An Image-Schematic Account of Spatial Categories Werner Kuhn Institute for Geoinformatics, University of Münster Robert-Koch-Str. 26-28, D-48149 Münster. [email protected] Abstract. How we categorize certain objects depends on the processes they afford: something is a vehicle because it affords transportation, a house because it offers shelter or a watercourse because water can flow in it. The hypothesis explored here is that image schemas (such as LINK, CONTAINER, SUPPORT, and PATH) capture abstractions that are essential to model affordances and, by implication, categories. To test the idea, I develop an algebraic theory formalizing image schemas and accounting for the role of affordances in categorizing spatial entities. 1 Introduction An ontology, according to Guarino [17], is “a logical theory accounting for the intended meaning of a vocabulary”. Ontologies map terms in a vocabulary to symbols and their relations in a theory. For example, an ontology might specify that a house is a building, using symbols for the two universals (house, building) and applying the taxonomic (is-a) relation to them; or it might explain what it means for a roof to be part of a building, using a mereological (part-of) relation [2]. What relations should one use to account for the meaning expressed by the italicized phrases in the following glosses from WordNet 1? • a house is a “building in which something is sheltered or located” • a boathouse is a “house at edge of river or lake; used to store boats ” • a vehicle is a “conveyance that transports people or objects ” • a boat is a “small vessel for travel on water ” • a ferry is a “boat that transports people or vehicles across a body of water and operates on a regular schedule” • a houseboat is a “barge that is designed and equipped for use as a dwelling ” • a road is an “open way (generally public) for travel or transportation .” These phrases express potentials for actions or processes, rather than actual processes. I will use the term processes for anything happening in space and time, and the term affordances for potentials of processes. This should not be taken as overextending Gibson’s notion [13], but as a shorthand covering a collection of phenomena whose best example is an affordance in Gibson’s sense (and which have been called telic relations in [33]). They all pose the same ontological challenge: how can a logical 1 http://wordnet.princeton.edu/perl/webwn theory capture the categorizing effect of potential processes? For example, how can it express that a vehicle is a vehicle because it affords transportation, even though it may never be used to transport anything, or that a house is a house because it can shelter something? The goal is not to capture peripheral cases of a category (e.g., the vehicle which never transports), but conversely, properties which are central (e.g., the transportation and sheltering affordances). As the above WordNet examples illustrate, affordances are indeed often central for categorization. What is the relevance of affordances to ontologies of spatial information? Ordnance Survey (the mapping agency of Great Britain) has identified affordance as one of five basic ontological relations to make their geographic information more explicitly meaningful, together with taxonomic, synonym, topological, and mereological relations [19]. Feature-attribute catalogues for geographic information abound with object definitions listing affordances as key characteristics [38]. Recent challenges to semantic interoperability have revolved around use cases that involve affordances. For example, the OGC geospatial semantic web Interoperability Experiment 2 worked on a query retrieving airfields based on their affordance of supporting certain aircrafts. Addressing the ontological challenge posed by affordances is necessary to capture the meaning of vocabularies in spatio-temporal information and to enable semantic interoperability. Affordances are also increasingly recognized as having a role to play in formal ontology [1]. The enduring core of objects, particularly of artifacts or organisms, has been sought in “bundles of essential functions” [31]. Frank sees affordances as the properties that define object categories in general and uses this idea in his ontological tiers [7]. Smith has proposed an ontology of the environment, and in particular the notion of niche [39], founded on Gibson’s affordances and underlying his Basic Formal Ontology . The Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE) introduces categories “as cognitive artifacts ultimately depending on human perception, cultural imprints and social conventions” and acknowledges a Gibsonian influence [11]. Recent formal ontology work has attempted to formalize image schemas as abstract descriptions [12]. While this gives an ontological account of the mental abstraction of image schemas, it does not yet allow for using it in category specifications. The latter would require integration with work on roles, particularly thematic roles, to address the categorizing power of objects participating in processes. Thematic roles are essentially a set of types of participation for objects in processes [40]. For example, a vehicle can play the thematic role of an instrument for transportation. The formalization of image schemas given in this paper does capture such thematic roles, but at a more generic level that has not yet been related to the thematic role types discussed in the linguistics literature. In the context of spatial information theory, affordances and image schemas have been the object of several formalization attempts [5,10,25,34,35,36,37]. At least one of them also made the relationship between the two notions explicit [37]. But none has developed an image-schema based formalization of affordances to the point where it can account for categorizations. The work presented here builds on these attempts 2 http://www.opengeospatial.org/initiatives/?iid=168 and develops them further in the context of spatial ontologies. Its major contribution is a formal algebraic theory of a set of image schemas and their affordances. What are the basic ontological modeling options for affordances? Unary relations (e.g., “affords-transportation”) leave the meaning of their predicates unspecified, produce an unlimited number of them, and suppress the object to which a process is afforded. To model affordances as a binary or ternary relation (“affords”), would require a kind of process as argument (e.g., “transportation”). For example, an individual vehicle (say, your car) affords a kind of transportation (i.e., of people), which subcategorizes the vehicle (e.g., as a car). However, first order theories do not permit process types as arguments, as long as these are not treated as individuals. The Process Specification Language PSL [16] takes the latter approach, but cannot state algebraic properties for the process types. Due to this expressiveness issue, formal ontology has not yet approached affordance relations (see also [2,3,31] for discussions of formal ontological relations). The participation relation comes closest, but relates individual objects to actual processes [31]. It is also much looser than affordance. For example, a boat might participate in a painting process, as well as a transportation event. Both conform to the usual intuition about participation, that there are objects involved in processes, but one is an “accidental participation” and the other an instance of a potential, afforded participation that categorizes the object. Ontological relations between classes have been proposed for capturing spatial relations [4]. However, they cover only classes of objects (not processes), and the approach would need to be extended to modal logic in order to cope with potential processes, not only with existence and universal quantification. Before taking this route of first order axiomatizations of affordance relations, one has to analyze what relations are necessary. This is the goal pursued here. The main novelty is the combined formalization of affordances and image schemas in a second order algebraic theory, accounting for spatial categories and establishing a framework for ontology mappings. In the remainder of the paper, I will state how image schemas form the basis for the theory (section 2), introduce the formalization method (section 3), present the results of the analysis (section 4), and conclude with implications and directions for future research (section 5). 2 Image Schemas as Theoretical Foundation The primary source on image-schematic categorization is Lakoff’s Women, Fire, and Dangerous Things [29]. It presents detailed case studies on image schemas and their role in language and cognition. Its main impact lay in demonstrating the inadequacy of traditional ideas about categorization, which are based on necessary and sufficient conditions. Formalizations, however, were not Lakoff’s goal, due to the perceived limitations of formal semantics at the time. Since then, a lot of work in cognitive semantics, including applications to ontology engineering [26] has built on Lakoff’s empirical evidence and informal models for image schemas. This section reviews the widely accepted characteristics and attempts to identify “ontological properties” of image schemas. 2.1 Key Characteristics of Image Schemas Image schemas are patterns abstracting from spatio-temporal experiences. For example, they capture the basic common structures from our repeated experience of containment, support, linkage,