Positions, Regions, and Clusters: Strata of Granularity in Location Modelling

Abstract. Location models are data structures or knowledge bases used in Ubiquitous Computing for representing and reasoning about spatial relationships between so-called smart objects, i.e. everyday objects, such as cups or buildings, containing computational devices with sensors and wireless communication. The location of an object is in a location model either represented by a region, by a coordinate position, or by a cluster of regions or positions. Qualitative reasoning in location models could advance intelligence of devices, but is impeded by incompatibilities between the representation formats: topological reasoning applies to regions; directional reasoning, to positions; and reasoning about set-membership, to clusters. We present a mathematical structure based on scale spaces giving an integrated semantics to all three types of relations and representations. The structure reflects concepts of granularity and uncertainty relevant for location modelling, and gives semantics to applications of RCC-reasoning and projection-based directional reasoning in location models

A splitting line model for directional relations

Directional relations are fundamental to spatial data queries, analysis and reasoning. Consequently there has been a significant amount of effort to determine directional relations between two regions. However, many existing methods do not perform well when the regions are neighboring or intertwined. In this paper we introduce a new model for directional relations which is based on a splitting line separating the two regions in question. We identify essential quality criteria for directional relation models and translate them into measurable properties of a given splitting line. We present an efficient algorithm that computes an optimal splitting line for two regions and perform extensive experiments. Our results show that the splitting line model captures directional relations very well and that it clearly outperforms existing approaches on pairs of neighboring or intertwined regions

Investigation of the tradeoff between expressiveness and complexity in description logics with spatial operators

Le Logiche Descrittive sono una famiglia di formalismi molto espressivi per la rappresentazione della conoscenza. Questi formalismi sono stati investigati a fondo dalla comunit\ue0 scientifica, ma, nonostante questo grosso interesse, sono state definite poche Description Logics con operatori spaziali e tutte centrate sul Region Connection Calculus. Nella mia tesi considero tutti i pi\uf9 importanti formalismi di Qualitative Spatial Reasoning per mereologie, mereo-topologie e informazioni sulla direzione e studio alcune tecniche generali di ibridazione. Nella tesi presento un\u2019introduzione ai principali formalismi di Qualitative Spatial Reasoning e le principali famiglie di Description Logics. Nel mio lavoro, introduco anche le tecniche di ibridazione per estendere le Description Logics al ragionamento su conoscenza spaziale e presento il potere espressivo dei linguaggi ibridi ottenuti. Vengono presentati infine un risultato generale di para-decidibilit\ue0 per logiche descrittive estese da composition-based role axioms e l\u2019analisi del tradeoff tra espressivit\ue0 e propriet\ue0 computazionali delle logiche descrittive spaziali.Description Logics are a family of expressive Knowledge-Representation formalisms that have been deeply investigated. Nevertheless the few examples of DLs with spatial operators in the current literature are defined to include only the spatial reasoning capabilities corresponding to the Region Connection Calculus. In my thesis I consider all the most important Qualitative Spatial Reasoning formalisms for mereological, mereo-topological and directional information and investigate some general hybridization techniques. I will present a short overview of the main formalisms of Qualitative Spatial Reasoning and the principal families of DLs. I introduce the hybridization techniques to extend DLs to QSR and present the expressiveness of the resulting hybrid languages. I also present a general paradecidability result for undecidable languages equipped with composition-based role axioms and the tradeoff analysis of expressiveness and computational properties for the spatial DLs

Qualitative modelling of place location on the linked data web and GIS

When asked to define where a geographic place is, people normally resort to using qualitative expressions of location, such as north of and near to. This is evident in the domain of social geography, where qualitative research methods are used to gauge people’s understanding of their neighbourhood. Using a GIS to represent and map the location of neighbourhood boundaries is needed to understand and compare people’s perceptions of the spatial extent of their neighbourhoods. Extending the GIS to allow for the qualitative modelling of place will allow for the representation and mapping of neighbourhoods. On the other hand, a collaborative definition of place on the web will result in the accumulation of large sets of data resources that can be considered “location-poor”, where place location is defined mostly using single point coordinates and some random combinations of relative spatial relationships. A qualitative model of place location on the Linked Data Web (LDW) will allow for the homogenous representation and reasoning of place resources. This research has analysed the qualitative modelling of place location on the LDW and in GIS. On the LDW, a qualitative model of place is proposed, which provides an effective representation of individual place location profiles that allow place information to be enriched and spatially linked. This has been evaluated using the application of qualitative spatial reasoning (QSR) to automatic reasoning over place profiles, to check the completeness of the representation, as well as to derive implicit links not defined by the model. In GIS, a qualitative model of place is proposed that provides a basis for mapping qualitative definitions of place location in GIS, and this has been evaluated using an implementation-driven approach. The model has been implemented in a GIS and demonstrated through a realistic case study. A user-centric approach to development has been adopted, as users were involved throughout the design, development and evaluation stages

A family of directional relation models for extended objects

In this paper, we introduce a family of expressive models for qualitative spatial reasoning with directions. The proposed family is based on the cognitive plausible cone-based model. We formally define the directional relations that can be expressed in each model of the family. Then, we use our formal framework to study two interesting problems: computing the inverse of a directional relation and composing two directional relations. For the composition operator, in particular, we concentrate on two commonly used definitions, namely, consistency-based and existential composition. Our formal framework allows us to prove that our solutions are correct. The presented solutions are handled in a uniform manner and apply to all of the models of the family. © 2007 IEEE

A family of directional relation models for extended objects

In this paper, we introduce a family of expressive models for qualitative spatial reasoning with directions. The proposed family is based on the cognitive plausible cone-based model. We formally define the directional relations that can be expressed in each model of the family. Then, we use our formal framework to study two interesting problems: computing the inverse of a directional relation and composing two directional relations. For the composition operator, in particular, we concentrate on two commonly used definitions, namely, consistency-based and existential composition. Our formal framework allows us to prove that our solutions are correct. The presented solutions are handled in a uniform manner and apply to all of the models of the famil