Reinhard Moratz

IJCAI Conference 2017 Conference Paper

Relations Between Spatial Calculi About Directions and Orientations (Extended Abstract)

• Till Mossakowski
• Reinhard Moratz

A qualitative representation of space and/or time provides mechanisms which characterize the essential properties of objects or configurations. The advantages over quantitative representations can be: (1) a better match with human concepts related to natural language, and (2) better efficiency for reasoning. The two main trends in qualitative spatial constraint reasoning are topological reasoning about regions and reasoning about directions between points and straight lines and orientations of straight lines or configurations derived from points. In this work, we apply universal algebraic tools to binary qualitative calculi and their relations.

JAIR Journal 2015 Journal Article

Relations Between Spatial Calculi About Directions and Orientations

• Till Mossakowski
• Reinhard Moratz

Qualitative spatial descriptions characterize essential properties of spatial objects or configurations by relying on relative comparisons rather than measuring. Typically, in qualitative approaches only relatively coarse distinctions between configurations are made. Qualitative spatial knowledge can be used to represent incomplete and underdetermined knowledge in a systematic way. This is especially useful if the task is to describe features of classes of configurations rather than individual configurations. Although reasoning with them is generally NP-hard, relative directions are important because they play a key role in human spatial descriptions and there are several approaches how to represent them using qualitative methods. In these approaches directions between spatial locations can be expressed as constraints over infinite domains, e.g. the Euclidean plane. The theory of relation algebras has been successfully applied to this field. Viewing relation algebras as universal algebras and applying and modifying standard tools from universal algebra in this work, we (re)define notions of qualitative constraint calculus, of homomorphism between calculi, and of quotient of calculi. Based on this method we derive important properties for spatial calculi from corresponding properties of related calculi. From a conceptual point of view these formal mappings between calculi are a means to translate between different granularities.

AIJ Journal 2012 Journal Article

Qualitative reasoning about relative direction of oriented points

• Till Mossakowski
• Reinhard Moratz

An important issue in qualitative spatial reasoning is the representation of relative directions. In this paper we present simple geometric rules that enable reasoning about the 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 m statements is very useful for solving spatial navigation tasks. It turns out that scalable granularity is useful in these navigation tasks.

AIJ Journal 2011 Journal Article

A condensed semantics for qualitative spatial reasoning about oriented straight line segments

• Reinhard Moratz
• Dominik Lücke
• Till Mossakowski

More than 15 years ago, a set of qualitative spatial relations between oriented straight line segments (dipoles) was suggested by Schlieder. 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 of dipole calculi. This new method, which we call condensed semantics, is based on an abstract symbolic model of a specific fragment of our domain. It is based on the fact that qualitative dipole relations are invariant under orientation preserving affine transformations. The dipole calculi allow 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 dipole calculi. We integrate our results into two reasoning tools which are publicly available.

AAAI Conference 2006 Conference Paper

Intuitive linguistic Joint Object Reference in Human-Robot Interaction: Human Spatial Reference Systems and Function-Based Categorization for Symbol Grounding

• Reinhard Moratz

The visionary goal of an easy to use service robot implies intuitive styles of interaction between humans and robots. Such natural interaction can only be achieved if means are found to bridge the gap between the forms of object perception and spatial knowledge maintained by such robots, and the forms of language, used by humans, to communicate such knowledge. Part of bridging this gap consists of allowing user and robot to establish joint reference on objects in the environment - without forcing the user to use unnatural means for object reference. We present an approach to establishing joint object reference which makes use of natural object classification and a computational model of basic intrinsic and relative reference systems. Our object recognition approach assigns natural categories (e. g. ”desk”, ”chair”, ”table”) to new objects based on their functional design. With basic objects within the environment classified, we can then make use of a computational reference model, to process natural projective relations (e. g. “the briefcase to the left of the chair”), allowing users to refer to objects which cannot be classified reliably by the recognition system alone.

ECAI Conference 2006 Conference Paper

Representing Relative Direction as a Binary Relation of Oriented Points

• Reinhard Moratz

A central issue in robotics is the representation of relative orientation. Currently, the standard solution utilizes metrical representations. The main reason for this might be that representing rela- tively fine distinctions is useful in many robotics tasks. If qualitative spatial constraint calculi are to be applied to cognitve robotics, they therefore have to afford relatively fine distinctions. The challenge for us then is to find a calculus which allows these fine distinctions, and yet is still simple enough to provide a provably minimal composition table. In this paper we introduce a new calculus about oriented points which has a scalable granularity. In this calculus, named, simple rules can generate the minimal composition table. Furthermore, the algebraic closure for a set of statements is sufficient to solve knowledge integration tasks in robotics.

IROS Conference 2003 Conference Paper

Propagation of distance and orientation intervals

• Reinhard Moratz
• Jan Oliver Wallgrün

We propose an approach that propagates distance and orientation intervals to integrate imprecise local knowledge into survey knowledge. In the context of mobile robot exploration this propagation scheme can be used to reason about the positions of landmarks or other salient positions and thus can be utilized to generate hypotheses for cycles in the environment. We describe a path-based and mainly topological representation and navigation approach based on the generalized Voronoi graph and demonstrate how the propagation method can be applied in this context.

ECAI Conference 2000 Conference Paper

Qualitative Spatial Reasoning about Line Segments

• Reinhard Moratz
• Jochen Renz
• Diedrich Wolter