Reasoning about Qualitative Direction and Distance between Extended Objects using Answer Set Programming

In this thesis, we introduce a novel formal framework to represent and reason about qualitative direction and distance relations between extended objects using Answer Set Programming (ASP). We take Cardinal Directional Calculus (CDC) as a starting point and extend CDC with new sorts of constraints which involve defaults, preferences and negation. We call this extended version as nCDC. Then we further extend nCDC by augmenting qualitative distance relation and name this extension as nCDC+. For CDC, nCDC, nCDC+, we introduce an ASP-based general framework to solve consistency checking problems, address composition and inversion of qualitative spatial relations, infer unknown or missing relations between objects, and find a suitable configuration of objects which fulfills a given inquiry.Comment: In Proceedings ICLP 2019, arXiv:1909.0764

Reasoning about Cardinal Directions between Extended Objects

Direction relations between extended spatial objects are important commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model, known as Cardinal Direction Calculus (CDC), for representing direction relations between connected plane regions. CDC is perhaps the most expressive qualitative calculus for directional information, and has attracted increasing interest from areas such as artificial intelligence, geographical information science, and image retrieval. Given a network of CDC constraints, the consistency problem is deciding if the network is realizable by connected regions in the real plane. This paper provides a cubic algorithm for checking consistency of basic CDC constraint networks, and proves that reasoning with CDC is in general an NP-Complete problem. For a consistent network of basic CDC constraints, our algorithm also returns a 'canonical' solution in cubic time. This cubic algorithm is also adapted to cope with cardinal directions between possibly disconnected regions, in which case currently the best algorithm is of time complexity O(n^5)

Temporal Sequences of Qualitative Information: Reasoning about the Topology of Constant-Size Moving Regions

International audienceRelying on the recently introduced multi-algebras, we present a general approach for reasoning about temporal sequences of qualitative information that is generally more efficient than existing techniques. Applying our approach to the specific case of sequences of topological information about constant-size regions, we show that the resulting formalism has a complete procedure for deciding consistency, and we identify its three maximal tractable sub-classes containing all basic relations

Generating approximate region boundaries from heterogeneous spatial information: an evolutionary approach

Spatial information takes different forms in different applications, ranging from accurate coordinates in geographic information systems to the qualitative abstractions that are used in artificial intelligence and spatial cognition. As a result, existing spatial information processing techniques tend to be tailored towards one type of spatial information, and cannot readily be extended to cope with the heterogeneity of spatial information that often arises in practice. In applications such as geographic information retrieval, on the other hand, approximate boundaries of spatial regions need to be constructed, using whatever spatial information that can be obtained. Motivated by this observation, we propose a novel methodology for generating spatial scenarios that are compatible with available knowledge. By suitably discretizing space, this task is translated to a combinatorial optimization problem, which is solved using a hybridization of two well-known meta-heuristics: genetic algorithms and ant colony optimization. What results is a flexible method that can cope with both quantitative and qualitative information, and can easily be adapted to the specific needs of specific applications. Experiments with geographic data demonstrate the potential of the approach

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

Extension of RCC*-9 to Complex and Three-Dimensional Features and Its Reasoning System

RCC*-9 is a mereotopological qualitative spatial calculus for simple lines and regions. RCC*-9 can be easily expressed in other existing models for topological relations and thus can be viewed as a candidate for being a “bridge” model among various approaches. In this paper, we present a revised and extended version of RCC*-9, which can handle non-simple geometric features, such as multipolygons, multipolylines, and multipoints, and 3D features, such as polyhedrons and lower-dimensional features embedded in ℝ3. We also run experiments to compute RCC*-9 relations among very large random datasets of spatial features to demonstrate the JEPD properties of the calculus and also to compute the composition tables for spatial reasoning with the calculus

Qualitative Spatial Reasoning with Holed Regions

The intricacies of real-world and constructed spatial entities call for versatile spatial data types to model complex spatial objects, often characterized by the presence of holes. To date, however, relations of simple, hole-free regions have been the prevailing approaches for spatial qualitative reasoning. Even though such relations may be applied to holed regions, they do not take into consideration the consequences of the existence of the holes, limiting the ability to query and compare more complex spatial configurations. To overcome such limitations, this thesis develops a formal framework for spatial reasoning with topological relations over two-dimensional holed regions, called the Holed Regions Model (HRM), and a similarity evaluation method for comparing relations featuring a multi-holed region, called the Frequency Distribution Method (FDM). The HRM comprises a set of 23 relations between a hole-free and a single-holed region, a set of 152 relations between two single-holed regions, as well as the composition inferences enabled from both sets of relations. The inference results reveal that the fine-grained topological relations over holed regions provide more refined composition results in over 50% of the cases when compared with the results of hole-free regions relations. The HRM also accommodates the relations between a hole-free region and a multi-holed region. Each such relation is called a multi-element relation, as it can be deconstructed into a number of elements—relations between a hole-free and a singleholed region—that is equal to the number of holes, regarding each hole as if it were the only one. FDM facilitates the similarity assessment among multi-element relations. The similarity is evaluated by comparing the frequency summaries of the single-holed region relations. The multi-holed regions of the relations under comparison may differ in the number of holes. In order to assess the similarity of such relations, one multi-holed region is considered as the result of dropping from or adding holes to the other region. Therefore, the effect that two concurrent changes have on the similarity of the relations is evaluated. The first is the change in the topological relation between the regions, and the second is the change in a region’s topology brought upon by elimination or addition of holes. The results from the similarity evaluations examined in this thesis show that the topological placement of the holes in relation to the hole-free region influences relation similarity as much as the relation between the hole-free region and the host of the holes. When the relations under comparison have fewer characteristics in common, the placement of the holes is the determining factor for the similarity rankings among relations. The distilled and more correct composition and similarity evaluation results enabled by the relations over holed regions indicate that spatial reasoning over such regions differs from the prevailing reasoning over hole-free regions. Insights from such results are expected to contribute to the design of future geographic information systems that more adequately process complex spatial phenomena, and are better equipped for advanced database query answering