Deriving topological relations from topologically augmented direction relation matrices

Topological relations and direction relations represent two pieces of the qualitative spatial reasoning triumvirate. Researchers have previously attempted to use the direction relation matrix to derive a topological relation, finding that no single direction relation matrix can isolate a particular topological relation. In this paper, the technique of topological augmentation is applied to the same problem, identifying a unique topological relation in 28.6% of all topologically augmented direction relation matrices, and furthermore achieving a reduction in a further 40.4% of topologically augmented direction relation matrices when compared to their vanilla direction relation matrix counterpart.

A Logic of Directions

We propose a logic of directions for points (LD) over 2D Euclidean space, which formalises primary direction relations east (E), west (W), and indeterminate east/west (Iew), north (N), south (S) and indeterminate north/south (Ins). We provide a sound and complete axiomatisation of it, and prove that its satisfiability problem is NP-complete.

Positioning Locality Based on Cognitive Directions and Context in Indoor Landmark Reference System

<p><strong>Abstract.</strong> Geographic information sciences (GIS) have been entering an era of information explosion. The data-related geographic can be divided into many classes, according to their sources and format, such as raster dataset, shape file, textual information, and voice. Locality description, which is a common form of voice, conveys considerable spatial information and can be derived from our daily communication. The issue of dealing with the locality description information is a research hot spot of next-generation GIS for many scholars.</p><p>Locality description reflects direct or indirect human interaction with environment directly. As an external expression of cognition, the uncertainty that is associated with locality description is inevitable. Locality description generally contains spatial relationships (i.e., topological, distance, and direction relations) and reference objects (ROs). Any feature with a name can be regarded as an RO. Topological relations, which convey rough information-related locality and can be refined by distance or direction relations, are seldom used directly in locality description positioning. The distance and direction relations are usually combined to describe locality, which conveys many clues to position locality.</p><p>Humans have a weak sense of direction indoors, and relative directions are used frequently in locality description. For example, locality description indoors can be given as follows: “Object A is in front of me, and object B is on my left. Context is an unavoidable topic of Locality description. The locality description is complex, either explicitly or implicitly, especially in a landmark reference system (i.e., a reference system where people can describe his locality with one or several landmarks), in which the nearest landmark can be selected easily to describe locality. On the basis of this context, the locality description (“Object A is in front of me, and object B is on my left”) stated above in an indoor landmark reference system (ILRS) implies that objects A and B are near the individual. Hence, the meaning of “Object A is in front of me, and object B is on my left” in ILRS is the same as that of “Object A is in front of me, object B is on my left, and they are all near to me”.</p><p>This paper introduces a novel method of positioning localities indoors by using locality description in ILRS. To achieve positioning of localities with directions description and context in ILRS, we propose a joint probability function that consists of qualitative distance (i.e., near relation) and relative direction membership function. The qualitative distance membership function that considers both minimum Euclidean distance and the stolen area is based on fuzzy set. For consistency with cognition, some definitions are provided during the calculation of relative direction, which can also reduce the number of points to be explored from an algorithmic point of view.</p>

Reasoning about Topological and Cardinal Direction Relations Between 2-Dimensional Spatial Objects

Increasing the expressiveness of qualitative spatial calculi is an essential step towards meeting the requirements of applications. This can be achieved by combining existing calculi in a way that we can express spatial information using relations from multiple calculi. The great challenge is to develop reasoning algorithms that are correct and complete when reasoning over the combined information. Previous work has mainly studied cases where the interaction between the combined calculi was small, or where one of the two calculi was very simple. In this paper we tackle the important combination of topological and directional information for extended spatial objects. We combine some of the best known calculi in qualitative spatial reasoning, the RCC8 algebra for representing topological information, and the Rectangle Algebra (RA) and the Cardinal Direction Calculus (CDC) for directional information. We consider two different interpretations of the RCC8 algebra, one uses a weak connectedness relation, the other uses a strong connectedness relation. In both interpretations, we show that reasoning with topological and directional information is decidable and remains in NP. Our computational complexity results unveil the significant differences between RA and CDC, and that between weak and strong RCC8 models. Take the combination of basic RCC8 and basic CDC constraints as an example: we show that the consistency problem is in P only when we use the strong RCC8 algebra and explicitly know the corresponding basic RA constraints.