Towards a general theory for modelling qualitative space

Qualitative spatial representation and reasoning are techniques for modeling and manipulating objects and relationships in space. Finding ways for defining the complete and sound (physically plausible) set of relationships between spatial objects is a prerequisite for the development and realization of qualitative representation and reasoning formalisms. Establishing the set of sound relationships is a complicated task especially when complex objects are considered. Hence, current approaches to qualitative representation and reasoning are limited to handling simple spatial objects. In this paper, we introduce a constraint-based approach to qualitative representation of topological relationships by defining a set of general soundness rules. The rules reduce the combinatorial set of relations produced by the method to the complete and physically possible ones. The rules are general and apply to objects of arbitrary complexity and together with the representation and reasoning formalism form a theory for qualitative space

Algebraic Properties of Qualitative Spatio-Temporal Calculi

Qualitative spatial and temporal reasoning is based on so-called qualitative calculi. Algebraic properties of these calculi have several implications on reasoning algorithms. But what exactly is a qualitative calculus? And to which extent do the qualitative calculi proposed meet these demands? The literature provides various answers to the first question but only few facts about the second. In this paper we identify the minimal requirements to binary spatio-temporal calculi and we discuss the relevance of the according axioms for representation and reasoning. We also analyze existing qualitative calculi and provide a classification involving different notions of a relation algebra.Comment: COSIT 2013 paper including supplementary materia

Case Adaptation with Qualitative Algebras

This paper proposes an approach for the adaptation of spatial or temporal cases in a case-based reasoning system. Qualitative algebras are used as spatial and temporal knowledge representation languages. The intuition behind this adaptation approach is to apply a substitution and then repair potential inconsistencies, thanks to belief revision on qualitative algebras. A temporal example from the cooking domain is given. (The paper on which this extended abstract is based was the recipient of the best paper award of the 2012 International Conference on Case-Based Reasoning.

Qualitative spatial representation and reasoning: A hierarchical approach

The ability to reason in space is crucial for agents in order to make informed decisions. Current high-level qualitative approaches to spatial reasoning have serious deficiencies in not reflecting the hierarchical nature of spatial data and human spatial cognition. This article proposes a framework for hierarchical representation and reasoning about topological information, where a continuous model of space is approximated by a collection of discrete sub-models, and spatial information is hierarchically represented in discrete sub-models in a rough set manner. The work is based on the Generalized Region Connection Calculus theory, where continuous and discrete models of space are coped in a unified way. Reasoning issues such as determining the mereological (part-whole) relations between two rough regions are also discussed. Moreover, we consider an important problem that is closely related to map generalization in cartography and Geographical Information Science. Given a spatial configuration at a finer level, we show how to construct a configuration at a coarser level while preserving the mereological relations. © The Author 2007. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved

Geospatial Narratives and their Spatio-Temporal Dynamics: Commonsense Reasoning for High-level Analyses in Geographic Information Systems

The modelling, analysis, and visualisation of dynamic geospatial phenomena has been identified as a key developmental challenge for next-generation Geographic Information Systems (GIS). In this context, the envisaged paradigmatic extensions to contemporary foundational GIS technology raises fundamental questions concerning the ontological, formal representational, and (analytical) computational methods that would underlie their spatial information theoretic underpinnings. We present the conceptual overview and architecture for the development of high-level semantic and qualitative analytical capabilities for dynamic geospatial domains. Building on formal methods in the areas of commonsense reasoning, qualitative reasoning, spatial and temporal representation and reasoning, reasoning about actions and change, and computational models of narrative, we identify concrete theoretical and practical challenges that accrue in the context of formal reasoning about `space, events, actions, and change'. With this as a basis, and within the backdrop of an illustrated scenario involving the spatio-temporal dynamics of urban narratives, we address specific problems and solutions techniques chiefly involving `qualitative abstraction', `data integration and spatial consistency', and `practical geospatial abduction'. From a broad topical viewpoint, we propose that next-generation dynamic GIS technology demands a transdisciplinary scientific perspective that brings together Geography, Artificial Intelligence, and Cognitive Science. Keywords: artificial intelligence; cognitive systems; human-computer interaction; geographic information systems; spatio-temporal dynamics; computational models of narrative; geospatial analysis; geospatial modelling; ontology; qualitative spatial modelling and reasoning; spatial assistance systemsComment: ISPRS International Journal of Geo-Information (ISSN 2220-9964); Special Issue on: Geospatial Monitoring and Modelling of Environmental Change}. IJGI. Editor: Duccio Rocchini. (pre-print of article in press