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 systems


INTRODUCTION
Geographic Information Systems (GIS) are confronted with massive quantities of micro and macro-level spatio-temporal data. In conventional GIS systems, this data takes the form of spatio-temporal databases of precise measurements pertaining to environmental features, aerial imagery, and more recently, sensor network databases that store real-time information about natural and artificial processes and phenomena. Within next-generation GIS systems, the fundamental information theoretic modalities are envisioned to undergo radical transformations: high-level ontological entities such as objects, events, actions and processes and the capability to model and reason about these is expected to be a native feature of nextgeneration GIS. Indeed, one of the crucial developmental goals in GIS systems of the future is a fundamental paradigmatic shift in the underlying 'spatial informatics' of these systems.

Time and GIS.
Integrating time with GIS is necessary toward the development of GIS capable of monitoring and analysing successive states of spatial entities [Claramunt and Thériault, 1995, Yuan, 2001, Yuan and Hornsby, 2008. Such capability, necessitating the representation of instances of geographic entities and their change over time rather than change to layers or scenes, is the future of GIS and has been emphasized in the National Imagery and Mapping Agency's (NIMA; now the National Geospatial-Intelligence Agency (NGA)) vision for Integrated Information Libraries [NIMA, 2000]. A (temporal) GIS should, in addition to accounting for spatial changes, also consider the events behind changes and the facts which enable observation of these changes [Beller, 1991]. In the words of Claramunt and Thériault [1995]: 'To respond adequately to scientific needs, a TGIS should explicitly preserve known links between events and their consequences. Observed relationships should be noted (e.g., entities A and B generate entity C) to help scientists develop models that reproduce the dynamics of spatio-temporal processes. Researchers will thus be able to study complex relationships, draw conclusions and verify causal links that associate entities through influence and transformation processes'.
Clearly, this facility necessitates a formal approach encompassing events, actions and their effects toward representing and reasoning about dynamic spatial changes. Such an approach will be advantageous in GIS applications concerned with retrospective analysis or diagnosis of observed spatial changes involving either fine-scale object level analysis or macro-level (aggregate) analysis of dynamic geospatial phenomena. For instance, within GIS, spatial changes could denote (environmental) changes in the geographic sphere at a certain temporal granularity and could bear a significant relationship to natural events and human actions, e.g., changes in land-usage, vegetation, cluster variations among aggregates of demographic features, and wild-life migration patterns.
Geospatial Semantics. Conceptual models for representing geospatial events and processes in general have been the focus of extensive research efforts in the last decade. Research in the area of geospatial semantics, taxonomies of geospatial events and processes, and basic ontological research into the nature of processes in a specific geospatial context has garnered specific interest from several quarters [Galton and Mizoguchi, 2009, Grenon and Smith, 2004, Hornsby and Cole, 2007, Renolen, January 2000, Worboys and Hornsby, 2004. Fundamental epistemological aspects concerning, for instance, event and object identity have received special attention in the community [Bennett, 2002, Hornsby andEgenhofer, 2000]. This has mainly been spurred by the realization that purely snapshot-based temporal GIS does not provide for an adequate basis for analyzing spatial events and processes and performing spatio-temporal reasoning. Event-based and object-level reasoning at the spatial level could serve as a basis of explanatory analyses within a GIS [Couclelis, 2009, Galton and Hood, 2004, Mondo et al., 2010, Worboys, 2005. For instance, a useful reasoning mechanism that applications may benefit from could be the task of causal explanation, which is the process of retrospective analysis by the extraction of an event-based explanatory model from available spatial data. Indeed, the explanation would essentially be an event-based history of the observed spatial phenomena defined in terms of both domain-independent and domain-dependent occurrences.
Narrative as a Model of Perceptual Sense Making. Researchers in computational logics of action and change have interpreted narratives in several ways (e.g., in the context of formalisms such as the situation calculus and event calculus) [McCarthy, 2000, McCarthy and Costello, 1998, Miller and Shanahan, 1994, Mueller, 2007, Pinto, 1998]: Advances in formal methods in the areas of commonsense reasoning, qualitative spatio-temporal representation and reasoning, reasoning about space, actions and change, and spatio-temporal dynamics [Bhatt, 2012, Bhatt et al., 2011a, Cohn and Renz, 2007 provide interesting new perspectives for the development of the foundational spatial informatics underlying next-generation GIS systems. The basic requirements within these systems encompass: -Knowledge engineering, semantics, and modelling: Introduction of the capability to include object, event and process based abstractions of spatio-temporal phenomena as native, first-class entities, enshrined with rich semantic characterizations within the ontology and conceptual model of the GIS system in a manner that is interoperable across systems and implementations. -Analytical reasoning: From a computational viewpoint, generic high-level reasoning mechanisms that leverage upon the semantics of the formally modelled or axiomatised properties of domain-independent and dependent aspects are necessary. These mechanisms could be used to ground and model environmental (natural and human) phenomena from domains such as epidemiology, urban dynamics, vegetation monitoring, wild-life biology, transportation dynamics, cultural heritage and so forth (Section 2.1).
Indeed, it is expected that these knowledge representation and reasoning capabilities will provide a basis for high-level analytical and decision-making tasks, either individually or in conjunction with other forms of analytical techniques from the field of spatial statistics, or quantitative analysis in GIS.

Contributions and Organization of the Paper.
This paper aims to bring formal methods concerning Knowledge Representation and Reasoning (KR) into the domain of Geographic Information Systems. In this context, and with a particular focus on the use of KR-based formal commonsense reasoning methods, this paper: demonstrates basic representation and computational challenges pertaining to space, actions, and change presents an overarching framework for high-level modelling and (explanatory) analysis for the geospatial domain, and addresses concrete representational and computational problems that accrue in this context and provides a unified view of a consolidated architecture in the backdrop of an illustrated application scenario from the domain of urban dynamics.
The paper is organised as follows: Section 2 presents application-guided perspectives from several domains where the notion of geospatial dynamics is recognised as being applicable; we also provide two concrete motivating scenarios concerning the spatio-temporal dynamics of urban narratives.
Section 3 presents a brief overview of formal methods in commonsense, qualitative spatial representation and reasoning, and may be skipped by readers familiar with the topic.
Section 4 presents an intuitive overview of the core spatial informatics-representational and computational challenges-that accrue whilst modelling and reasoning with dynamic geospatial phenomena.
Section 5 contextualizes the dynamic geospatial spatial informatics by way of a consolidated framework: We describe the overall architecture and its components using a running example, and illustrate how basic representational and computational challenges may be met within the formal theory of space, events, actions and change.
Section 6 concludes the paper with a discussion of our research perspective and summary of contributions.

GEOSPATIAL DYNAMICS: APPLICATION PERSPECTIVES
In recent years, modelling and analysis of dynamic geospatial phenomena and the integration of time in GIS have emerged as major research topics within the GIS community. Although at present the representational and analytical apparatus to examine the dynamics of such phenomena is nascent at best, the issue has been considered as a major research priority in GIS [Yuan et al., 2004].
Here, we briefly indicate a select range of domains where the notion of geospatial dynamics is applicable, and also provide motivating scenarios from the field of urban dynamics and environmental development.

Application Areas
A wide-range of priority areas where high-level analytical ability is crucial come to the fore: § Epidemiology. This is a classic application domain, which from a spatial perspective, involves the study of diffusive processes (e.g. spread of disease) with either point-based or aggregate entities in space and time. § Moving Data Analysis. This domain involves the analysis of (typically people-centered) motion data for purposes of prediction and explanation. For instance, studies involving vehicles / people trajectories, transportation data, crime statistics have found significant attention in this area. § Land-use Analysis. This corresponds to the analysis of land-use patterns, e.g., in urban areas, on the basis of remote sensing and other ground data. For instance, one objective here could be to study the nature of land-use dynamics either together or in isolation with data involving socio-economic dimensions. § Disaster Management. This corresponds to assistive technologies that provide managerial and analytical capabilities both before / after and in times of natural and man-made calamities (e.g., fire, flooding, hurricanes, tornado, landslides, earthquakes). § Environmental Modelling, Wildlife Biology. These domains involve modelling and analysis of environmental phenomena at the ecological level, e.g., integrated systems and relationships involving flora and fauna. Typical studies involve vegetation monitoring (e.g., forestry / deforestation), climatic change (e.g., glaciers, sea level change), and monitoring of pollution, soil, air quality, water quality etc. § Archeology, Cultural Heritage. GIS technology is employed by archaeologists to reconstruct historical events and developments as well as to predict sites of potential archeological interest. Resulting archeological records are made accessible to the public in the form of cultural heritage portals. To facilitate intuitive access to cultural heritage information, for instance by tourists, a spatio-temporal ontology of changes in political and administrative regions is required.

Urban Narratives, and their Spatio-Temporal Dynamics: An Example
Urbanization and high-level narratives of urban dynamics can be interpreted with respect to the sum total of a range of demographic, environmental (both natural and artificial), sociological, and economic processes. Indeed, urban dynamics, and 'the urban narrative' may not be trivialised as being strictly as such, but for the present discussion, this interpretation suffices.
Urbanization over 28 Years. As an example, consider the phenomena of urbanisation during 1984-2012 for the cities of Las Vegas (USA) and Dubai (UAE); the following expert analyses in (N1-N2) describes the high-level geospatial, demographic, economic, environmental and other related processes pertaining to urbanisation. The strictly spatio-temporal determinants of urbanisation in these cities are depicted in Fig. 1 and Fig. 2 respectively. The data and analyses have been sourced via the publicly available TimeLapse initiative (Listing 1).
TimeLapse.. TimeLapse is a collaborative project involving Google, the U.S. Geological Survey (USGS), NASA, TIME, and Carnegie Mellon University's CREATE Lab. TimeLapse has recently released an interactive animation constructed from satellite images of the Earth; the satellite images, sourced from the Landsat program, represent images dating back to 1984 detailing a year-by-year progression of changes to the surface of the Earth.
Preliminary view of the generated data depicts phenomena such as deforestation in the Amazon, the effects of coal mining in Wyoming, the urban expansion of Shanghai and Las Vegas, and the drying of the largest lake in the Middle East, Lake Urmia. We use some of these publicly available examples from TimeLapse to establish a context for the overall context of this paper, and introduce the idea of narrative-centred interpretation in the geospatial domain.

N1. Las Vegas
"Throughout the 1990s and much of the 2000s, the boundaries of metro Las Vegas kept expanding, as new housing developments were thrown up to accommodate the throngs of Americans who wanted to take advantage of the regions booming economy. From 2000 to 2010, the city's population grew by nearly 50% -a rate thats hard to find outside the developing world. But if Las Vegas boomed along with the housing sector during the first several years of the 21st century, it went bust when the recession hit. The city was ground zero for the foreclosure crisis. As late as 2012, Las Vegas had one foreclosure filing for every 99 housing units, good for the fourth highest rate in the country. And as economically unsustainable as Las Vegas' growth has proved to be over the past several years, it may be even more environmentally unsustainable. The city receives almost no rain, and most of its water comes from nearby Lake Mead. But as can be clearly seen in the TimeLapse images, Lake Mead is drying up, the victim of a prolonged drought -potentially abetted by climate change -and the increasing demand placed on it by Las Vegas' growing population. Lake Meads water level has fallen from a little over over the past couple of decades Dubai has built out into the sea. Sand dredged from the seafloor has been used to create artificial islands of recognizable shapes -including a pair of palm trees. In the lower-right corner of the Timelapse images, areas of empty sand are filled up with new buildings, as the city grows further and further away from the sea, pushing into the desert. That breakneck pace of development has slowed somewhat in recent years, as Dubai was hit hard by the global recession of 2008." In general, high-level expert analysis encompassing commonsense, qualitative interpretation (e.g., the underlined parts in N1-N2 above) of urban / geospatial processes may be identified from measurable lowlevel spatial and temporal features, themselves obtainable from a range of data sources such as satellite imagery and remote sensing, land-surveys, physical environmental sensing a la sensor networks, etc. In particular, the complex dynamics underlying the identification of urbanisation processes may encompass several data sources such as: 1. Satellite imagery 2. Remote sensing 3. Land use statistics and databases, Gazetteers 4. Demographic data (e.g., from census surveys) 5. Economic data (income, growth, economic activity, currency and stock market performance, etc.) The focus of the narrative-centred model presented in this paper is strictly on the spatio-temporal aspects of the dynamic geospatial phenomena that underlie perceivable geospatial change at the object or feature level. The spatio-temporal aspects can be co-related with other kinds of quantitative and qualitative data (e.g., economic and demographic measures, census studies); however, a formal treatment of such correlations is beyond the scope of this paper. We emphasise that modelling and reasoning about such correlations would indeed be possible, and also be within the scope of the overall narrative based analytical framework for GIS that has been proposed in this paper.

QUALITATIVE SPATIAL REPRESENTATION AND REASONING
The field of qualitative spatio-temporal representation and reasoning (QSTR) seeks to define formal models of spatial and temporal relations dealing with different aspects of space such topology, direction, distance, size, etc. QSTR has evolved as a specialised discipline within Artificial Intelligence [Allen, 1983, Bhatt et al., 2011a, Cohn and Renz, 2007, Freksa, 1991b, Renz and Nebel, 2007. Formal methods in QSTR provide a commonsensical interface to abstract and reason about quantitative spatial information.
The common characteristic of the developed formal models, often termed qualitative calculi, is that, in contrast to quantitative approaches, just a small number of basic relations is distinguished. Qualitative spatial / temporal calculi are relational-algebraic systems pertaining to one or more aspects of space. They abstract from metrical details and focus on properties that make a difference in a particular application domain. This allows for an analysis of spatio-temporal data on a high-level of abstraction and directly with respect to human spatio-temporal concepts and commonsense reasoning. As such, they provide one means to represent and analyse data in an abstract way that is more natural to humans, a key challenge identified for future GIS (e.g., Gahegan [1996], Mennis et al. [2000], Peuquet [1988]). The basic tenets in QSTR consist of constraint based reasoning algorithms over an infinite (spatial) domain to solve consistency problems in the context of spatial calculi. The key idea here is to partition an infinite quantity space into finite disjoint categories, and utilise the special relational properties of such a partitioned space for reasoning purposes.
In general, qualitative spatial calculi can be classified into two groups: topological and positional calculi.
With topological calculi such as the Region Connection Calculus (RCC), the primitive entities are spatially extended regions of space, and could possibly even be 4D spatio-temporal histories, e.g., for motionpattern analyses. Alternatively, within a dynamic domain involving translational motion, point-based abstractions with orientation calculi suffice. Examples of orientation calculi include [Cohn and Renz, 2007]: the Oriented-Point Relation Algebra (OPRA m ), the Double-Cross Calculus, and the line-segment based Dipole Calculus.
Similar to these works, which are situated within an Artificial Intelligence / Knowledge Representation (KR) context, many crucial advances have accrued from other communities concerned with the development of formalisms and algorithms for modelling and reasoning about spatial information, a prime example here being the domain of spatial information theory for Geographic Information Systems (GIS) [Egenhofer andMark, 1995, Egenhofer andFranzosa, 1991]. Most widely adopted and applied qualitative spatial (topological) calculi are the RCC-8 calculus Randell et al. [1992] and 9-Intersection Model Egenhofer [1991] which both essentially distinguish the same eight basic topological relations between two spatial regions as shown in Fig. 3. 1 Relevant Applications in GIS, and Urban Planning. Qualitative spatial calculi have, for instance, been utilized in the GIS domain to describe spatial relationships in query and retrieval scenarios Abdelmoty et al. [2009], Clementini et al. [1994], to formalize (geo)spatial concepts and processesClaramunt et al.
externally connected partially overlapping equal tangential proper part non-tangential proper part tangential proper part inverse non-tangential proper part inverse  [Worboys, 2005] [1997], Duckham et al. [2010], Jiang and Worboys [2008], Klippel et al. [2008], and to specify background knowledge and integrity constraints in the context of spatial and spatio-temporal database applications Haarslev and Möller [1997], Khan and Schneider [2010], Rodríguez et al. [2010]. The notion of conceptual neighborhood Egenhofer and Al-Taha [1992], Freksa [1991a] has been introduced to describe spatial change on the level of qualitative spatial relations and forms the basis to perform temporal reasoning in the form of simulation, interpolation, and planning.

THE SPATIAL INFORMATICS OF GEOSPATIAL DYNAMICS
The spatial information theoretic challenges underlying the development of high-level analytical capability in dynamic GIS consist of fundamental representational and computational problems pertaining to: the semantics of spatial occurrences, practical abduction in GIS, and to support these, problems of data abstraction, integration, and spatial consistency.

Spatial Occurrences: Analyses with Events and Objects
Our objective is to develop the functionality that enables reasoning about spatio-temporal narratives consisting of events and processes at the geographic scale. We do not attempt an elaborate ontological characterisation of events and processes, a topic of research that has been addressed in-depth in the state-of-theart. For the purposes of this paper, we utilise a minimal, yet rich, conceptual model consisting of a range of events such that it may be used to qualitatively ground metric geospatial datasets consisting of spatial and temporal footprints of human and natural phenomena at the geographic scale.
These occurrences are those that may be semantically characterized within a general theory of space and spatial change. These may be grounded with respect to either a qualitative theory, or an elaborate typology of geospatial events (e.g., Fig. 4 illustrates a typology for object level changes).

Spatial Changes at a Qualitative Level.
In so far as a general qualitative theory of spatial change is concerned, there is only one type of occurrence, viz -a transition from one qualitative state (relation) to another state (relation) as (possibly) governed by the continuity constraints of the relation space. At this level, the only identifiable notion of an occurrence is that of a qualitative spatial transition that the primitive objects in the theory undergo, e.g., the transition of an object (o 1 ) from being disconnected to another object (o 2 ) to being a tangential-proper-part (see again Fig. 3). At the level of a spatial theory, it is meaningless to ascribe a certain spatial transition as being an event or action; such distinctions demand a slightly higher level of abstraction. For instance, the example of a transition from disconnected to tangential-proper-part could either coarsely represent the volitional movement of a person into a room or the motion of a ball. Whereas the former is an action performed by an agent, the latter is a deterministic event that will necessarily occur in normal circumstances. Our standpoint here is that such distinctions can only be made in a domain specific manner; as such, the classification of occurrences into actions and events will only apply at the level of the domain with the general spatial theory dealing only with one type of occurrence, namely primitive spatial transitions that are definable in it.

Typology of Events and Patterns.
At the domain independent level, the explanation may encompass behaviours such as emergence, growth & shrinkage, disappearance, spread, stability, etc., in addition to the sequential/parallel composition of the behavioural primitives aforementioned, e.g., emergence followed by growth, spread / movement, stability and disappearance during a time-interval. Certain kinds of typological elements, e.g., growth and shrinkage, may even be directly associated with spatial changes at the qualitative level. Appearance of new objects and disappearance of existing ones, either abruptly or explicitly formulated in the domain theory, is also characteristic of non-trivial dynamic (geo)spatial systems. Within event-based GIS, appearance and disappearance events are regarded to be an important typological element for the modelling of dynamic geospatial processes Thériault, 1995, Worboys, 2005]. For instance, Claramunt and Thériault [1995] identify the basic processes used to define a set of low-order spatio-temporal events which, among other things, include appearance and disappearance events as fundamental. Similarly, toward event-based models of dynamic geographic phenomena, Worboys [2005] suggests the use of the appearance and disappearance events at least in so far as single object behaviours are concerned (see Fig. 5). Appearance, disappearance and re-appearances are also connected to the issue of object identity maintenance in GIS [Bennett, 2002, Hornsby andEgenhofer, 2000].

II. Domain-Specific Spatial Occurrences
At a domain-dependent level, behaviour patterns may characterize high-level processes, environmental / natural and human activities such as deforestation, urbanisation, land-use transformations etc. These are domain-specific occurrences that induce a transformation on the underlying spatial structures being modelled [Couclelis, 2009]. Basically, these are domain specific events or actions that have (explicitly) identifiable occurrence criteria and effects that can be defined in terms of qualitative spatial changes, and the fundamental typology of spatial changes. For instance, in the example in Fig. 5, we can clearly see that region a has continued to shrink during 1950 to 1990, eventually disappearing altogether. The following general notion of a 'spatial occurrence' is identifiable Bhatt and Loke [2008]: 'Spatial occurrences are events or actions with explicitly specifiable occurrence criteria and/or pre-conditions respectively and effects that may be identified in terms of a domain independent taxonomy of spatial change that is native to a general qualitative spatial theory'.
As an example, consider an event that will cause a region to split or make it grow / shrink. Likewise, an aggregate cluster of geospatial entities (e.g., in wildlife biology domain) may move and change its orientation with respect to other geospatial entities. Thinking in agent terms, a spatial action by the collective / aggregate entity, e.g., turn south-east, will have the effect of changing the orientation of the cluster in relation to other entities. In certain situations, there may not be a clearly identifiable set of domain-specific occurrences with explicitly known occurrence criteria or effects that are definable in terms of a typology of spatial change, e.g., cluster of alcohol-related crime abruptly appearing and disappearing at a certain time. However, even in such situations, an analysis of the domain-independent events and inter-event relationships may lead to an understanding of spatio-temporal relationships and help with practical hypothesis generation [Beller, 1991].

Practical Abduction for GIS
Explanatory reasoning requires the ability to perform abduction with spatio-temporal information. In the context of formal spatio-temporal calculi, and logics of action and change, this translates to the ability to provide scenario and narrative completion abilities at a high-level of abstraction.
Consider the GIS domain depicted in Fig. 5, and the basic conceptual understanding of spatial occurrences described in Section 4.1. At a domain-independent level, the scene may be described using topological and qualitative size relationships. Consequently, the only changes that are identifiable at the level of the spatial theory are shrinkage and eventual disappearance -this is because a domain-independent spatial theory may only include a generic typology (appearance, disappearance, growth, shrinkage, deformation, splitting, merging, etc.) of spatial change. However, at a domain-specific level, these changes could characterize a specific event (or process) such as deforestation. The hypotheses or explanations that are generated during a explanation process should necessarily consist of the domain-level occurrences in addition to the underlying (associated) spatial changes (as per the generic typology) that are identifiable. Intuitively, the derived explanations more or less take the form of existential statements such as: "Between time-points t i and t i , the process of deforestation is abducible as one potential hypothesis". Derived hypotheses / explanations that involve both domain-dependent and as well their corresponding domain-independent typological elements are referred to as being 'adequate' from the viewpoint of explanatory analysis for a domain. At both the domain-independent as well as dependent levels, abduction requires the fundamental capability to interpolate missing information, and understand partially available narratives that describe the execution of high-level real or abstract processes. In the following, we present an intuitive overview of the scenario and narrative completion process.

Scenario and Narrative Completion
Explanation problems demand the inclusion of a narrative description, which from the logic-based viewpoint of this paper is essentially a distinguished course of actual events about which we may have incomplete information [Miller andShanahan, 1994, Pinto, 1998]. Narrative descriptions are typically available as observations from the real / imagined execution of a system or process. Since narratives inherently pertain to actual observations, i.e., they are temporalized, the objective is often to assimilate / explain them with respect to an underlying process model and an approach to derive explanations.
Given partial narratives that describe the evolution of a system (e.g., by way of temporally ordered scene observations in event-based GIS datasets) in terms of high-level spatio-temporal data, scenario and narrative completion corresponds to the ability to derive completions that bridge the narrative by interpolating the missing spatial and action / event information in a manner that is consistent with domain-specific and domain-independent rules / dynamics. Fig. 6 for a branching / hypothetical situation space that characterizes the complete evolution of a system. In Fig. 6 -the situation-based history ă s 0 , s 1 , . . . , s n ą represents one path, corresponding to an actual time-line ă t 0 , t 1 , . . . , t n ą, within the overall branching-tree structured situation space. Given incomplete narrative descriptions, e.g., corresponding to only some ordered timepoints in terms of high-level spatial (e.g., topological, orientation) and occurrence information, the objective of causal explanation [Bhatt and Loke, 2008] in a spatio-temporal context is to derive one or more paths from the branching situation space, that could best-fit the available narrative information. Of course, the completions that bridge the narrative by interpolating the missing spatial and action/event information have to be consistent with domain-specific and domain-independent rules/dynamics.

Consider the illustration in
Explanation, in general, is regarded as a converse operation to temporal projection essentially involving reasoning from effects to causes, i.e., reasoning about the past [Shanahan, 1989]. Logical abduction is one inference pattern that can be used to realise explanation. In Section 5, we present a practical illustration of the concept of scenario and narrative completion (by abduction) for explanatory analysis in the GIS domain.

Temporal Partitioning and Qualitative Abstraction
In the geographic domain, the input data often stems from multiple sources, for instance from different sensors, remote sensing data, map data, etc., and the data itself is afflicted by measurement errors and uncertainty. To perform explanatory analysis on a level of qualitative spatial relations, geo-referenced quantitative input data about spatial objects from different sources needs to be translated into relations from several qualitative spatial models or calculi dealing with different aspects of space, a process we refer to as qualitative abstraction. A prerequisite for applying the qualitative abstraction procedure is that the input data is temporally partitioned such that each part is associated with a particular time point in an ordered sequence of time points. For each time point, the qualitative abstraction procedure takes the associated quantitative data and derives the spatial relations from the given qualitative models holding between the involved objects. The result is a static qualitative spatial description for each time point. If uncertainty of quantitative information is explicitly represented, this needs to be taken into account and may lead to disjunctions of relations on the qualitative level.

Integration and Spatial Consistency
Due to the mentioned measurement errors and uncertainty of the quantitative input data, the qualitative descriptions resulting from the qualitative abstraction for particular time points may contain contradictions or violate integrity constraints stemming from background knowledge about the domain. Fig. 7 illustrates the case of a spatial inconsistency on the level of topological relations when combining the information from four different sources (all concerning the same time point): From combining the fact that objects C and D (e.g., two climate phenomena) are reported to overlap by one source (a) with the reported relations C is completely contained in A (b) and D is completely contained in B (c), it follows that the two regions A and B would need to overlap as well. This contradicts the information from the fourth source (d)which could, for instance, be a spatial databases containing boundaries of administrative regions-that says that A and B are externally connected. Instead of the fourth source, we could also have introduced a general integrity constraint stating that administrative regions on the same level never overlap. This would have resulted in the same contradiction rendering the given information inconsistent.
As a result of the possibility of inconsistent input information occurring in geographic applications, frameworks for explanation and spatio-temporal analysis need the ability to at least detect these inconsistencies in order to exclude the contradicting information or, as a more appropriate approach, resolve the contradictions in a suitable way. Removing logical inconsistencies is crucial in the context of a logic-based abductive reasoning approach as we suggest in this paper, as otherwise, incorrect conclusions can be abduced from an inconsistency which will ultimately lead to incorrect results. While the view that logical inconsistencies are undesirable has been challenged (see Gabbay and Hunter [1991]), explanatory analysis with inconsistent information raises many challenges going beyond the scope of this paper. In certain applications, it may be possible to derive that certain information is irrelevant for the explanatory task at hand and filter out this information in advance such that no removal of inconsistencies wrt. this information is required.
Deciding consistency of a set of qualitative spatial relations has been studied as one of the fundamental reasoning tasks in qualitative spatial representation and reasoning [Cohn and Renz, 2007]. The complexity of deciding consistency varies significantly over the different existing qualitative calculi. For most common qualitative calculi such as RCC-8, the consistency can be decided in cubic time when the input description is a scenario which means it does not contain disjunction of relations. This is achieved by the path consistency or algebraic closure method Mackworth [1977] which is ultimately based on a set of composition axioms that state which relation can hold between objects A and C given the relations holding between object A and B and between B and C. For general description including disjunctions a more costly backtracking search has to be performed. Integrity constraints have been investigated in the (spatial) database literature Cockcroft [1997], Fagin and Vardi [1984]. As the example above shows, integrity rules in a geographic context often come in the form qualitative spatial relations that have to be satisfied by certain types of spatial entities. These kinds of spatial integrity constraints can be dealt with by employing terminological reasoning to determine whether a certain integrity rule has to be applied to a given tuple of objects and feeding the resulting constraints into a standard qualitative consistency checker together with the qualitative relations coming from the input data.

Conflict Resolution
As indicated in the previous section, when conflicts arise during the integration of spatial data, it is often desirable to not only detect the inconsistencies but also resolve conflicts in a reasonable manner to still be able to exploit all provided information in the actual logical reasoning approach for explanation and analysis. Methods for data integration and conflict resolution have for instance been studied under the term information fusion Grégoire and Konieczny [2006]. They are commonly classified into quantitative approaches and symbolic approaches. Quantitative approaches mainly employ statistical methods such as least-square adjustment to deal with multiple observations, while symbolic information fusion is concerned with the revision of logical theories under the presence of new evidence. An important distinction here is that between revision and update. In the case of revision, additional information about a particular state of the world becomes available and needs to be combined with what was known before. In the case of update, one assumes that the state may have changed and that the new information is more up-to-date than the previous knowledge. These different information fusion settings have led to the formulation of different rationality criteria that corresponding computational approaches should satisfy such as the AGM postulates for belief change Alchourron et al. [1985]. Such computational solutions often consist of merging operators that compute a consistent model that is most similar to the inconsistent input data. In distancebased merging approaches this notion of similarity is described using a distance measure between models. This idea has been applied to qualitative spatial representations Condotta et al. [2008],  using the notion of conceptual neighborhood Egenhofer and Al-Taha [1992], Freksa [1991a] to measure distance in terms of the number of neighborhood changes that need to be performed to get from inconsistent qualitative descriptions to consistent ones.
To illustrate the operation of a qualitative merging approach for conflict resolution, let us consider the example in Fig. 8 in which information from two sources providing information about the city of Dubai (see again Fig. 2) at a given time needs to be merged: Let us say the first source G provides geometries for two districts, G Deira and G Mirdif (shown as polygons with fully drawn borders in Fig. 8(a)), while the second source G 1 provides geometries for another district, G  Fig. 9. Overview of narrative-based architecture for geospatial modelling, explanatory analysis, querying, and visualization (both shown as polygons with dashed boundaries in Fig. 8(a). Let us further assume that we also have two integrity constraints for the integration result in this scenario. The first one states that the geometries of districts cannot overlap and, thus, have to be disjoint or touching (disjunction tec, dcu in terms of RCC-8 relations). The second constraint demands that each geometry of a city district has to be completely contained in the geometry of the city. This corresponds to a disjunction of tntpp, tppu in terms of RCC-8 relations and applies to the relation of each of the three districts to G 1 Dubai . As Fig. 8(a) illustrates, superimposing the geometries of both sources results in violations of both integrity constraints: G Deira and G 1 Bur Dubai overlap (RCC-8 relation po) and G Mirdif and G 1 Dubai overlap as well. A qualitative merging approach would now resolve these conflicts on the qualitative level by computing the consistent scenario that is closest to the qualitative interpretation of the input information. A possible result is shown in Fig. 8(b). The relation between G Deira and G 1 Bur Dubai has been changed to tecu and that of G Mirdif and G 1 Dubai to ttppu, which corresponds to the actual spatial configuration depicted in Fig. 8(c).

GEOSPATIAL ANALYTICS: A NARRATIVE BASED FORMAL FRAMEWORK
The discussions in Section 3 encompassed a range of representation and computational challenges that accrue in the context of dynamic geospatial analysis. We now describe our formal framework, and its corresponding conceptual architecture, for high-level qualitative modeling and explanatory analysis for the domain of geospatial dynamics illustrated in Fig. 9.

Overview of Architecture
Our proposed architecture comprises the entire range of steps required to perform explanatory analysis of geospatial dynamics on a qualitative level of abstraction starting with the processing of the actual (typically quantitative) data to form a consistent qualitative description, to the usage of abductive reasoning for narrative completion, and to the recognition of high-level processes leading to a knowledge base that can be queried and utilized by application systems and decision makers. The main aspects of the proposed architecture are the following: -Input datasets. The input consists of data sets from several sources such as remote sensing data, spatial databases, sensor data, etc. -Preprocessing. These data sets are then processed to derive qualitative spatial observations associated with specific time points to hand over to the actual reasoning component. This preprocessing is done by the Temporal partitioning and Integration module responsible for partitioning the input data into time points and integrating data associated with the same time point including the resolution of spatial conflicts. -Qualitative abstraction. This module is itself supported by the Qualitative abstraction module for performing the abstraction from quantitative to qualitative information and the Consistency checking module for testing whether a qualitative spatial descriptions is consistent or contains logical contradictions. -Scenario and (Partial) Narrative Descriptions. The qualitative temporally-ordered observations generated by the Temporal partitioning and Integration module constitute the scenario and narrative descriptions, and serve as the input to the Reasoning module, which embeds in itself one or more forms of (explanatory) reasoning capabilities. -Explanatory Reasoning. The reasoning component leads to the derivation of spatio-temporal knowledge that can be utilized by external services and application systems that directly interface with humans (e.g., experts, decision makers). Access can be provided by a Query Processing module that allows for identifying high-level abducibles in the derived knowledge base.
In the following, we further explain the architecture and provide practical examples of the problems and solutions that we previously elaborated on in Section 4 in the context of a case-study.

The Urban Dynamics Domain
Consider the following significantly trivialised urban narrative (inspired from the dynamics of a real city); the textual description has also been illustrated as a timeline in Fig. 10, and the object-level changes along with their temporal progression are illustrated in Fig. 11: The Story of Bombaj. The contemporary city of Mumbaj was once a collection of closely located tiny islands, surrounded by mangroves and other thick forests, along the coast of a huge landmass in the arabian sea. Guided by Bombaj's proximity to the sea and the Western world, humans deforested massive parts of the mangrove forests, and undertook reclamation of the islands to form one continuous entity connected to the huge landmass; this continuous entity came to be know as the city of Bombaj (subsequently Mumbaj).
Migration. Initially, there exists a thick Forest (subsequently becoming an endangered National Park) in the north-east, the Sea on the west, and small pockets of human settlements by way of semi-urban / low-rise, and rural settlements. The idea of Bombaj -its semantic characterization as a place-is centred around these human settlements.
Basic infrastructure setup. Infrastructure gets established in an attempt to provide accessibility / coverage within the city: major transportation links gets established in addition to other initiatives. New conceptual zones gets established and place-names are formed based on the division created by the transportation link; primarily, two main zones that get created and persist even today come to be known as East-Bombaj and West-Bombaj.
Residential development. New residential areas come up, and the West Zone, by virtue of its proximity to the sea, acquires a socio-economic privilege. Thereafter, powerful economic forces dictate that low income / low-rise areas, populated by recent immigrants (i.e., worker groups), come up in the lesser attractive East Zone. The city now starts to acquire its real character.
Industrialisation. The East Zone, which is socio-economically perceived as being less attractive, starts to attract isolated pockets of industrialisation. New Industrial Zones get established in close proximity to the human settlements.
Infrastructure development. Industrialisation, reinforced with further migration into the city, necessitates further infrastructure development. New transportation networks get built up, and major points of intersection / junctions get established / created -these junctions acquire significance as point of economic agglomeration. New industrial zones get established around these hubs of economic activity.
Rapid urban migration. Large-scale deforestation of the thick forests and mangrove areas is undertaken as a result of high financial value of land in the West Zone, and massive population influx and re-development in the East Zone. Economic prosperity means that people in a lower income bracket are lifted, and there is a market for semi-urban settlements in the East Zone, which previously primarily consisted of rural settlements.
From the viewpoint of high-level narrative reasoning, the components of the theory that need to be formally modeled include: (1) domain constraints, spatial relationships (based on observational data), and other existential properties concerning the (appearance and disappearance) of objects, (2) process dynamics, or the laws of the domain, that determine occurrence criteria and effects for domain-specific events, (3) high-level abducibles that provide the causal rules that may be used as a basis of process extraction from a logically abduced model consisting only of domain-independent events.
The domain constraints and the high-level abducibles together constitute the overall specification, referred to as the domain-theory, for the urban dynamics domain. The high-level abducibles do not play a direct role in the narrative completion process, but are only required during a post-processing stage (as a means to query abduced / derived knowledge).W ithin an object and event-based GIS system, one may imagine high-level symbolic information to be available from a range of data sources. Performing explanatory analysis with this information first requires temporal partitioning, qualitative abstraction, and integration capabilities, presented next. 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 Train

Temporal Partitioning, Qualitative Abstraction, Integration
To illustrate the role of temporal partitioning and integration with qualitative abstraction, consistency checking, and conflict resolution (discussed previously in Sect. 4.3) in our example, let us assume that the input data (a) stems from different sources and (b) each piece of information is associated with a timestamp specifying when the underlying measurement or observation has been performed. More specifically, let us say that Source 1 provides information about different land use zones including parks, residential zones, industrial zones, which are derived by analyzing aerial images, while Source 2 provides information about natural reservoirs, that is about the park and mangroves, stemming from a spatial database. All other information in our example comes from additional sources but does not play a role in this here. Let us furthermore assume that the land use types are defined in a mutual exclusive way such that two different zones cannot overlap.
Since all geometries we get from Source 1 and Source 2 are timestamped, the first thing that has to happen is a partitioning of the total covered time period into time intervals and by this inducing groups of spatial facts that are associated with each interval based on their timestamps. Each interval is represented by a time point t i in an ordered sequence of time points. Fig. 12(a) illustrates part of the combined information from all sources that after temporal partitioning fall into time period t 4 shown in Fig. 11(d). Source 1 and Source 2 both contain geo-referenced polygons for the park but this information does not match. To derive a consistent qualitative description for time period t 4 , the integration procedure follows Alg. 1 that takes the set of observed geometries O with object identifiers and a set of integrity constraints IC as input. The first step is to use the Qualitative Abstraction module to translate the combined geometric data into qualitative spatial relations which results in a qual- itative constraint network Q. 2 Using the relations from the RCC-8 calculus this network looks as shown in Fig. 12(b) (p and p 1 represent the different geometries for the same park object). Next, the Consistency Checking module is used to test whether network Q is consistent and compliant with the integrity constraints. If this is the case, the result can directly be handed over as a qualitative observation for t 4 to the reasoning module. However, as also shown in Fig. 12(b) this is not the case as integrity constraints are violated in three places. These violations are indicated by listing possible relations following from the integrity constraint in brackets below the original relation. The relation between p and p 1 should be eq simply because it is known that both represent the same object. The relation between rz 2 and p should be either ec or dc because of the integrity constraints, and the same holds true for the relation between p 1 and iz 2 . Therefore, the qualitative conflict resolution component needs to be called to find a qualitative representation that is as close as possible to the network from Fig. 12(b) but is overall consistent.
To achieve the conflict resolution, an operator Λ based on the idea of distance-based merging operators for qualitative spatial representations Condotta et al. [2008],  is applied to Q. Our resolution operator Λ is based on a distance measure dps, s 1 q between two scenarios over the same set of objects. It is computed by simply summing up the distance of two base relations in the conceptual neighborhood graph of the involved calculus given by d B pC ij , C 1 ij q over all corresponding constraints C ij , C 1 ij in the input scenarios: The resolved network ΛpQq is then constructed by taking the union of those scenarios that are consistent, compliant with the integrity constraints, and have a minimal distance to Q according to dps, s 1 q 3 : with SpQq " ts P QCN | @s 1 P QCN : dps 1 , Qq ě dps, Qqu where QCN stands for the set of all scenarios that are consistent and compliant with the integrity constraints. Following the approach described in , ΛpQq can be computed by incrementally relaxing the constraints until at least one consistent scenario has been found. This is illustrated in Alg. 2 where we assume that the function relax(Q,i) returns the set of scenarios s which have a distance dps 1 , Qq " i to Q.
The result of applying the resolution operator to the network from Fig. 12(b) is shown in Fig. 12(c): Both violations of integrity constraints have been resolved by assuming that instead of 'overlap' the correct relation is 'externally connected'. Interestingly, the resulting consistent qualitatively model contains two disjunctions basically saying that the relation between the park and iz 1 is either ec or dc. This is a consequence of the fact that both qualitative models are equally close to the input model such that it is not possible to decide between the two hypotheses.

Observation Data -Urban Narrative Description
Given the qualitative abstraction, consistency detection and integration capabilities (as described so far), the objective now is to generate a temporally-ordered narrative of the processes that are reflected by the pre-processed data sets. Before exemplifying the narrative, some basic notation that we use from hereon follows: Notation. We use a first-order many-sorted language (L) with the following alphabet: t ,^, _, @, D, Ą, "u. There are sorts (and corresponding variables) for: events -Θ " tθ 1 , θ 2 , . . . , θ n u, time-points -T " tt 1 , t 2 , . . . , t i u, spatial objects -O " to 1 , o 2 , . . . , o j u, regions of space -S " ts 1 , s 2 , . . . , s k u, and a function symbol pextent: O Ñ Sq that determines the time-dependent spatial location of an entity. We only consider binary topological relationships of spatially extended regions in space. However, the theory encompasses point and line-segment based spatial calculi of arbitrary arity.
Let R " tr 1 , r 2 , . . . , r n u denote a reified n-ary qualitative spatial relationship space over an arbitrary qualitative spatial calculus. Φ " tφ 1 , φ 2 , . . . , φ l u is the set of propositional and functional fluents, e.g., φ sp po i , o j q P Φ is a functional fluent denoting the spatial relationship from R between objects o i and o j . The special event-predicate tranpr i , o i , o j q P Θ denotes a transition to a spatial relation r i between objects o i and o j . Finally, the ternary Holdspφ, r, tq Ă rΦˆRˆT s predicate is used for temporal property exemplification, and Happenspθ, tq denotes event occurrences. For notational convenience, we use the following syntactic sugar for fluent terms (φ): P pφpr xi, . . . xn sqq transforms to r P pφpx i qq.
. .^P pφpx n qq s. The use of r xi, . . . xn s with events terms (Θ) represents a vector argument, and is interpreted differently.

Partial Description and Extension
When spatial relationships (Φ space ) between some objects are omitted, a complete description (with disjunctive labels) can be derived on the basis of the composition theorems (cmp. Section 5.5), and other integrity constraints for the spatial domain under consideration. In the following, we elaborate the treatment for a partial situation description using the notion of a monotonic extension. Let Ω denote a partial spatial state description consisting of facts expressed using the ternary Holds predicate. The following notion of a 'monotonic extension' is necessary: Definition 5.1 (Monotonic Extension) The monotonic extension of a partial spatial state description Ω is another description Ω 1 such that Ω Ă Ω 1 , and all semantic entailments with respect to the spatial information present in Ω are preserved in Ω 1 . For lack of space, we leave out the formal definition for the monotonicity condition.T he observation set (Ψ) constitutes the input to a high-level reasoning component. In the section to follow, we develop the formal domain-independent spatial theory that is used as the basis of reasoning, or in this specific case, for practical abductive reasoning in GIS.

A Domain-Independent Spatial Theory
From a dynamic spatial systems perspective, a domain-independent spatial theory (most crucially) consist of: (1) high-level axiomatic aspects that characterise a qualitative theory of spatial change; (2) phenomenal aspects inherent to dynamic (geo)spatial systems [Bhatt and Loke, 2008]. We adapt this general notion for the domain of geospatial dynamics.

I. Axiomatic Characterisation of a Spatial Theory
Many spatial calculi exist, each corresponding to a different aspect of space. Here, it suffices to think of one spatial domain, e.g., topology, with a corresponding mereotopological axiomatisation by way of the binary relationships of the RCC-8 calculus. From an axiomatic viewpoint, a spatial calculus defined with respect to an arbitrary relationship space R has some general properties (described below in (P1-P5)). For any spatial calculus, it can be assumed that (P1-P5) are known apriori, i.e., these are the intensional properties that define the constitution of the calculus. To realize a domain-independent spatial theory that can be used for reasoning (e.g., spatio-temporal abduction) across different dynamic (geospatial) domains, it is necessary to preserve the high-level axiomatic semantics of these generic properties, and implicitly, the underlying algebraic properties, that collectively constitute a qualitative spatial calculus. A domainindependent spatial theory (Σ space ) may be obtained by axiomatising (P1-P5) as follows: 5 (P1-P2). Basic Calculus Properties (Σ cp ).
R has the jointly exhaustive & pair-wise disjoint (JEPD) property, i.e., for any two entities in O, one and only one spatial relationship from R holds in a given situation. The joint-exhaustiveness can be expressed using n ordinary state constraints of the form in (6a).
As we mentioned, the primitive relations of a qualitative calculus have a continuity structure, referred to as its conceptual neighbourhood (CND) (see Egenhofer and Al-Taha [1992], Freksa [1991a], Galton [2000]), which determines the direct, continuous changes in the quality space (e.g., by deformation and / or translational motion). The binary (reflexive) predicate neighbourpr, r 1 q denotes a continuity relation between relations r and r 1 .
P ossptranpr, o i , o j q, tq " rtextentpo i , tq " s i^e xtentpo j , tq " s j u^tpD r 1 q Holdspφ sp p s i , s j q, r 1 , tq^neighbourpr, r 1 qus Continuity constraints are only useful in scenarios involving spatio-temporal continuity (e.g., diffusive phenome, movement in (geo)space), and may serve a useful role in spatio-temporal interpolation, and prediction, especially in scenarios where the available data is incomplete and/or error-prone.
From an axiomatic viewpoint, a spatial calculus defined on R is (primarily) based on the derivation of a set of composition theorems between the JEPD set R. In general, for a (spatial, temporal or spatio-temporal) calculus consisting of n JEPD relationships (i.e., n " |R|), rnˆns compositions are precomputed. Each of these composition theorems is equivalent to an ordinary state constraint (9), which every spatial situation description should satisfy.
These are applicable when more than one spatial calculus is modelled in a non-integrated manner (i.e., with independent composition theorems). These axioms explicitly characterize the relative entailments between inter-dependent aspects of space, e.g., topology and size. For instance, a spatial relationship of one type may directly entail or constrain a spatial relationship of another type (10a). Such axioms could also possibly be compositional in nature, making it possible to compose spatial relations pertaining to two different aspects of space in order to yield a spatial relation of either or both spatial types used in the composition (10b).
p@tq. rHoldspφ sp1 ps, s 1 q, r, tq Ą Holdspφ sp2 ps, s 1 q, r 1 , tqs p@tq. rHoldspφ sp1 ps i , s j q, r 1 sp1 , tq^Holdspφ sp2 ps j , s k q, r 1 sp2 , tq Ą Holdspφ sp ps i , s k q, r sp , tqs II. Phenomenal Aspects -Geospatial Events (Σ ph ) Here, we define our exemplary interpretation for the geospatial events based on the semantic characterisation in Section 4.1. The definitions also utilise additional (binary) boolean function symbolsmerge cond and split condthat extralogically define (e.g., in a geometric sense) the conditions needed to check for events. 6

II.1 Appearance and Disappearance
This is the simplest case where the existential status of an object undergoes a change (11). Here, we assume that identity is handled outside of the reasoning framework.

II.2 Split
A split involves an existing object that disintegrates into a set of n previously non-existing objects (12) s denote a domain-independent spatial theory that is based on the axiomatisations encompassing (P1-P5), and the phenomenal aspects in Σ ph .
Corresponding to each spatial situation (e.g., within a hypothetical situation space; Fig. 6), there exists a situation description that characterizes the spatial state of the system. It is necessary that the spatial component of such a state be a 'complete specification', possibly with disjunctive information. For k (binary) spatial calculi being modelled, the initial situation description involving n domain objects requires a complete specification with rnpn´1q{2s spatial relationships for each calculus. 7 Definition 5.2 (C-Consistency) A scene description is C-Consistent, i.e., compositionally consistent, if the state or spatial situation description corresponding to the situation satisfies all the composition constraints of every spatial domain (e.g., topology, orientation, size) being modelled, as well as the relative entailments as per the axioms of interaction among inter-dependent spatial calculi when more than one spatial calculus is modelled.
From the viewpoint of model elimination of narrative descriptions during an (abductive) explanation process, C-Consistency of scenario descriptions is a key (contributing) factor determining the commonsensical notion of the physically realizability of the (abduced) scenario completions. 8

Practical Abduction in GIS with Σ space
Let Σ be the background theory and Φ be an observation sentence whose assimilation demands some explanation. According to the abductive approach to computing explanations, the task of assimilating Φ involves finding formulae ∆ that when conjoined to Σ yield Φ as a logical consequence (i.e., Σ Y ∆ |ù Φ).
Appendix A provides details of the precise abductive approach for computing explanations, as the details are not central for this paper. Instead, we focus on illustrating the nature of the high-level domainindependent abducibles that are generated as a result of the reasoning process in (A1-A3).

A1. Abducing Appearances and Disappearances
The following is with respect to the illustration in Fig. 6: 9 data set). For instance, high-level abducibles (16) (referring to high-level processes) may be inferred given the primary abductions in (14-15): geospatial processprural expansion, t, t 1 q ÐÝ r pD rz j , . . . , rz m , rz n q. RuralZonespr rz j , . . . , rz m , rz n sq st r pD t i , q. duringpt i , t, t 1 q^Happenspmergepr rz j , . . . , rz m s, rz n q, t i q s |ù ∆ 1 u geospatial processpmangrove def orestation, t, t 1 q ÐÝ r pD mgq. M angroveZonespmgq st geospatial processppark encroachment, t, t 1 q ÐÝ r pD rz, prkq. RuralZoneprzq^P arkpprkq st The set of high-level (domain-dependent) abducibles may be either dynamically constructed within a query-based environment, or may be pre-specified and invoked via some interfacing mechanism that connects the analytical capability with the real stake-holders in the analytical process. This would enable users and software services that utilise the narrative-based GIS architecture to independently define the semantics of the spatio-temporal phenomena in domain-specific ways.
For instance (building on the argument provided by one of the referees of this paper), a high-level domainspecific abducible could characterize the social and economic forces (e.g., gentrification, industrial agglomeration) that drove such spatial expressions of urban development to occur per se. Such linking of high-level complex and / or subjectively interpreted geographic processes such as industrial agglomeration to spatial-temporal data that capture readily observable properties (e.g., via satellite imagery and land use) depends on problem-specific considerations: -An analyst may decide to completely correlate observable spatio-temporal processes (e.g., shrinkage, splits, disappearance) with complex socio-spatial phenomena such as urbanisation. -Spatio-temporal analysis (e.g., continual growth or shrinkage of a polygon) may be complemented with other data sources, and the influence of non-spatial datasets and quantitative analytical methods could be formally accounted for in the narrative framework such that the abductive explanation framework consists of both spatio-temporal as well as other kinds of abducibles (i.e., non-spatial evidences can be used to further enrich the interpretation of macro geospatial processes).
As discussed already in the paper, the focus of the narrative-centred model of this paper has been on the spatio-temporal aspects of the dynamic geospatial phenomena. A formal treatment of incorporating nonspatial datasets as evidences in the explanation process, albeit possible, is beyond the scope of this paper. Our focus has been on employing formal methods from the field of commonsense reasoning about space, actions, and change into the domain of dynamic GIS.

DISCUSSION AND CONCLUSION
The ability of semantic and qualitative analytical capability to complement and synergize with statistical and quantitiatively-driven methods has been recognised to be important within and beyond the range of GIS application domains (discussed in Section 2.1). Researchers in GIS and spatial information theory have investigated several fundamental ontological aspects concerning the modelling of events, processes, the practical development of taxonomies of events relevant to a geospatial context, and construction of formal methods in qualitative spatial information theory.
As we have emphasised, event and object based explanatory analysis is especially important (e.g., in the context of a query-based GIS system) where the available data needs to be analysed for various purposes such as managerial decision making, policy formation and so forth. Indeed, the development of high-level analytical capability within the emerging object, temporal and event-based geographic information systems has been identified to present a range of fundamental representational and computational challenges -it has been the objective of this paper to: explicitly address some of these challenges from the viewpoint of the application of formal knowledge representation and reasoning methods concerning space, events, actions, and change.
The broad technical question that has been addressed in this paper is: what is it that constitutes the core spatial informatics underlying (specific kinds) of analytical capability within a range of dynamic geospatial domains?
From a methodological viewpoint, the concrete goal of our research has been to: investigate the theoretical foundations necessary to develop the computational capability for high-level commonsense, qualitative analysis of dynamic geospatial phenomena within next generation event and object based GIS systems.
We have presented an overarching framework for narrative-centred high-level modelling and explanatory analyses in the geospatial domain, and have provided a unified view of a consolidated architecture in the backdrop of an illustrated application scenario from the domain of urban dynamics. Building on existing foundations in the GIS community, and spatial information theory in particular, we have demonstrated fundamental challenges and presented solutions thereof encompassing aspects such as qualitative abstraction and integration, spatial consistency, and practical geospatial abduction within a logical setting.
Most importantly, we believe that we have developed inroads from classical Knowledge Representation and Reasoning (KR) sub-disciplines in artificial intelligence, specifically formal methods in spatial and temporal reasoning, reasoning about action and change, and commonsense reasoning. We believe that these interdisciplinary inroads in GIScience open-up interesting possibilities toward the realization of next-generation analytical GIS software systems. From a topical viewpoint, we propose that this particularly demands a transdisciplinary scientific perspective that brings together Geography, Artificial Intelligence, and Cognitive Science.

ACKNOWLEDGEMENTS
We would like to thank the anonymous reviewers for their valuable comments and feedback.
Mehul Bhattt gratefully acknowledges the funding and support of the German Research Foundation (DFG), www.dfg.de, via the Spatial Cognition Research Center (SFB/TR 8), and the SFB/TR 8 Project DesignSpace.

APPENDIX A Computing Explanations -Logic-based Abduction in GIS
Let Σ be a background theory and Φ be an observation sentence whose assimilation demands some explanation. According to the abductive approach, the task of assimilating Φ involves finding formulae ∆ that when conjoined to Σ yield Φ as a logical consequence (i.e., Σ Y ∆ |ù Φ). Additionally, a set of predicates are distinguished as being abducible in order to avoid trivial explanations. It is essential that the explanation ∆ must be in terms of predicates that have been designated as being abducible. Finally, an approach is needed to incorporate the non-effects, and indirect effects of events and actions thereby overcoming the frame and ramification problems. This is achieved by the use of a relevant minimisation policy, which typically involves the use of circumscription (CIRC) [McCarthy, 1980]. Furthermore, it is also necessary that the explanation be minimal, i.e., the derived explanation should not be subsumed by other explanations. Definition (6.1) formalises the commonly-understood notion of explanation by logical abduction [Shanahan, 1989].
Definition 6.1 (Explanation) A formula ∆, essentially an existential statement, is an explanation of a ground observation sentence Φ obs of language L in terms of the abduction policy η˚given a background theory rΣ " Σ change Y Σ space s and a circumscription policy that minimizes ρ˚and allows σ˚to vary if: -CIRCrΣ^∆ ; ρ˚; σ˚s is consistent, and the models themselves are C-Consistent (as per Definition 5.2) -∆ mentions only predicates in η˚, and -CIRCrΣ^∆ ; ρ˚; σ˚s |ù Φ obs -There is no explanation ∆ 1 of Φ obs such that ∆ |ù ∆ 1 and ∆ 1 * ∆ (i.e., the minimality criteria)˝