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

Connecting qualitative spatial and temporal representations by propositional closure

This paper establishes new relationships between existing qualitative spatial and temporal representations. Qualitative spatial and temporal representation (QSTR) is concerned with abstractions of infinite spatial and temporal domains, which represent configurations of objects using a finite vocabulary of relations, also called a qualitative calculus. Classically, reasoning in QSTR is based on constraints. An important task is to identify decision procedures that are able to handle constraints from a single calculus or from several calculi. In particular the latter aspect is a longstanding challenge due to the multitude of calculi proposed. In this paper we consider propositional closures of qualitative constraints which enable progress with respect to the longstanding challenge. Propositional closure allows one to establish several translations between distinct calculi. This enables joint reasoning and provides new insights into computational complexity of individual calculi. We conclude that the study of propositional languages instead of previously considered purely relational languages is a viable research direction for QSTR leading to expressive formalisms and practical algorithms

Spatial reasoning about qualitative shape compositions. Composing Qualitative Lengths and Angles

Shape composition is a challenge in spatial reasoning. Qualitative Shape Descriptors (QSD) have proven to be rotation and location invariant, which make them useful in spatial reasoning tests. QSD uses qualitative representations for angles and lengths, but their composition operations have not been defined before. In this paper, the Qualitative Model for Angles (QMAngles) and the Qualitative Model for Lengths (QMLengths) are presented in detail by describing their arity, reference systems and operators. Their operators are defined taking the well-known temporal model by Allen (1983) as a reference. Moreover, composition tables are built, and the composition relations of qualitative angles and lengths are proved using their geometric counterparts. The correctness of these composition tables is also proved computationally using a logic program implemented using SwiProlog

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

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

Qualitative constraint satisfaction problems : algorithms, computational complexity, and extended framework

University of Technology, Sydney. Faculty of Engineering and Information Technology.Qualitative Spatial and Temporal Reasoning (QSTR) is a subfield of artificial intelligence that represents and reasons with spatial/temporal knowledge in a qualitative way. In the past three decades, researchers have proposed dozens of relational models (known as qualitative calculi), including, among others, Point Algebra (PA) and Interval Algebra (IA) for temporal knowledge, Cardinal Relation Algebra (CRA) and Cardinal Direction Calculus (CDC) for directional spatial knowledge, and the Region Connection Calculus RCC-5/RCC-8 for topological spatial knowledge. Relations are used in qualitative calculi for representing spatial/temporal information (e.g. Germany is to the east of France) and constraints (e.g. the to-be-established landfill should be disjoint from any lake). The reasoning tasks in QSTR are formalised via the qualitative constraint satisfaction problem (QCSP). As the central reasoning problem in QCSP, the consistency problem (which decides the consistency of a number of constraints in certain qualitative calculi) has been extensively investigated in the literature. For PA, IA, CRA, and RCC-5/RCC-8, the consistency problem can be solved by composition-based reasoning. For CDC, however, composition-based reasoning is incomplete, and the consistency problem in CDC remains challenging. Previous works in QCSP assume that qualitative constraints only concern completely unknown entities. Therefore, constraints about landmarks (i.e., fixed entities) cannot be properly expressed. This has significantly restricted the usefulness of QSTR in real-world applications. The main contributions of this thesis are as follows. (i) The composition-based method is one of the most important reasoning methods in QSTR. This thesis designs a semi-automatic algorithm for generating composition tables for general qualitative calculi. This provides a partial answer to the challenge proposed by Cohn in 1995. (ii) Schockaert et al. (2008) extend the RCC models interpreted in Euclidean topologies to the fuzzy context and show that composition-based reasoning is sufficient to solve fuzzy QCSP, where 31 composition rules are used. This thesis first shows that only six of the 31 composition rules are necessary, and then introduces a method which consistently fuzzifies any classical RCC models. This thesis also proposes a polynomial algorithm for realizing solutions of consistent fuzzy RCC constraints. (iii) Composition-based reasoning is incomplete for solving QCSP over the CDC. This thesis provides a cubic algorithm which for the first time solves the consistency problem of complete basic CDC networks, and further shows that the problem becomes NP-complete if the networks are allowed to be incomplete. This draws a sharp boundary between the tractable and intractable subclasses of the CDC. (iv) This thesis proposes a more general and more expressive QCSP framework, in which a variable is allowed to be a landmark (i.e., a fixed object), or to be chosen among several landmarks. The computational complexity of the consistency problems in the new framework is then investigated, covering all qualitative calculi mentioned above. For basic networks, the consistency problem remains tractable for Point Algebra, but becomes NP-complete for all the remaining qualitative calculi. A special case in which a variable is either a landmark or is totally unknown has also been studied. (v) A qualitative network is minimal if it cannot be refined without changing its solution set. Unlike the assumptions in the literature, this thesis shows that computing a solution of minimal networks is NP-complete for (partially ordered) PA, CRA, IA, and RCC-5/RCC-8. As a by-product, it has also been proved that determining the minimality of networks in these qualitative calculi is NP-complete

On the Use of Automated Reasoning Systems in Ontology Integration.

Ontology Integration is a challenge in the field of Knowledge Engineering, whose solution is indispensable for the envisioned Semantic Web. Some approximations suffer from logical confidence, and others are hard to mechanize. In this paper a method – assisted by Automated Reasoning Systems – to solve a subproblem, the merging of ontologies, is presented. A case study of application is drawn from the field of Qualitative Spatial Reasoning.Junta de Andalucía Minerva Services in Mobility Platform Project WeTeVe (2C/040

SPARQS: a qualitative spatial reasoning engine

In this paper the design and implementation of a general qualitative spatial reasoning engine (SPARQS) is presented. Qualitative treatment of information in large spatial databases is used to complement the quantitative approaches to managing those systems, in particular, it is used for the automatic derivation of implicit spatial relationships and in maintaining the integrity of the database. To be of practical use, composition tables of spatial relationships between different types of objects need to be developed and integrated in those systems. The automatic derivation of such tables is considered to be a major challenge to current reasoning approaches. In this paper, this issue is addressed and a new approach to the automatic derivation of composition tables is presented. The method is founded on a sound set-theoretical approach for the representation and reasoning over arbitrarily shaped objects in space. A reasoning engine tool, SPARQS, has been implemented to demonstrate the validity of the approach. The engine is composed of a basic graphical interface where composition tables between the most common types of spatial objects are built. An advanced interface is also provided, where users are able to describe shapes of arbitrary complexity and to derive the composition of chosen spatial relationships. Examples of the application of the method using different objects and different types of spatial relationships are presented and new composition tables are built using the reasoning engine

From research to practice: The case of mathematical reasoning

Mathematical proficiency is a key goal of the Australian Mathematics curriculum. However, international assessments of mathematical literacy suggest that mathematical reasoning and problem solving are areas of difficulty for Australian students. Given the efficacy of teaching informed by quality assessment data, a recent study focused on the development of evidence-based Learning Progressions for Algebraic, Spatial and Statistical Reasoning that can be used to identify where students are in their learning and where they need to go to next. Importantly, they can also be used to generate targeted teaching advice and activities to help teachers progress student learning. This paper explores the processes involved in taking the research to practice