Nebel [5, 6] or the uses of modal logic by Bennett and colleagues [7]. Simply ..... [18] Anthony G. Cohn, Brandon Bennett, John Gooday, and Nicolas M. Gotts.
Towards a generic foundation for spatial ontology John Bateman, Scott Farrar The Collaborative Research Center for Spatial Cognition SFB/TR8, University of Bremen, Germany
Abstract. In this paper we describe the results of our current efforts to establish a foundation for combining spatial ontologies. We draw on the state of the art in computational ontological engineering, ontologies for geographic information systems and qualitative reasoning in order to build a framework within which these, and other, approaches may be placed. The skeleton of the framework is provided by the DOLCE ontology augmented by several important components of Smith’s BFO. We point out the particular importance of including notions of variable granularity, layers and sites in order to do justice to the requirements of practical ontological application. The target applications for our own work are spatial reasoning for robotic systems and natural language interaction.
Introduction There are now many proposals for describing space, spatial relationships, and relations between entities and their locations that have been developed within broadly ‘ontological’ frameworks. We are currently involved in an attempt to reconcile and combine these approaches into a collective toolset for dealing with space. This toolset is intended to support representation and reasoning in various domains of application where space plays a central role—including robotics, spatial assistance and navigation, spatial perception, communication and spatial problem solving—as well as ‘purer’ ontological description. A fundamental organizational principle for this reconciliation is ontological perspectivalism in the sense of Barry Smith and colleagues.1 We explicitly reject reconciliation in terms of reductionism—e.g., attempting to reduce spatial aspects to Euclidean geometry, etc.—and seek instead a generic foundation within which alternative accounts may be couched. This is a significant undertaking—primarily due to the wide range of approaches that we need to consider. These include traditional AI ontologies such as Cyc and SUMO, formal ontologies such as DOLCE and BFO, recent ontological formalizations for Geographic Information Systems (GIS), and qualitative spatial reasoning (QSR) invoking connection calculi, regionbased geometries, and accounts of orientation [1]. Although we do not consider it our task to legislate for or against any of these perspectives, we do argue that spatial ontologies need now to be integrated into broader ontological accounts in order to progress and find application. We believe it is important to consider space and spatial relations as one component of general ontological accounts of the world in order to avoid overly narrow formalizations. At the same time, we consider it a deficit of, particularly, 1
We refrain in this draft paper from giving exhaustive references for all of the positions and accounts mentioned: positions that we consider standard to the field are simply mentioned by name.
AI-based ontologies that when including spatial accounts much of the formal underpinnings are no longer explicitly available. These methodological considerations do combine in a way that occasionally favors certain design decisions rather than others. We prefer to proceed in a top-down fashion, considering the most general entities and ontological relationships, arriving at an account where space has a natural home. As we shall see, this is also to reject ‘space-centric’ views where formalization begins within space or spatial regions as basic and attempts to construct the rest of ontology on this narrow foundation. This is part of our concern to avoid ‘over-atomistic’ accounts—with small microtheories or fragment formalizations being developed in isolation of very similar accounts elsewhere— similiarites even among the same collections of authors (cf. Smith and colleagues discussions of niches, layers and granular partitions: all of which are usefully applied to spatial questions but whose interrelationships remain under-developed). We consider that it is now an appropriate time to bring these diverse accounts together in a responsible fashion that respects their individual contributions to the whole. The outline of the paper is as follows. We first briefly review a selection of ontological accounts that have dealt with space and in terms of which we might draw a foundation for spatial representation. We then consider some extensions necessary for achieving reconciliation and conclude with an extremely simple illustration. We consider this as a first level of specification for a more inclusive view of space which can later serve as input for a full formalization. 1 Space in ontology Our description in this section will not be historical; we will not delve into the foundational works on space from the history of philosophy but concentrate instead rather narrowly on current attempts to include space within formal and computational ontologies. We take the fact that there is still much active debate concerning how space is to be treated ‘correctly’ as indirect support for a strongly perspectivalist approach. Our discussion will also of necessity be extremely brief; for a more detailed presentation of this background material, we refer the reader to Bateman and Farrar [2]. Some computational ontologies currently under development already attempt a combination of approaches to space. For example, the Suggested Merged Upper Ontology, SUMO [3], deliberately unites the theory of holes from Casata and Varzi [4] as well as elements of Smith’s and Guarino’s respective mereotopologies. The basic axiom of location from SUMO is:2 . ( (instance ?PHYS Physical) (exists (?LOC ?TIME) (and (located ?PHYS ?LOC) (time ?PHYS ?TIME))))
where the second parameter of the located predicate is restricted to be a region. Regions obey some basic mereological properties and allow the definition of some variant spatial relations such as partlyLocated, exactlyLocated as well as connection, meet and overlap. Connection is defined solely in terms of parthood and sharing parts is a necessary and sufficient condition for spatial overlap. There are, therefore, a variety of axioms drawn from a broad range of approaches. While this is very similar to the direction that we wish to follow, we also find it problematic that once 2
Descriptions of SUMO relate to version 1.60 available at http://ontology.teknowledge.com/
the axioms have been adopted, from this mereotopology of from that connection calculus, their individual motivations as belonging to a particular system of formalization are lost. This is more than simply a question of maintaining modularity or of recognizing sources of information. Particularly within the qualitative spatial reasoning community there has been extensive investigation of the computational and formal properties of particular combinations of spatial axiomatizations; see here, for example, the complexity results reported by Renz and Nebel [5, 6] or the uses of modal logic by Bennett and colleagues [7]. Simply adding axioms into the ontology appears then to lose valuable information. 3 An alternative approach to reconciliation is offered by the ontological modelling of the Descriptive Ontology for Linguistic and Cognitive Engineering, DOLCE [8, 9]. This is because it actually says very little about how space is to be captured. What it does say is how any treatment of space is to be bound into the framework as a whole. For DOLCE, space is a kind of quality, analogous to colors or taste. DOLCE separates actual qualities from their abstract values, which are defined and located in quality space. Instances of Quality (non-abstractions) are said to “inhere” in their associated hosts, but their values are defined as points in abstract quality space. This is inspired by the work on conceptual spaces by G¨ardenfors [10]. The difference between a Quality and a point in quality space may be explained by reference to a distinction observable in the natural language sentences given in (1-3). (1) This rose is red. (2) The color of this rose is red. (3) The color of this rose changed from red to brown. The word red in (1) is used as an adjective and refers to a particular instance of Quality. This is the color that the particular rose described has. This quality of color is uniquely that of this particular rose. In contrast, the red of (2), is being used as a nominal rather than an adjective refers instead to an instance of a color quale, or position in abstract color space, subsumed under the concept Region. That this is necessary is argued by the existence of statements such as that of (3): here it makes little sense to say that it is the color ‘red’ itself that is changing from red to brown. It is only the particular instantial color that the rose has that is taking up different color values within the abstract color region. We need then to keep these two layers of the account separate: the instantial quality and the quale that it takes as value. This relationship between a host, its quality, and a quale is shown in Figure 1. The categories from the taxonomy are shown as boxes and subsumption is represented by spatial inclusion in the diagram. Thus, a ‘rose’ is a subclass of a Non-Agentive Physical Object, which is itself a subclass of Physical Object. The particular rose that we are discussing in (1-3) is then the dot labelled rose#1. By inheritance, this entity is an instance of a concept ‘Red Object’. In addition to this subsumption information, we also have the ‘horizontal’, cross-links established by the axiomatization. This is shown as arrows relating particular boxes. Thus, the rose itself stands in the quality relationship qt C with an instance of Color, which is a kind of Physical Quality. This instance is the precise and particular color that rose#1 has. The value of this particular color is then given by the further quale relationship with one of the colors defined in the Color Region, which is itself a subclass of Physical Region. 3
We see similar problems with other AI ontologies such as, for example, that of Cyc—despite its microtheory modularity [2].
Figure 1: Quality and quality spaces (taken from Masolo et al., 2003)
This relationship is also indexed by time and so can change. What then occurs is that the particular color that is the color of the rose is linked with a different point in the color region. The color ‘red’ does not then change; and the particular color that is the rose’s color is always that rose’s color. Slightly more formally, we then have, following the DOLCE nomenclature, that for some rose rose#1 and its particular unique color c#1: PED (rose#1) ∧ PQ (c#1) ∧ qt (c#1, rose#1) i.e., the particular rose is a physical endurant (PED), the particular color is a physical quality (PQ), and there is a quality relationship holding between them. The particular value of the color quality is then given by the further description: PR (color#1) ∧ P (color#1, color space) ∧ ql (color#1, c#1, t) That is, a particular point color#1 is within (part-of: P) the physical region (PR) of color; that point might be, for example, ‘red’. This point is then the quale (value) of the particular color c#1 that the rose has. This level of indirection is necessary in order to stop actual colors (such as ‘red’) changing when the rose begins to droop and is no longer red. The possibility of the value of the color changing over time is allowed for with the time index given as parameter t. Space is then treated in a precisely analogous way. Thus, within DOLCE there are also physical regions that correspond to ‘space’; this as a whole is termed the space region. A particular location that an object or event may have is then given a value by relating it to this general space region. The relationships are exactly as illustrated for color. Therefore, the rose, in addition to color and by virtue (as we shall see below) of being a physical endurant (PED), has a spatial location: PQ (l#1) ∧ qt (l#1, rose#1) That spatial location, l#1, then also enters into a quale relationship such as: PR (location#1) ∧ P (location#1, space region) ∧ ql (location#1, l#1, t) Again, there is a temporal parameter to the quale relation which means that the location of objects can change over time (i.e., they have a different value within the space region) but, crucially, an object cannot become separated from its own location (the quality l#1).
The basic spatial properties and relationships between entities are then captured within the axiomatization of DOLCE as follows. P ED(x) → ∃y(qt(SL, y, x)) i.e., all physical endurants have a spatial location (this ternary form of qt specifies additionally the type of quality that holds). MSDS (P Q, P ED) This guarantees that there is a mutual specific spatial dependence between physical qualities and physical endurants; that is, physical qualities can only exist when there is some specific physical endurant to ‘carry’ them and specific particular physical objects have their own particular qualities (not someone else’s). Moreover (by the definition of MSD S ), both the physical endurant and the physical quality are present in the same settings (s, s , . . . ) and at the same times—where being present is defined as: P RE(x, s, t) ≡ P RE(x, t) ∧ ∃s (qlS (s , x, t) ∧ P (s, s)) which, in addition to specifying that being present has a temporal aspect, also states that if something is present there is also some setting that is the spatial location of that something (qlS ). Being present simply requires that there be some spatial location but does not further specify what that might be. The relation qlS ranges not only over physical endurants, but also over physical qualities and perdurants, i.e., events and states, although differently for each. The case for physical endurants we have just seen, whereas for both physical qualities and perdurants the spatial aspect of being present is indirect: the spatial quality only comes via their associated physical endurants. For physical qualities, this is straightforward; for perdurants, the relevant physical endurants are defined by the maximal physical participants, which draws on the DOLCE view of how participants are involved in activites, states and events. The details are not relevant at this point, but the intuition is well-known in the modelling of perdurants—i.e., that while physical objects have their own locations, for example, those of activies and events only have locations by virtue of where their participants are. Despite these finely specified dependencies, the actual approach to space as such is still left completely open within DOLCE itself. As Masolo et al. explain, treating treating space in terms of quality spaces “...allows an homogeneous approach that remains neutral about the properties of the geometric/temporal space adopted (for instance, one is free to adopt linear, branching, or even circular time)” [9]. The axiomatization of particular views of the space region and its parts is left to particular extensions that may be built on the DOLCE foundation. This is then amenable to other diverse ontological decisions concerning space precisely as we require. The space region may be purely geometric—i.e., defined in terms of space-points—or it might be defined more qualitatively. All of these decisions leave the foundational connections and dependencies between physical endurants, perdurants, qualities and locations unaffected. Finally, we draw attention to the rather different treatment of space in Smith and colleagues Basic Formal Ontology, BFO [11, 12], before proceeding to an attempt at some further reconcilation in the section following. An essential component of BFO is its separation of reality into two sorts of ontologies: SNAP and SPAN. SNAP-ontologies do not involve time and are ‘snapshot’ perspectives; SPAN-ontologies necessarily involve time and are 4D perspectives. Although we will not be able to build more on this distinction in this paper, a full description of space will require both types of ontologies and the mechanisms for relating entities of the two; for the present purposes of discussion, we will concentrate on BFO SNAP-ontologies.
Within a BFO-SNAP ontology, space itself is considered an identifiable whole, namely “the entire spatial universe (the maximal spatial region)” of which all spatial regions are parts [11, p148]: SpatialRegion(x) ≡ P art(x, space) This means that all instances of SpatialRegion are parts of space itself. No other sorts of SNAP entities are parts of spatial region, but all other SNAP entities (BFO is still primarily concerned with physical reality) must be located in some spatial region. Space regions on all levels of scale act as locations for other SNAP entities; this is sometimes called the container or absolutist view of space [11, p148]. In addition, there is a particularly spatial kind of independent entity, termed a site. A site differs from a substance in that the former acts as a location for the latter. The two are related by the predicate occupies: substances, then, occupy sites. This is considered ontologically distinct from the notion of ‘location’ which is only used with reference to space region; location in this sense is purely mereotopological. Examples of Site include a room in a house or a landing strip or the alimentary tract of a person. They are not instances of SpaceRegion, but are more object-like, in that both substances and sites are located in space. Three subcategories of sites, i.e., sites where an object might be, are: ‘holes’, ‘places’ and ‘niches’; we see here a rather more carefully articulated division of the notion of region seen above for SUMO. Of these categories, the notion of the niche is the most distinctive; in Smith and Varzi [13], the niche is proposed as a further fundamental spatial relationship in addition to part of, boundary for and located at. Niches build on ‘physical-behavioral units’ in order to characterize natural, bounded, unitary entities that separate “some organized internal (foregrounded) pattern from a different external (backgrounded) pattern.” [13] BFO therefore differs from DOLCE with respect to its treatment of space in several ways. BFO allows a specification of location in terms of objects functioning as locations (sites: e.g., a room), suggests distinctive relationships between objects and sites and between sites and locations, and already appears to suggest a characterization of space in terms of a three dimensional space from which extracts of lower dimensionality can be extracted and maintains space as a distinct high-level ontological category in its own right. There is no straightforward correspondence between the views of space and spatial relationships present in the two accounts. Two further constructs useful for space that we will incorporate below also developed by Smith and colleagues are layers (particularly with Donnelly [14]) and granular partitions (with Bittner [15]); of these partitions are already part of the BFO framework. Layers are invoked in order to avoid the various problems of (temporally-)spatially coinciding entities which belong to separate mereology chains. They can be seen as another approach to naturally constraining the very general application of the parthood relationship to only construct transitive chains that ‘make sense’. In short, layers augment mereotopology so as to allow (temporally)-spatially coincident entities not to overlap mereologically. This account is very much aligned with the DOLCE and BFO approaches where objects are distinguished from the spatial regions that they occupy. Two objects coincide when they occupy overlapping regions of space. Objects coincide with their regions but also potentially with other objects. Overlap is construed mereologically and this makes coincidence a broader relationship in that coincidence is possible between objects that do not share parts. Donnelly and Smith offer several examples; for example, one of contaminated fish in a lake: the parts of mercury contaminating the fish are not part of the fish, and the fish do not overlap with the lake—but they are all may be coincident. The water, the fish, and the mercury all exist within their own layers and are thereby isolated from each other with respect to parthood. This appears a useful and necessary aspect of reality. Both the occupies and located-at relations of
BFO proper appear to be definable in terms of the relationship of coincidence. Granular partitions also contribute to restricting parthood transitivity. They define the entities and relations which are considered relevant for some purpose. This semantic granularity allows a flexible atomism where parts lying beyond the grain of the partition are no longer accessible. This offers a sophisticated treatment of essential and non-essential parts—nonessential parts are simply excluded by the granularity of the adopted partition. Particularly relevant for us here, however, is Bittner’s notion of qualitative coordinates. This allows locations to be specified for objects in terms of qualitative relations drawn with respect to locations that are known. A qualitative scheme might provide relationships of cardinal directions (N, NE, E, ...) and so an area might be describable as ‘northeast of Mount Everest’. Below we will apply granularity to all components of this description: Mount Everest is an entity at a given degree of granularity, as is the qualitative spatial relationship ‘northeast’. 2 Towards a reconciled foundation A foundational ontology needs to provide for the different perspectives that can be taken on phenomena in the world. For space, an excellent starting point appears to be offered by the DOLCE framework as described above because it encourages an open description that might be parameterized according to different views of space. Part of that parameterization may be provided by mechanisms such as layers and granular partitions. Such parameterization is necessary and will be made depending on particular purposes and intentions. Moreover, in order to make such parametric choices, further information may need to be associated with particular ontological perspective choices—rationales for adopting one perspective rather than another. This may be in terms of particular properties that a perspective then ‘picks out’ or generically in terms of overall computational properties of the concerned body of theory. We need to see all of these aspects as important components of a complete ontological account. Whereas the DOLCE formalization provides a convenient starting point, we must also extend it somewhat in order to include the useful insights from the BFO-tradition and also, as we shall see albeit very briefly in a moment, to make stronger contact with some of the connection calculus approaches. First, space or a position is not something that an entity ‘has’, like a color or a weight, the relationship is in some sense weaker, in that a location is nothing intrinsically ‘to do with’ the object at all. There appears to be no ontological dependence between the two entities: something else could have been where some entity was—both the entity and the location are unaffected, whereas nothing else could have had some particular rose’s color. Thus, a physical entity must necessarily have some location, but not any particular location. Moreover, the existence of some location does not necessarily involve an object that occupies it: one can describe locations regardless of their occupancy; indeed, some locations are habitually empty. Locations and colors therefore appear to have radically different kinds of identity and identification criteria that raises doubts about considering color and space regions as similar. This suggests that the relationship at issue for location is perhaps generic rather than specific and one-sided rather than mutual. The relationship is nevertheless also strong in that an entity has some location simply by virtue of its being a physical entity: no particular properties of its material are relied upon. The essential component is the spatial region with which the object coincides: this is the closest equivalent to the color quality of the rose. But within DOLCE, physical endurants themselves involve a complex of categories, including amounts of matter which constitute physical objects, which may additionally have dependent features (holes, bumps, etc.). It
could be suggested that it is perhaps more accurate to state that it is matter and location that are strongly linked, rather than the physical objects that are constituted by matter. 4 Then individuals would only achieve their spatial extension indirectly via their material substrate. An amount of matter always takes up some particular space, and that space can be located; the location would take place in the region layer proposed by Donnelly and Smith. Such a position can certainly be criticized, however, as favoring a view inherited from physics rather than one that is cognitively or ‘naively’ motivated. The object that is most salient, e.g., a particular book lying on the table, would be being made less significant as far as location is concerned than the matter which constitutes the book. There is then much in favor of following DOLCE’s lead in which location is specified as ranging over all physical endurants—i.e., over physical objects as well as over amounts of matter. This attempts to bind objects and their constituting matter together ontologically sufficiently tightly that we can still sensibly talk of the book’s location rather than the location of the matter out of which the book is constituted—which must come out in the axiomatization as equivalent. With respect to the DOLCE indirect relationship between objects and places within a space region, both halves of the relationship appear in need of further refinement but nevertheless offer a good starting point. Although it is not yet clear how these relationships should be formalized in order to bring out the difference between, e.g., colors and locations, the indirection remains useful. Consider, first, the notion of a site. We alluded above to the fact that site appears to be used in the sense of an object that is functioning as a location; this is not how it is introduced in the BFO description where it is simply stated that there are entities in the world which are sites. If any object that can be a container is automatically also a site, then this appears to require entities to change their ontological status depending on how we are considering them. Moreover, it appears that a room-as-a-room and a room-as-a-site share identity criteria, which makes their joint recognition as independent entities even more curious. We take these to be undesirable features for any ontology and turn instead to qualitative coordinates. Rather than say that a room (which is also an independent physical object of some kind) is also a site, we can make any object that has spatial extent serve as a component of a scheme for structuring location that can be utilized for qualitative coordinates. This is then one way of filling out the parameterizable space regions left open in DOLCE. These objects are further subject to granularity selections, in that a description can be ‘in the room’, ‘in the corner of the room’, ‘in the drawer of the desk in the corner of the room’, etc. Just as with the case with quality regions and color, the labels for the qualities are drawn from the quality region (e.g., ‘red’): thus the particular location descriptions are similary drawn from the make-up of a space region. We can also at this point move the DOLCE dependent category of places (a type of feature) including such induced locations as ‘underneath the table’, ‘in front of the house’, etc. to play a simlar role to sites within a structuring scheme for locations. These developments relate the description of possible space regions to traditional talk of landmarks and relators: the site is simply an extended kind of landmark that is adopted (at a particular granularity) and the relators are simply the qualitative spatial relations provided (at a particular granularity). Sites appear to be ‘container’-landmarks. These characteristics taken together constitute a location scheme. We suggest that making extended objects take a primary role in the structuring of location schemes assigns a cognitively plausible central role to objects when considering locations and space. The regions which are taken up by 4
This is also similar to Bennett’s [16] account where region terms include constructs such as ext(a) or ext(m), which give the spatial extension of individuals or distributions of matter at the history/time index of evaluation. Space precludes further consideration here however.
such objects are more implicit (as is the particular color of the rose which, while perceptually immediate, cannot have a simple form of description). We take space to be necessarily structured; but in a way that differs from the structuring of a conceptual space such as color. There are no observables that can be measured directly; we prefer to see the structure of space as purely Gibsonian in that it is measured by how we can move in it and how objects can be placed within it—particularly in relation to other objects.5 It is only recently, with the advent of global positioning, that location has been made into an ‘observable’ in this sense for anyone who cares to purchase the necessary devices; previously, this would only be accessible to those trained in astronavigation and is unlikely to have had any strong effect on the human conception of space. Whereas particular colors that may exist (such as the particular red of this particular rose) depend on their bearing objects for their existence, locations depend on their location scheme and given a scheme all reachable locations exist. We take this to be the case for both Newtonian/Galilean and Leibnitzian views of space. Thus any physical object will always be placed within an entire framework of spatial relationships and the precise characterization of that placement depends on the location scheme adopted. This is also necessary because, particularly when we consider representations of space such as that of the Region Connection Calculi (RCC) and related schemes, it is not the case that we have singular entities that receive a location (as is the case with a rose being linked to its individual color). This complicates considerable a simple extension of DOLCE to include a space region structured by RCC. Within such perspectives, we have instead a configuration of objects which are together placed in a relationship with the locations defined by a location scheme. Thus, for example, x is inside y would mean (in one reading: for others see: [18, 19]) that both the entities x and y are located at regions which, according to a location scheme that includes the non-tangential proper part relationship, conform to this description. The location of x is a region that lies in an NT P P relationship with a further region, and that further region is the location of y. The spatial configuration of some collection of objects resides in taking up a particular range of locations with particular inter-location relationships holding. For this to be the case, we must ensure that located-at does not become too ‘individualistic’: it is not possible for a single object to be located, as soon as one is, all are. It is this aspect that makes our account neutral between the Newtonian/Galilean vs. Leibnitzian division. Of course, we might not know what the location of some entity is, but that does not mean that ontologically it has no location; indeed this does not represent a question for ontology at all. A location scheme thus induces a rich structure on ‘locations’ in a way that color quality spaces are not assumed to induce structure on the quality regions. Both actions in space and linguistic descriptions can then access those locations regardless of whether something happens to occupy them. This will need to be a correspondingly clear difference in the formalization of the two constructs. 3 Locating entities We now have numerous components that are to be combined in a complete model that nevertheless maintains sufficient flexibility to employ a variety of perspectives on space and the world. In order to specify location of an entity e 1 we need the following: • a selection of an appropriate granular partition of the world that picks out the entity that we wish to locate with respect to other relevant entities, to purpose, and to appropriately related layers; 5
See, for example, the study of Egenhofer and Rodr´ıguez [17] where spatial relations are derived from schemes of action.
Figure 2: Qualitative entity location in terms of parameterized space regions and relations
• a selection of an appropriate space region formalization that brings out or makes available relevant spatial relationships; • a selection of an appropriate partition over the space region (e.g., from RCC to RCC-8 or RCC-5, or to qualitative distance, or cardinal directions, etc.); • the identification of the location of the entity with respect to the selected space region description. Moreover, in order to describe a location of some additional entity e 2 or further location in terms of the previously specified entity e1 , we need to select a fitting relation from those made available in the space region. All of these selections may involve more or less precise information as determined by the granularity of the partitions selected and their inherently qualitative nature. We depict this graphically in Figure 2. This uses as an example an office environment as envisaged for several of our current application scenarios. For the current simple example, we consider the task of a robotic system needing to identify an entity by its location—a very common task given the fact that artificial agents can still only recognize a rather small range of objects. The granularity of the selected partition picks out an office and some items of office furniture, such as chairs and desks. Similarly, the space region is decomposed according to a selected specification involving spatial relations. This, represented by the inner box, is a parameterized module that may be selected freely for describing a particular location scheme. This determines the perspective on space that is being taken. We can then give relative spatial specifications using those relations (e.g., ‘in front of’ / ’behind’ or connects, etc.) that are available within that persepective. We can also identify locations (e.g., l 1 ) using the objects that inhabit particular locations: such as the ‘chair’ (e 1 ). Then, in order to describe the location of some additional entity that may not already be ordered within the adopted partition (e.g., e1 ), we can select a relation (R) from the space region in order to capture that location (l2 ). This can then stand behind descriptions such as: The e2 is in front of the chair The e2 is near the chair depending on how the space region is structured. All of the categories used are of course to be grounded in the basic categories of an appropriate foundational ontology, such as physical endurant, etc.
Acknowledgements The Collaborative Research Center for Spatial Cognition (Sonderforschungsbereich/Transregio SFB/TR8) of the Universities of Bremen and Freiburg is funded by the Deutsche Forschungsgemeinschaft (DFG), whose support we gratefully acknowledge. References [1] A.G. Cohn and S.M. Hazariki. Qualitative spatial representation and reasoning: an overview. Fundamenta Informaticae, 43:2–32, 2001. [2] John Bateman and Scott Farrar. Spatial ontology baseline. SFB/TR8 internal report I1-[OntoSpace]: D2, Collaborative Research Center for Spatial Cognition, University of Bremen, Germany, April 2004. [3] I. Niles and A. Pease. Origins of the Standard Upper Merged Ontology: A Proposal for the IEEE Standard Upper Ontology. In Working Notes of the IJCAI-2001 Workshop on the IEEE Standard Upper Ontology, pages 37–42, 2001. [4] Roberto Casati and Achille C. Varzi. Holes and other superficialities. MIT Press (Bradford Books), Cambridge, MA and London, 1994. [5] J. Renz and B. Nebel. On the complexity of qualitative spatial reasoning: a maximal tractable fragment of the region connection calculus. Artificial Intelligence, 108(1–2):69–123, 1999. [6] J. Renz. Maximal tractable fragments of the region connection calculus: A complete analysis. In T. Dean, editor, Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI-99), pages 448–454. Morgan Kaufman Publishers, San Francisco, CA, 1999. [7] Brandon Bennett, Frank Wolter, and Michael Zakharyaschev. Multi-dimensional modal logic as a framework for spatio-temporal reasoning. Applied Intelligence, 17(3):239–251, 2002. [8] A. Gangemi, N. Guarino, A. Oltramari, and L. Schneider. Sweetening ontologies with DOLCE. In Proceedings of EKAW 2002, Siguenza, Spain, January 2002. [9] Claudio Masolo, Stefano Borgo, Aldo Gangemi, Nicola Guarino, and Alessandro Oltramari. Ontologies library (final). WonderWeb Deliverable D18, ISTC-CNR, Padova, Italy, December 2003. [10] P. G¨ardenfors. Conceptual spaces: the geometry of thought. MIT Press, Cambridge, MA., 2000. [11] Pierre Grenon and Barry Smith. SNAP and SPAN: Prolegomenon to geodynamic ontology. In Spatial Cognition and Computation. forthcoming. [12] Barry Smith and Pierre Grenon. The cornucopia of formal-ontological relations. Dialectica, forthcoming. [13] Barry Smith and Achille C. Varzi. The Niche. No uˆ s, 33(2):214–238, 1999. [14] Maureen Donnelly and Barry Smith. Layers: A new approach to locating objects in space. In W. Kuhn, M. F. Worboys, and S. Timpf, editors, Spatial Information Theory: Foundations of Geographic Information Science, number 2825 in Lecture Notes in Computer Science, pages 50–65. Springer, Berlin, 2003. [15] Thomas Bittner and Barry Smith. A taxonomy of granular partitions. In Proceedings of the Conference on Spatial Information Theory - COSIT 2001, Lecture Notes in Computer Science, pages 28–43. SpringerVerlag, Berlin-Heidelberg, 2001. [16] B. Bennett. Physical objects, identity and vagueness. In D. Fensel, Deborah McGuinness, and Mary-Anne Williams, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the Eighth International Conference (KR2002), San Francisco, CA, 2002. Morgan Kaufmann. [17] M. Egenhofer and A. Rodr´ıguez. Relation algebras over containers and surfaces: An ontological study of a room space. Spatial Cognition and Computation, 1(2):155–180, 1999. [18] Anthony G. Cohn, Brandon Bennett, John Gooday, and Nicolas M. Gotts. Representing and reasoning with qualitative spatial relations. In Olivero Stock, editor, Spatial and temporal reasoning, pages 97–132. Kluwer Academic Publishers, Dordrecht, 1997. [19] E. Davis, N.M. Gotts, and A.G. Cohn. Constraint networks of topological relations and convexity. Constraints, 4(3):241–280, 1999.
