Fuzzy region connection calculus: Representing vague topological information

Steven Schockaert, Martine De Cock, Chris Cornelis, Etienne E. Kerre
2008 International Journal of Approximate Reasoning  
Qualitative spatial information plays a key role in many applications. While it is well-recognized that all but a few of these applications deal with spatial information that is affected by vagueness, relatively little work has been done on modelling this vagueness in such a way that spatial reasoning can still be performed. This paper presents a general approach to represent vague topological information (e.g., A is a part of B, A is bordering on B), using the well-known region connection
more » ... lus as a starting point. The resulting framework is applicable in a wide variety of contexts, including those where space is used in a metaphorical way. Most notably, it can be used for representing, and reasoning about, qualitative relations between regions with vague boundaries. theatres near Gent, Belgium). On one hand, this could be achieved by finding addresses, transforming these addresses to geographical coordinates, and comparing these coordinates with available (structured) information. However, there is also a lot of relevant geographical information available in the form of qualitative relations, either extracted from natural language texts, or a priori available in geo-ontologies [40] . In most existing work, qualitative relations are crisp relations, e.g., p is either far from q or not far from q, and regions are assumed to have precisely defined boundaries. These assumptions stand in stark contrast to the nature of real-world geographical information. For example, most non-political geographical regions, such as Western Europe, Downtown Seattle, or the Alps, have vague boundaries [18, 26, 28, 29] . Also the concept of nearness of places is generally perceived as a vague property, where a proposition like p is close to q is often considered true to some degree in a given context [3, 6, 19, 20, 27] . Hence, there is a clear need for formalisms that describe qualitative spatial properties in a graded way. In this paper, we will focus on topological relations. Usually, information such as A is a part of B is formally expressed using either the Region Connection Calculus (RCC) [4] or the 9-intersection model [2]. We will focus on the former, since it is more tailored towards reasoning. In the RCC, spatial relations are defined using a primitive dyadic relation C which expresses the notion of connection between regions. For example, we may think of regions as sets of points, and define C such that for two regions a and b, C(a, b) holds iff a and b have a point in common. Other topological relations are defined in terms of the relation C, as shown in Table 1 . The intuitive meaning of some of these relations is shown in Fig. 1 . Throughout this paper, we will use upper case letters like A, B, C, . . . to denote specific regions, and lower case letters like a, b, c, . . . to denote variables that take values from the universe of regions U. Clearly, the crisp nature of the RCC relations is a major limitation in many application domains. For example, while the relations EC and DC are mutually exclusive, in practical applications it is often difficult, or even undesirable, to differentiate between situations where two regions are very close to each other, but disconnected, and situations where two regions are connected. For example, it is commonplace to say that a cabinet is located against a wall even if there is a gap of a few millimeters between the cabinet and the wall. When modelling such a spatial configuration using the RCC relations, EC would hold if the cabinet is actually located against the wall, while DC would hold as soon as there is a gap, irrespective of its size. A cognitively more adequate approach would be to define relations like EC and DC such that EC holds to the extent that the Table 1 Definition of topological relations in the RCC Name Relation Definition Disconnected from DC(a, b) :Cða; bÞ Part of P(a, b) ( "c 2 U)(C(c, a) ) C(c, b)) Proper part of PP(a, b) P ða; bÞ^:P ðb; aÞ Equal to EQ(a, b) P(a, b)^P(b, a) Overlaps with O(a, b) ( $c 2 U)(P(c, a)^P(c, b)) Discrete from DR(a, b) :Oða; bÞ Partially overlaps with PO(a, b) Oða; bÞ^:P ða; bÞ^:P ðb; aÞ Externally connected to EC(a, b) Cða; bÞ^:Oða; bÞ Non-tangential part of NTP(a, b) P ða; bÞ^:ð9c 2 UÞðECðc; aÞ^ECðc; bÞÞ Tangential proper part of TPP(a, b) PP ða; bÞ^:NTP ða; bÞ Non-tangential proper part of NTPP(a, b) :P ðb; aÞ^NTP ða; bÞ a and b denote regions, i.e., elements of the universe of regions U. Fig. 1. Intuitive meaning of some RCC relations.
doi:10.1016/j.ijar.2007.10.001 fatcat:35tmoftfrveclm7yrdboykvlzu