
relations to space. The corner of a desk top, the midpoint of a desk edge or the balance
point of a desk surface are examples for physical endurants which are in space, yet
which do not extend in space, since they do not entertain qualities like volume, area or
length. Here, we depart from the assumptions made in Asher and Vieu [7] and Borgo et
al. [8], that the entities we deal with in space do necessarily extend in three dimensions.
We assume that surfaces, edges or corners do play a role in our every day interactions
in space and that it is exactly their lower dimensional spatial extent that plays a crucial
role in the way we assign spatial qualities (indirectly) to physical objects. We see some
support for this assumption in the approach to deal with boundaries presented by Casati
and Varzi [9].
Spatial Features and Spatial Qualities
A prominent argument why the spatial qualities extension and shape are most central is
given by Kant [10, p. 17]: "Thus, if I take away from our representation of a body all
that the understanding thinks as belonging to it, as substance, force, divisibility, etc.,
and also whatever belongs to sensation, as impenetrability, hardness, color, etc.; yet
there is still something left us from this empirical intuition, namely, extension and
shape.”
We assume that Kant’s notion of body refers here to what we will define as spatial
feature. In our approach, we restrict spatial extension qualities and shape qualities to
inhere exclusively in spatial features. This in turn leaves physical objects to entertain
spatial qualities only indirectly via the spatial features that they necessarily have.
We propose the category SPATIAL FEATURE as a direct sub-category to FEATURE
with four sub-categories: 1D-FEATURE, 2D-FEATURE, 3D-FEATURE AND EXTESNIONLESS FEATURES (Fig. 1). All spatial features do necessarily have a host that is a physical
object.
DOLCE: physical endurant
DOLCE: feature
spatial feature
extensionless feature 1D-feature
2D-feature
3D-feature
Fig. 1. Proposed sub categories of FEATURE. DOLCE is intentionally not restricted to a certain
dimensionality of space. To be practically applicable in geospatial application we introduce three feature
types classified according to their dimensionality. The position of extension-less-features is debatable.
3D-Features.The feature body is conceptualized as extending in all three dimensions
of physical space. In other words, its spatial location quality is located at a space
region that extends in all three spatial dimensions of physical space. All features whose
spatial location quality is located at a 3D region are individuals of the category 3DFeatures.
2D-Features. The feature surface is conceptualized as extending only in two spatial
dimensions. For example, an apple’s surface has a two-dimensional extent since the
space region at which its spatial location quality is located extends only along two of
the three spatial dimensions. Still, the surface’s two-dimensional region is part of the
three-dimensional physical space. In contrast, the apple’s peel is a physical object and
as such located at a three dimensional region.
1D-Features. Features with a spatial location quality that is located at a region that
extends only along one of the three spatial dimensions belong to the category 1DFEATURE. For example, a tabletop can have edges.
Extension-less Feature. Finally, a feature that is located in physical space but does not
extend in physical space is an extension-less feature. Being located in physical space
but at the same time being extension-less means to have an atomic spatial location
quality in either a 1D-, 2D-, or 3D-region. In this sense, extension-less features are
special kinds of the above defined feature types. Apart from the spatial location
quality, an extension-less feature has consequently no spatial extent qualities like a
volume, area or shape. For this reason, we can observe extension-less features only
indirectly via features which extend in space. The category of extension-less features
requires further investigation.
Types of Space Regions
The spatial location quality is located in a quality region that accounts directly for a
region in physical space. The region is-a space region.
We assume three types of physical space regions that are distinguished according
to their number of spatial dimensions: 1D-, 2D-, and 3D- space regions.
1D-S(x)  2D-S(x)  3D-S(x)  S(x)
(from DOLCE [1]: S :: space region)
(1)
We can imagine that an individual of each of these region types can shrink to an
atomic extent. This leaves us with three kinds of atomic space regions. Only an
extension-less (0D) feature can be located at such atomic regions. We leave the
discussion about extension-less features open. The focus is on features that are located
in non-atomic regions with one, two or three dimensions.
In the following, we introduce the relations is-spatial-location-quality and isspatial-location-quale, which we require for defining spatial feature (4). A spatial
feature is a feature which has a spatial location quality which in turn can be located at
either a 1D-, a 2D,- or a 3D-spatial region. The fact that a spatial feature can be located
at any space region type differentiates it form a physical object.
“x is a spatial location quality of y”
slqt(x,y) ≜ qt(x,y)  SL(x)  (SF(y)  SQ(y))
(2)
(from DOLCE [1]: SL:: spatial location (quality)3; qt:: is-quality-of (Ad38). The
characterizations of the predicates SF (spatial feature) and SQ (spatial quality) are
given in (4) and (5).)
“x is a spatial location quale of y (at time t)”
slql(x,y,t) ≜ ql(x,y,t)  (1D-S(x)  2D-S(x)  3D-S(x))  SL(y)
(from [1]: ql:: is-quale-of (Ad 58))
(3)
Spatial Feature
SF(z) → F(z)  (y (slqt(y,z))
 x,t (slql(x,y,t) )  (1D-S(x)  2D-S(x)  3D-S(x))
(from [1]: F::Feature )
3
(4)
For better readability we would prefer the label SLQ over SL to indicate that spatial location is
a quality, but we keep the notation introduced in DOLCE [1].
A spatial feature has a spatial location quality that has its quale in a one-, two- or threedimensional region of physical space (1D-S; 2D-S; 3D-S).
Dimensionality of Spatial Qualities
The previous section introduced spatial features. Relevant for our classification of
features is their spatial location quality that accounts for being in space, or more
precisely, that accounts for the dimensionality of the space region in which the spatial
location quality is located.
Additionally to that spatial quality essential for any physical endurant, we
introduce the categories SHAPE QUALITY and SPATIAL EXTENT QUALITY. Fig. 2 shows
three sub-categories of SPATIAL QUALITY.
According to DOLCE, any physical quality has the same location in physical space
as its bearer [1, axiom Dd37], and is called a spatial quale. We do not follow this
approach here. In DOLCE, a depth quality would have the same spatial location as the
lake it inheres in. For our purposes we need the possibility to state that the location
quale of a quality is either identical with the location quale of its bearer or that it is a
lower dimensional part of its bearer’s location quale (8). This requires that any spatial
quality itself has an individual spatial location quality, independently of the location
quality of its bearer.
DOLCE: physical quality
spatial quality
shape quality
has quality
spatial extent
quality
DOLCE: physical region
DOLCE: physical space region
DOLCE: spatial
location quality
located at
has quality
Fig. 2. Proposed extension of the category SPATIAL QUALITY. Note, any spatial extent quality and any shape
quality themselves have a spatial location quality that in turn is located at a region in physical space.
Spatial Quality
SQ(z) → PQ(z)  y (slqt(y,z))
(from DOLCE [1]: PQ :: Physical Quality)
(5)
We define a spatial quality (SQ) as a physical quality (PQ) which, at any time it exists,
has a spatial location quality (SL). Spatial extent qualities (SEQ) can have spatial
location qualities that are located at 1D-, 2D-, or 3D-space regions. This is axiomatized
in the relation is-spatial-location-quality-of (2). As Casati and Varzi [9, p.123] state,
“regions are those things that are located at themselves”. This allows to categorize
spatial location qualities as spatial qualities. We do not provide formalizations for
shape qualities since they are not in the scope of this paper.
Spatial Extent Quality
SEQ(z) → SQ(z)
(6)
“x is a spatial extent quality of y”
seqt(x,y) ≜ SEQ(x)  SF(y)
(7)
Spatial features and spatial extent qualities are related via the is-spatial-extent-qualityof relation (seqt). Both, spatial extent qualities and features can entertain spatial
location qualities (2) these in turn can be located at any of the previously defined space
regions (1),(3).
In Fig. 3, the three proposed sub-categories of SPATIAL EXTENT QUALITY are
depicted. The individual spatial extent qualities are categorized according to the region
type to which the regions of their spatial location quality belong. A spatial extent
quality that has a spatial location quality that is located at a 3D-space region is
categorized as 3D-spatial extent quality.
At this point, we draw the attention to a possible source of confusion. Central to a
quality is that it is an observable entity. This is reflected by the fact that is has a quale
(Ausprägung). The quale is a region in the quality’s quality space. According to
DOLCE, a quale is an abstract particular. In turn, a quality is understood as an entity
which itself can have qualities.
It is important to distinguish between the direct quale of a quality and the qualia of
its qualities. Direct and indirect qualia are located in different quality spaces. In the
case of spatial extent qualities, the quality has a direct quale for a spatial extent, e.g. a
volume, an area or an elongation. Additionally, any spatial extent quality has a location
quality. The location quality has its quale in the quality space corresponding to
physical space.
DOLCE: physical region
spatial quality
shape quality
1D-extent-q
has quality
DOLCE: physical space region
spatial extent quality
2D-extent-q
has quality
3D-extent-q
1D-space
region
2D-space
region
3D-space
region
has quality
located at
located at
located at
DOLCE: spatial location quality
Fig. 3. Any spatial extent quality does itself have a spatial location quality. The spatial location quality of a
spatial extent quality is located in a 1D-, 2D-, or 3D-space region. (All statements made above for spatial
extent quality do apply in analogy for shape quality, too. Yet, they are omitted for readability.)
Non-Atomic Quality Regions
In the previous sections, we introduced the spatial dimensionality of features and
spatial qualities. We continue by discussing the possible consequences arising when a
spatial feature and its spatial extent quality entertain spatial location qualities that are
located in space regions of different types.
The mereological relations between the physical space region at which the spatial
extent quality is located and the physical space region at which the spatial feature is
located are at the core of the investigations presented here. We identify the following
relations between the space region of a feature and the space region of its spatial extent
quality.
“x is a lower dimensional part of y” In order to distinguish the dimensionality of a
spatial extent quality and the dimensionality of its bearer, the type of space region at
which their location qualities are located need to be compared. If a space region is
located in another space region and if this space region has a lower dimensionality than
the space region in which it is located, the following relation applies:
ldp(x, y) ≜ PP(x,y) 
((1D-S(x)  (2D-S(y)  3D-S(y)))  (2D-S(x)  3D-S(y)))
(from DOLCE [1]: PP:: proper part (Dd14))
(8)
“v is an atomic-quale-quality of w”. A feature and its spatial extent qualities each are
located at a spatial region. If the space regions are identical, then the spatial extent
qualities each have an atomic quale. Such an atomic quale can be approximated with a
single value, e.g. 2km3. This relation applies for example between a water body and its
volume quality:
aqlqt(v,w) ≜ seqt(v,w)  y,y’((slqt(y,v)  slqt(y’,w))
 t (x,x’(slql(x,y,t)  slql(x’,y’,t)))) → x  x’
(from DOLCE : P(x,y)  P(y,x) → x = y (Ad6), P :: Parthood)
(9)
”v is a non-atomic-quale-quality of (spatial feature) w” If the region at which the
spatial extent quality’s spatial location quality is located is a lower dimensional part
of the region at which the spatial feature’s spatial location quality is located, then the
spatial extent quality has a non atomic quale. This relation applies for example
between a water body and its depth quality. This relation is depicted in the lower part
of Fig 5. The relations are labelled “q-location of depth quality” and “q-location of
feature”:
naqlqt(v,w) ≜ seqt(v,w)  y,y’(slqt(y,v)  slqt(y’,w))
 t (x,x’(slql(x,y,t)  slql(x’,y’,t))) → ldp(x, x’)
(10)
These definitions entail: If a quality is conceptualized to be inherent in a feature that
occupies a higher dimensional space region, then the spatial location of the quality is
not exactly defined. It can “move” within the region of the feature. A 1D-space region
has one degree of freedom within a 2D-space region, and two degrees of freedom
within a 3D-space region. Fig. 4 shows an example for a depth quality inherent in the
feature water body of river. In the example, the depth quality is conceptualized as 1D
quality, thus its spatial location quality is located at a 1D-space region. The depth
quality has two degrees of freedom within the 3D-space region occupied by the water
body.
Thus, it is impossible to locate a spatial extent quality at an atomic region (assign a
single value to it) if the dimensionality of its location quality differs from that of the
feature it inheres in. In other words, the quale of a quality with a lower dimensionality
does not only vary in time but also in space. Such a quality takes a range of possible
values at a time. It is located at a non-atomic region in its quality space.
depth 3
depth 2
depth1
Fig. 4. Example: The water body of a stream is located at a 3D space region. If a depth quality is assigned to
it, then the 1D space region of the quality has two degrees of freedom within the region of the water body.
Exemplarily, three possible locations are depicted.
In the context of information sources dealing with observations and measurements, it
appears essential to make sure that the observed quality, e.g. the depth of a river is
located at an atomic region of its quality space. This requires that qualities with lower
dimensionality than their bearers are further specified. This can be achieved in two
ways.
1. The spatial location of the quality is defined exactly. In the river example, this
is achieved when the water level at a certain location is measured. The depth
quality is further specified as the depth quality at a certain location and a
certain time.
2. The quality is defined to take an atomic quale that takes a clearly identifiable
location in the quality space at a certain time. In the river example, this could
be the maximum depth, the average depth, or any other quale that can be
singled out of the range of possible atomic-regions at which the quality can be
located.
A
DOLCE: feature
DOLCE: physical quality
DOLCE: physical region
spatial quality
spatial feature
1D volume
region
3D-quality
q-location
DOLCE: physical
space region
3D-space
region
3D feature
has quality
volume quality
has quality
water body
q-location of
volume quality
has quality spatial location
quality
q-location of feature
B
DOLCE: feature
DOLCE: physical region
DOLCE: physical quality
elongation
region
spatial quality
spatial feature
1D-quality
DOLCE: physical
space region
q-location
1D-space
region
3D feature
depth quality
has quality
has quality
water body
has quality spatial location
quality
3D-space
region
q-location of
depth quality
lower-dimensional part
q-location of feature
Fig. 5. A: The volume quality of a water body has exactly one “value” (quale). The region to which the
volume quality refers has no degree of freedom, since it is identical with the space region the water body
occupies. B: The depth quality has a “value range” since the depth quality’s spatial location quality is located
in a space region that has two degrees of freedom within the space region of the water body.
Summary and Conclusion
To enable successful discovery of geospatial information sources providing observation
results, the first step is to specify precisely the qualities for which observation results
are provided and in which physical endurants the quality is inherent.
We presented a first cut at an ontology for spatial qualities based on the
foundational ontology DOLCE. Central to our approach is the spatial dimensionality of
spatial qualities. This implies that a spatial quality itself has a spatial location quality,
and thus a location in physical space. In our approach, a spatial extent quality has a
direct location in its associated quality space as well as an indirect location in physical
space via its spatial location quality. For example, the spatial extent quality volume is
located directly in its one-dimensional quality space for volume as well as indirectly in
a three-dimensional region in the quality space accounting for physical space.
In order to talk about dimensionality we introduced the categories 1D-SPACE
REGION, 2D- SPACE REGION, and 3D- SPACE REGION as subcategories of SPACE
REGION, as well as four subcategories for SPATIAL FEATURE (4), where the individuals
are classified according to their spatial dimensionality.
A consequence of our approach is that a spatial feature and its spatial extent
quality both have an individual spatial location quality. Central to our approach is that
the space regions (spatial qualia) of these two spatial location qualities can be
 identical. In this case, the relation atomic-quale-quality-of (9) holds between the
feature and its spatial extent quality. It indicates that the quality has a single
“value” at a time. For example, the volume of a lake has exactly one value at a
time.
 different. In this case, the relation non-atomic-quale-quality-of (10) holds
between the spatial extent quality and its feature. It indicates that the quality has a
value range at a certain time. For example, the depth of a lake has a value range at
a time.
In the context of information source discovery, discovery systems that implement
ontology based-search according to our approach will allow the information requester
to start her search with basic level concepts [11]. For example, assume a user interested
in observation results of depth qualities of lakes in a certain region. An information
discovery system will allow the user to start his search with the notions depth and lake.
Since the depth quality is a one-dimensional quality (see Fig. 5) and the water body of
the lake is a three-dimensional spatial feature, the spatial location quale of quality and
feature are not identical. Thus, the relation defined in (10) holds, indicating that the
depth quality has a value range at a certain time. At this point, the information
discovery system informs the user that she can request only value ranges for this
combination of quality type and feature type. It is possible that the user implicitly
assumed that the notion “lake depth” always refers to the maximum depth quality.
Information discovery systems based on our approach would enforce to state these
assumptions explicitly, e.g. the user has to choose the qualities for which it is possible
to return a single observation value, such as the maximum depth quality.
In addition to that, our approach allows to specify variances, or any other quality
characterizing the value range of a quality. The variance accounts for the way in which
the “values” of a quality vary. Variance is a quality frequently used in geospatial
applications, thus it is important that the underlying ontology can account for it.
Variance qualities are only possible if lower dimensional spatial qualities are
conceptualized to inhere in higher dimensional spatial features.
Future Work
Spatial extent qualities like height or volume are often assigned as direct qualities
to physical objects. In this paper, we proposed that only spatial features should have
spatial extent qualities. One could further require that only amounts of matter, which
constitute physical objects, can have physical qualities like temperature, mass or color.
Temporal qualities in turn are direct qualities of perdurants in which a physical object
participates. A physical object may play a certain role. Yet, it is the role, which
entertains abstract qualities like monetary or historical value. This raises the question:
Which direct qualities can be assigned to a physical object?
This investigation was focused on qualities understood as unary characteristics of
entities. Further investigations are required to incorporate other kinds of observable
entities into the approach, for example binary characteristics such as directions or
distances between spatial entities.
Acknowledgements
Discussions with Krzysztof Janowicz, Eva Klien, Claudio Masolo, Stefano Borgo,
Michael Lutz and Werner Kuhn have greatly influenced the ideas presented here. The
work has been supported by the German Research Foundation (DFG) grant KU
1368/4-1 (Semantic Reference Systems) and the SWING project (IST-FP6-26514).
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