Qualitative Spatial Reasoning about Internal Cardinal Direction Relations

A class of novel spatial relation, internal cardinal direction (ICD) relation, is introduced and discussed. Applying ICD-9 model, the characteristics and the simplification rule of ICD relations are discussed at first. Then the ICD related qualitative spatial reasoning is discussed in a formal way. Four composition cases are presented. They are 1) composing two nesting ICD relations and composing two coordinate ICD relations to deduce 2) conventional (or external) cardinal relations, 3) qualitative distance relations and 4) topological relations respectively. When ICD relations are taken into account, the container determines analysis scale and forms a positioning framework together with ICD relations. So the research on ICD related qualitative spatial reasoning would con-tribute to the representation and reasoning about survey knowledge. * Corresponding author. 1. INTERNAL CARDINAL-DIRECTION RELATIONS AND ICD-9 MODEL 1.1 Internal cardinal-direction relations In fields of geographical information system (GIS), artificial intelligence (AI) and databases, qualitative spatial reasoning (QSR) has drawn lot of attention. Spatial relations, including topological relations, cardinal direction relations and metric relations, play essential roles in QSR. To the author’s knowledge, without concerning temporal factors, the research of QSR mainly focuses on three aspects until recently. They are: 1. Formalizing one type of spatial relations and discussing their attributes, such as concept neighbourhood graph, computability, etc. (Egenhofer, 1992; Randell, 1992; Duckham, 2001; Skiadopoulos 2004). 2. Composing two or more spatial relations to obtain a previously unknown relation. This aspect includes composition of topological relations (Ligozat, 1999; Renz, 2002), composition of cardinal direction relations (Skiadopoulos, 2001; Isli, 2000), and composition of topological relation and metric relation (Giritli, 2003). Furthermore, the other SQR problems, such as pathconsistency problem, minimal labels problem, can be solved based these compositions. 3. Determining a place’s position according to provided spatial relations (Clementini, 1997; Isli, 1999; Moratz, 2003), where cardinal direction relations and metric relations are more often applied. In this paper, internal cardinal-direction (ICD) relation related QSR is in discussion. Different from the other types of spatial relations, ICD is applied to represent the direction relations between an object and another area entity containing it. The ICD relations between the containee and the container depend on the containee’s relative position in the latter. It is well known that spatial knowledge development includes three stages, i.e. landmark knowledge, route knowledge and survey knowledge (Montello, 2001). In order to express and transfer survey knowledge, some base landmarks are usually selected and described using ICD relations at first. Then the other places are determined according to the base landmarks using topological, cardinal direction or qualitative distance relations. A typical statement to represent survey knowledge might be “A locates in the west-east of B, and C lies to the north of A”. In (Mennis, 2000), a pyramid framework to model geographic data and geographic knowledge is developed based on geographic cognition (Fig. 1). According to this framework, geo-knowledge includes two parts, i.e. taxonomy (superordinate-subordinate relationships) and partonomy (partwhole relations). Obviously, ICD implies part-whole relations and conduces to the representation of partonomy knowledge. Figure 1. A pyramid framework for spatial knowledge (Mennis, 2000) This paper is structured as follows. At first, ICD-9 model and its characteristics are described briefly. Then some fundamental concepts are defined. Based on these concepts, simplification rules of ICD-9 are established. In the third part of this paper, ICD-relation based qualitative spatial reasoning is in discussion. A series of composition tables are provided to demonstrate the QSR about ICD relations with ICD relations, ECD relations, topological relations and qualitative distance relations respectively. At last, we conclude the paper and present an agenda for future work.