Bilateral Spatial Reasoning about Street Networks: Graph-based RAG with Qualitative Spatial Representations

This paper deals with improving the capabilities of Large Language Models (LLM) to provide route instructions for pedestrian wayfinders by means of qualitative spatial relations.

Towards Applying the OPRA Theory to Shape Similarity

The motivation for using qualitative shape descriptions is as follows: qualitative shape descriptions can implicitly act as a schema for measuring the similarity of shapes, which has the potential to be cognitively adequate. Then, shapes which are similar to each other would also be similar for a pattern recognition algorithm. There is substantial work in pattern recognition and computer vision dealing with shape similarity. Here with our approach to qualitative shape descriptions and shape similarity, the focus is on achieving a representation using only simple predicates that a human could even apply without computer support.

Qualitative shape representation based on the qualitative relative direction and distance calculus eOPRAm

This document serves as a brief technical report, detailing the processes used to represent and reconstruct simplified polygons using qualitative spatial descriptions, as defined by the eOPRAm qualitative spatial calculus.

Extending Binary Qualitative Direction Calculi with a Granular Distance Concept: Hidden Feature Attachment

In this paper we introduce a method for extending binary qualitative direction calculi with adjustable granularity like OPRAm or the star calculus with a granular distance concept. This method is similar to the concept of extending points with an internal reference direction to get oriented points which are the basic entities in the OPRAm calculus. Even if the spatial objects are from a geometrical point of view infinitesimal small points locally available reference measures are attached. In the case of OPRAm, a reference direction is attached. The same principle works also with local reference distances which are called elevations. The principle of attaching references features to a point is called hidden feature attachment.

Qualitative Reasoning about Relative Direction on Adjustable Levels of Granularity

An important issue in Qualitative Spatial Reasoning is the representation of relative direction. In this paper we present simple geometric rules that enable reasoning about relative direction between oriented points. This framework, the Oriented Point Algebra OPRA_m, has a scalable granularity m. We develop a simple algorithm for computing the OPRA_m composition tables and prove its correctness. Using a composition table, algebraic closure for a set of OPRA statements is sufficient to solve spatial navigation tasks. And it turns out that scalable granularity is useful in these navigation tasks.

Oriented Straight Line Segment Algebra: Qualitative Spatial Reasoning about Oriented Objects

Nearly 15 years ago, a set of qualitative spatial relations between oriented straight line segments (dipoles) was suggested by Schlieder. This work received substantial interest amongst the qualitative spatial reasoning community. However, it turned out to be difficult to establish a sound constraint calculus based on these relations. In this paper, we present the results of a new investigation into dipole constraint calculi which uses algebraic methods to derive sound results on the composition of relations and other properties of dipole calculi. Our results are based on a condensed semantics of the dipole relations. In contrast to the points that are normally used, dipoles are extended and have an intrinsic direction. Both features are important properties of natural objects. This allows for a straightforward representation of prototypical reasoning tasks for spatial agents. As an example, we show how to generate survey knowledge from local observations in a street network. The example illustrates the fast constraint-based reasoning capabilities of the dipole calculus. We integrate our results into two reasoning tools which are publicly available.