Natural-Language Spatial Relations Between Linear and Areal Objects: The Topology and Metric of English-Language Terms

Spatial relations are the basis for many selections users perform when they query geographic information systems (GISs). Although such query languages use natural-language-like terms, the formal definitions of those spatial relations rarely reflect the same meaning people would apply when they communicate among each other. To bridge the gap between computational models for spatial relations and people’s use of spatial terms in their natural languages, a model for the geometry of spatial relations was calibrated for a set of 59 English-language spatial predicates. The model distinguishes topological and metric properties. The calibration from sketches that were drawn by 34 human subjects identifies ten groups of spatial terms with similar properties and provides a mapping from spatial terms onto significant geometric parameters and their values. The calibration’s results reemphasize the importance of topological over metric properties in the selection of English-language spatial terms. The model provides a basis for high-level spatial query languages that exploit natural-language terms and serves as a model for processing such queries. 1 . Introduction Communication is paramount to people understanding each other. Among the most critical measures of the success of verbal communication is the effective capture and conveyance of the semantics of words. The better the recipient of words reconstructs the meaning the sender attaches to them, the better the recipient will understand the sender. This measure also applies to the interaction between users and geographic information systems (GISs). Although the interaction with current GISs occurs primarily through structured query languages (Egenhofer and Herring 1993), future GISs are expected to support more natural interactions with geographic data through such modalities as sketching a spatial query and simultaneously describing aspects of the sketch * This work was partially supported by the National Science Foundation (NSF) under grant number SBR-8810917 for the National Center for Geographic Information and Analysis (NCGIA) and by the Scientific and Environmental Affairs Division of the North Atlantic Treaty Organization. This work was performed while Rashid Shariff was with the NCGIA at the University of Maine and his work was partially supported by a fellowship from the Malaysian Government. Max Egenhofer’s work is further supported by NSF grants IRI-9309230, IRI-9613646, SBR-9600465, and BDI-9723873; by grants from Rome Laboratory under grant number F30602-95-1-0042, the National Imagery and Mapping Agency under grant number NMA202-97-1-1023, and the National Aeronautics and Space Administration, and by a Massive Digital Data Systems contract sponsored by the Advanced Research and Development Committee of the Community Management Staff. Natural-Language Spatial Relations Between Linear and Areal Objects:The Topology and Metric of English-Language Terms A. R. Shariff, M. Egenhofer, and D. Mark International Journal of Geographical Information Science, 12 (3): 215-246, 1998. through spoken language (Egenhofer 1996). Likewise, future GISs are likely to complement the presentation of query results in a graphical or tabular form through the generation of naturallanguage-like instructions or responses to spatial queries (Mark and Gould 1991). In order to move towards GISs with which users could interact much like they would communicate with other people, it is necessary to gain a better understanding of the semantics of the spatial terms that would play a major role in such interactions. The focus of this work is on capturing the geometry that is associated with natural-language spatial relations. Spatial relations refer to the way people perceive spatial configurations, how they reason about such configurations, and how they describe them in a variety of languages. Based on different mathematical concepts, the GIS literature distinguishes three major types of spatial relations (Pullar and Egenhofer 1988; Worboys 1992): topological relations require the concept of neighborhood and are invariant under consistent topological transformations, such as rotation, translation, scaling; cardinal direction relations are based on the existence of a vector space and are subject to change under rotation, while they are invariant under translation and scaling of the reference frame; and distance relations express spatial properties that reflect the concept of a metric and, therefore, change under scaling, but are invariant under translation and rotation. Capturing the semantics of spatial relations has a long-standing history (Freeman 1975; Peuquet 1986), with a wave of formal models for spatial relations developed in the 1990s (Egenhofer and Herring 1990; Egenhofer and Franzosa 1991; Egenhofer and Herring 1991; Frank 1991; Hernández 1991; Frank 1992; Freksa 1992; Hazelton et al. 1992; Randell et al. 1992; Clementini et al. 1993; Cui et al. 1993; Papadias and Sellis 1993; Zimmermann 1993; Hernández 1994; Papadias and Sellis 1994; Clementini et al. 1995; Cohn 1995; Egenhofer and Franzosa 1995; Hernández et al. 1995; Hong et al. 1995; Nabil et al. 1995; Clementini and di Felice 1996; Cohn and Gotts 1996; Nabil et al. 1996; Papadias et al. 1996; Sharma 1996), these models have often stood for themselves, leading to query language extensions based on mathematically well-defined concepts (Herring 1991; de Hoop and van Oosterom 1992; Hadzilacos and Tryfona 1992; Keighan 1993), but there have been only few attempts to link these models with the way people use spatial terms in natural language. Most previous approaches to characterizing the meanings of spatial relations worked primarily with informal models and treated spatial relations case by case (Talmy 1983; Herskovits 1986). An approach in computational linguistics, based on a connectionists model, provides a framework for the definition of a set of spatial relations (Regier 1995), however, it does not lead immediately to explaining differences among relations in a high-level, visually-related domain and results in computational models (e.g., neural networks) that do not integrate well with current architectures of GISs and spatial database systems. This paper makes an effort to narrow the gap between formal models of spatial relations as developed for GISs and people’s intuitive understanding of spatial relations as expressed in everyday language so that future GISs would become more natural and easier to use. The semantics of spatial relations have many facets and aspects that may influence people’s choices of words, such as the meaning of the objects, their shape, their scale, and the spatial relations among the objects, as well as the culture, education, and natural language of the individuals using the terms (Mark et al. 1995). Since GISs are primarily engaged in the recording of geometric and some semantic information, future GISs that could listen to and talk with users (Egenhofer 1996) require links between geometric representations and natural spatial languages; therefore, this paper focuses on the topological and metric aspects of natural-language spatial relations. We build on a model for topological relations and enhance it with metric refinements that capture details beyond topological aspects. Aspects of direction or orientation have been reserved for future investigations as possible extensions to the currently used model. The model of topological relations with metric refinements was calibrated for a set of 59 English-language spatial terms, for which 34 human subjects had generated sketches. The calibration shows ten groups with different topological and metric characteristics, and identifies for each term its significant metric parameters and their value ranges. This model enables the generation of simple sentences to Natural-Language Spatial Relations Between Linear and Areal Objects:The Topology and Metric of English-Language Terms A. R. Shariff, M. Egenhofer, and D. Mark International Journal of Geographical Information Science, 12 (3): 215-246, 1998. describe spatial scenes and the processing of spatial queries with natural-language spatial terms (Shariff 1996). The remainder of this paper is structured as follows: Section 2 summarizes the topological and metric models used to specify spatial relations. Section 3 describes the experiment conducted to calibrate the model for 59 English-language terms. To analyze the effect of topology and metric, the terms were grouped into clusters with similar properties (Section 4) and within these clusters, significant parameters were identified leading to a dictionary of topological and metric parameters for the 59 terms (Section 5). Section 6 confirms the significant parameters with results from another experiment and Section 7 demonstrates the implications of this model for spatial query processing. Section 8 provides conclusions and discusses future work. 2 . Computational Model for Spatial Relations Following the premise that topology matters, metric refines (Egenhofer and Mark 1995), we use a two-tier model for the analysis of natural-language spatial relations. It consists of (1) capturing the topology of the configuration and (2) analyzing the topological configuration according to a set of metric properties. 2 . 1 9-Intersection for Line-Region Relations The 9-intersection model is a comprehensive model for binary topological spatial relations and applies to objects of type area, line, and point (Egenhofer and Herring 1991). It characterizes the topological relation between two point sets, A and B , by the set intersections of A’s interior ( A°), boundary ( ¶A), and exterior ( A ) with the interior, boundary, and exterior of B , called the 9-intersection (Equation 1). I A, B ( ) = A°ÇB° A°Ç¶B A°ÇB ¶A Ç B° ¶A Ç ¶B ¶A Ç B A Ç B° A Ç ¶B A Ç B æ