Accepted for publication in book of ESF GISDATA Conference on Modelling Change in Socio-Economic Units, Napthlion, Greece, 1998
Modelling changes and events in dynamic spatial systems with reference to socio-economic units Michael F. Worboys Department of Computer Science Keele University, Staffs ST5 5BG UK phone: +44782583078 fax: +44782713082 email:
[email protected]
1. Introduction The large majority of current systems for handling geospatial information are static, concentrating on a single temporal snapshot, usually the current state. Changes in the application domain are tracked in the system by performing updates and erasing information on the past. In recent years there has evolved a body of research, both in the general database community (Snodgrass 1992) and in the spatial database community (Al Taha et al 1993) for adding temporal dimensions. That research addresses the issue of ‘time in the system’, where the challenge is to provide computational models that enable past, current and future states of the application domain (valid time) and the system (transaction time) to be handled in the temporal database. Work presented in this chapter, however, is concerned with a different aspect of temporal systems, referred to as ‘the system in time’, where we are concerned to handle in a dynamic system a model of the real world as it changes in both the spatial and temporal dimensions. Such dynamic, spatial systems will have a wide range of applications, including transportation networks and environmental monitoring. They have been termed responsive GIS (Williams 1995), with the following characteristics: •
large amounts of spatially referenced data are required to be readily available;
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a sizable proportion of the data is regularly updated from external data sources;
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some of the data are noisy, conflicting and incomplete;
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rapid decision-making is to be supported.
The purpose of this chapter is to explore modelling constructs that may be useful in constructing dynamic or responsive spatial systems. At first sight, it seems that the notion of time is key here, since by adding temporality to our systems (rather in the same way that we added space) it would appear that we then provide the required functionality. However, time is merely a framework in which change is possible. As expressed by 1
Accepted for publication in book of ESF GISDATA Conference on Modelling Change in Socio-Economic Units, Napthlion, Greece, 1998 Shoham and Goyal (1988), ‘The passage of time is important only because changes are possible with time. ... The concept of time would become meaningless in a world where no changes were possible.’ The principal thesis that is explored in this chapter is that it is not time that is the key to conceptual modelling of dynamic systems, but change and related constructs such as event and process. The object-oriented approach has provided a large amount of power to modelling and implementing complex spatial systems, so might naturally be thought to be applied in the context of dynamic spatial systems. However, we immediately run into some deep philosophical questions, like ‘Is an event an object?’, for which a positive answer would open up the entire object-oriented approach. The chapter attempts to carefully consider the fundamental constructs of change, event and process, placing the discussion in a spatial context, and concludes by using some of the ideas to propose a base model for dynamic spatial systems. Our principal application is the main theme of the book, namely socio-economic units (SEUs). The chapter includes a classification of change at is applies to SEUs. We begin with a brief review of the object-oriented approach to geospatial phenomena.
2. Modelling geospatial objects In this section, for the sake of completeness, we summarize the basic concepts of the object-oriented approach from the conceptual modelling perspective. Objects model abstract and concrete things in the world. Objects have attributes, describing aspects of their state (e.g. name of a person) and operators, describing ways in which they may behave (e.g. birth, marriage, death of a person). Objects with the same structure of attributes and operators may be gathered together in an object class, of which each member is an instance (e.g. object: me, class: person). Each object has a unique identity which is immutable, even if its state and behaviour changes. Object classes my be structured into hierarchies in two different ways. Firstly, an object class A may be a subclass of class B if every member of A is a member of B. Thus the class woman is a subclass of person. Note that a subclass may not only inherit state and behaviour from its superclass, but also have its own individual state and behaviour. The hierarchy of classes structured in this way is called the inheritance hierarchy. A second relationship between classes is that of composition. For example class car is composed of classes body, wheels, engine, etc. Such a hierarchy of classes may be termed a composition hierarchy. The object-oriented approach is a natural modelling method for geospatial information, because the underlying spatial entities have a complex structure and composition. Spatial object classes have been modelled by several researchers (e.g. Egenhofer and Frank 1987, 1992, Worboys 1992, 1994,).
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Accepted for publication in book of ESF GISDATA Conference on Modelling Change in Socio-Economic Units, Napthlion, Greece, 1998 Socio-economic units are discussed elsewhere in the book. For our purposes, they have the following properties. •
SEUs can be modelled as objects.
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An SEU has an attribute that is an aggregate of people.
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An SEU has a spatial location attribute that is of class region.
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SEUs may change over time.
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The location attributes of a collection of SEUs, at an instance of time, combine to form a ‘coverage’ of a spatial region.
3. Spatial change 3.1 What is change? In the object model, the focus is the collection of object classes. Although objects in the classes may change, the changes themselves are not explicitly handled but are implicit in the variations in the properties of the objects. A fine but important distinction to be made is between change and the results or effects of change. We may contrast two distinct definitions of change: Change - Definition 1 An object o changes if and only if there exists a property P of o and distinct times t and t’ such that o has property P at t and o does not have property P at t’. Change - Definition 2 A change occurs if and only if there exists a proposition Π and distinct times t and t’ such that Π is true at t but false at t’. The first definition of change can be traced back to the ancient Greek philosophers (e.g. Aristotle, Physics, Book 1, chapter 5). In this case, change is a verb that applies to objects. The focus is on the objects. The second definition (Russell 1903) makes the notion of change explicit as a noun; it commits to change as an explicit occurrence in the world, without prior reference to objects.
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Accepted for publication in book of ESF GISDATA Conference on Modelling Change in Socio-Economic Units, Napthlion, Greece, 1998 Pursuing definition 1 a little further, there are two distinct ways in which an object may change. Consider a land parcel; it may change ownership or its boundary. In the case of change of boundary, the land parcel alters in the sense that its attributes change. With change of ownership, the object itself does not alter, but its relationship to other objects changes. So it seems that we should extend definition 1 to at least allow changes to relationships between objects. 3.2 Classification of change There have been several attempts to classify change. Mark Johnson (1987) defines image schemata of change in terms of ‘force’ structures as follows: • • • • • •
compulsion: stability, diffusion blockage: disappearance, split counterforce: disappearance diversion: transformation, split removal of restraint: appearance, stability, transformation, union enablement (potential forces)
A commonly occurring construct associated with change is that of production, where one or more objects contribute to the creation of a new set of objects or transmit properties to an existing collection of objects. There are several possibilities: • Production and death, where the parent and child objects are of the same type. An example is the merging of several land parcels to form a new parcel. The new parcel is a composite of the original parcels. In this case the original parcels cease to exist. • Production and death, where the parent and child objects are of different types. For example, a building collapses, producing a pile of bricks. The pile of bricks is a decomposition of the building into component parts, of different type from the original building. • Production and continuation, where the parent and child objects are of the same type. For example, two parents (re)produce a child. Note that there is limited use of the composition construct here, since the parents cannot be thought of as components of the child. • Production and continuation, where the parent and child objects are of different types. For a first example, consider states associating into a union. The union is a composition of the states. Both states and union continue in existence. The states continue to have a relationship with the union. Thus, if a state ceases to exist, so the union changes or may itself cease to exist. The second example is a ship having a spillage and creating a pool of oil. The pool of oil is a new type created from a component of the composite object - ship. Eventually, the pool of oil ceases to have a relationship with the ship. The ship may sink but the pool is still present. Example 3 4
Accepted for publication in book of ESF GISDATA Conference on Modelling Change in Socio-Economic Units, Napthlion, Greece, 1998 is people constructing a building. In this case, people are agents in the construction event, but have little connection themselves with the final type. The building eventually has little relationship to the constructors; it continues to exist even if the people cease to exist.
4. Events and processes 4.1 Events An event is maybe the key notion in the modelling of dynamic systems. A dictionary definition is ‘a happening, occurrence or episode’. In terms of change, an event has been taken to be a change or composite of changes (it may be absence of change, e.g. ‘the lawn stays wet’, ‘I remained still for five minutes’). Some writers define an event to be instantaneous while others allow it to have a duration. As with objects, we should take care to distinguish event type from event occurrence, for example horse race is the type and the 1996 Grand National is the occurrence. There have been several attempts to extend traditional modelling methods, such as the entity-relationship (ER) approach, to handle events. The entity-relationship approach has proved to be enormously successful in modelling fairly simple static systems, but has the limitation that only entities, attributes and relationships are provided as primitive constructs. Thus ER will only be successful if events can be considered as entities or relationships. The attempt to introduce temporal relationships to stand for events results in methods such as ERT (van Assche et al 1988), ERAE (Dubois et al 1986), EVORM (Proper et al 1995) and dynamic modelling (Rumbaugh et al, 1991). ERT (van Assche et al 1988) is an extended version of ER that includes inheritance and composition constructs, as well as the capability to timestamp entities and relationships. It does not support schema evolution. An example of its notation is shown in figure 1, modelling the change above, where a building collapses, producing a pile of bricks.
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Accepted for publication in book of ESF GISDATA Conference on Modelling Change in Socio-Economic Units, Napthlion, Greece, 1998 Building
T
1 0,1 Collapse
T
0,N Pile of bricks T 0,1
Brick
Figure 1: ERT model of the collapse of a building producing a pile of bricks ERAE (Dubois et al 1986) has constructs entity, relationship, attribute and event. The modelling approach is predicated on the Newtonian view that space is a container for objects and time is a container for occurrences. An event is defined as ‘an instantaneous happening of interest’. Each event has an associated function returning a time, while each entity has an associated existence predicate. Figure 2 shows the collapse of the building modelled using ERAE.
Building occurred at
Collapse
resulted in Pile of bricks
Figure 2: ERAE model of the collapse of a building producing a pile of bricks The EVolving Objects Relationships and Methods (EVORM) approach (Proper et al 1995) allows models of evolving application domains. The schema itself is allowed to change. Based on ER, its primitives are: evolvable elements (object types, relationship types, operations, etc.), actions (occurring as events), and application model histories.
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Accepted for publication in book of ESF GISDATA Conference on Modelling Change in Socio-Economic Units, Napthlion, Greece, 1998 In the dynamic modelling of Rumbaugh et al (1991), an event is viewed as an instantaneous one-way transmission of information from one object to another. A sequence of events is defined to be a scenario. State and event are seen as dual concepts, where a state separates events and an event separates states. The relationship between states and events in a model is represented by a transition diagram. For Rumbaugh, dynamic modelling consists in identifying scenarios of events and constructing a transition diagram. 4.2 Events and the object-oriented approach This section considers how events fit with the object-oriented approach. There could be a very close coupling if we were able to treat events as objects. Objects are items that: • • • • •
possess properties, stand in relation to one another, undergo changes which constitute events, possess determinate and objective identity conditions, take their place in predicates.
The distinction between events/changes and things/objects is problematic. It seems that events and objects belong to distinct categories. Events occur, but objects do not occur. As above (ERAE), space is a container for objects but time is a container for occurrences. Events/changes are reportable. The whole of an object is usually present at any time in its existence, while usually only part of an event is present at any one time. An alternative view (Broad 1959) is that ‘a thing ... is simply a long event’. Conversely, many philosophers have reduced objects to a series of events. Closely related is the question of event identity. Two intensional definitions have been provided by Davidson (1980). 1. Events are identical when they have exactly the same causes and effects. 2. Events are identical when they occupy the same space and time. An extensional definition is the following, due to Kim (1969) is that events are identical when they consist in the same objects having the same properties at the same times. Unfortunately this makes no provision for changes in objects or relationships between objects. We should note the changes in the objects (or objects before and after the event). We should also consider changes in the relationships between the objects and in the inheritance and composition hierarchies. Therefore, an event (type) may be defined by its time varying collection of participating objects (types) and their time-varying attributes (types) and relationships. 4.3 The concept of process
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Accepted for publication in book of ESF GISDATA Conference on Modelling Change in Socio-Economic Units, Napthlion, Greece, 1998 A process is a series of changes with some sort of unity or unifying principle. Process is to change/event as syndrome is to symptom. In order to model process, it is useful to view a process as a composite event. Processes are a setting in which events occur and are related to each other. The next section discusses this setting in more detail.
5. Modelling dynamic systems: an object-oriented model of process, event and change Any object-oriented model of process, event and change needs to frame these concepts in an object-oriented setting. Thus, for the concept of event, for example, are the following constructs appropriate? • • • • •
identity attributes relationships inheritance hierarchy composition hierarchy
Event identity has been considered in the previous section. It makes sense for events to have attributes, for example ‘our house move (event) took two days (attribute)’. The granularity of an event will be one of its attributes. Similarly relationships between events can obtain, for example ‘the first war (event 1) ended 21 years before(relationship) the second war (event 2)’. An inheritance hierarchy of events may be constructed, for example the event type ‘war’ is a subtype of the event type ‘European war’. Event composition is a natural construct, where temporally composite events become processes if there is an underlying thread. Other kinds of composition are also possible, for example spatial composition. We explore the possibility of relationships between events in more detail. A broad subdivision for relationship types is temporal, spatial and causal/control. Under the heading of temporal come relationships such as concurrency, the Allen relationships, and the notion of temporal relativism (Knight and Ma, 1994). Events may be spatially related, for example ‘their weddings took place one mile from each other’, although this example stretches the notion of event and raises the question whether ‘pure’ events have spatial attributes/relationships. Causal/control relationships, such as independence and synchronization, are important. Causality is a powerful notion in this context. A useful definition is that of ‘causally before’ (Reiter and Gong 1995). Event e is causally before event f if • e happened before f • e could possibly have affected the occurrence of f In object-oriented terms, what could it mean for one event to cause another? Suppose that events have methods send and receive, allowing them to communicate with each
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Accepted for publication in book of ESF GISDATA Conference on Modelling Change in Socio-Economic Units, Napthlion, Greece, 1998 other. Define the one-step causality relation between events e and f as the smallest relation satisfying the properties: • If events e and f occur simultaneously at the same process, then e⇒f • For any m send(m) ⇒ receive(m) A question that we leave this section asking is, what is the relationship between agents and events?
6. A responsive system for socio-economic units A system that can handle information about SEUs must be both responsive to change (dynamic) and be able to handle current and previous states (temporal). Change may impact both individual SEUs and the whole coverage, including the hierarchy in which the SEUs may be structured. Some of the salient properties of change in this context are: •
stability of the results of change;
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rate of change;
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reversibility of the effects of change
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continuity vs. discreteness of the events and processes underlying the change;
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magnitude of change.
Changes to individual SEU may be changes to their geospatial attributes (topological and metric) or to non-geospatial attributes. In order to give some idea of the range of changes possible, we list some topological geospatial changes below. •
Changes to interior of SEU: cohesiveness, internal structure.
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Changes to boundary of SEU: geometry, permeability, fuzziness, one-way vs. twoway, recognizability, salience, dissonance.
Examples of changes to SEU coverages include: •
Creation, modification, and deletion of individual SEUs in the collection.
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Changes in the geometry of the coverage.
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Accepted for publication in book of ESF GISDATA Conference on Modelling Change in Socio-Economic Units, Napthlion, Greece, 1998 Examples of changes to a hierarchy of SEUs include: •
Introduction and elimination of levels of the hierarchy.
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Movement of SEUs between levels.
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Merging and splitting of levels.
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Changes of linkages between levels.
7. Conclusions This chapter has considered the notions of change, event and process and compared them with more familiar modelling constructs such as object, entity, identity, attribute and relationship. The main thesis is that to model dynamic systems, we must include extra concepts from those present in temporal information systems. In some ways this is similar to the distinction between temporal data management vs. temporal reasoning. There is a need for temporal data management in the handling of inventories of objects as they evolve through time. But this is only part of the story. Temporal reasoning includes: • Prediction; • explanation (we know: how things were, rules of change; we want: explanation of why things are as they are); • planning; • finding the rules of change. In order to be able to tackle these higher-order tasks, a richer model of change must be used. This model must then be comprehensive enough to be able to handle some of the aspects of change of socio-economic units discussed here.
References Al-Taha, K.K., Snodgrass, R.T. and Soo, M.D. 1993. Bibliography on spatiotemporal databases. Association for Computing Machinery Association for Computing Machinery SIGMOD Record, 22: 59-67, and International Journal of Geographical Information Systems 8(1): 95-103. Broad, C.D. 1959. Scientific Thought, Paterson, NJ. Davidson, D. 1980. Essays on Actions and Events, Clarendon Press, Oxford.
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Accepted for publication in book of ESF GISDATA Conference on Modelling Change in Socio-Economic Units, Napthlion, Greece, 1998 Dubois, E., Hagelstein, J., Lahou, E., Ponsaert, P., Rifaut, A. and Williams, F. 1986. The ERAE model: A case study. In Sol, H.G., Olle, T.W., Verrijn-Stuart, A.A. (Eds.), Information System Design Methodologies: Improving the Practice. Elsevier, Holland. Egenhofer, M.J. and Frank, A. 1987. Object-oriented databases: Database requirements for GIS. In Proceedings of the International GIS Symposium: The Research Agenda, Vol. 2, US Government printing Office, Washington DC, pp. 189-211. Egenhofer, M.J. and Frank, A. 1992. Object-oriented modeling for GIS. Journal of the Urban and Regional Information Systems Association: 4: 3-19. Johnson, M. 1987. The Body in the Mind. University of Chicago Press, Chicago. Knight, B. and Ma, J. 1994. A temporal database model supporting relative and absolute time. Computer Journal, 37(7): 588-597. Proper, H.A. and van der Weide, T.P. 1995. A general theory for evolving application models. IEEE Transactions on Knowledge and Data Engineering, 7(6): 984-996. Reiter, M. and Gong, L. 1995. Securing causal relationships in distributed systems. Computer Journal, 38(8): 633-642. Rumbaugh, J., Blaha, M., Premerlani, W., Eddy, F. and Lorensen, W. 1991. ObjectOriented Modeling and Design. Prentice-Hall, Englewood Cliffs, NJ Russell, B. 1903. Principia Mathematica. Cambridge University Press, Cambridge. Shoham, Y. 1987. Reasoning about change. MIT Press, Boston, MA. Shoham, Y. and Goyal, N. 1988. Temporal reasoning in artificial intelligence. In Shrobe H. (ed.), Exploring Artificial Intelligence, pp. 419-438, Morgan Kaufmann. Snodgrass, R.T., 1992. Temporal databases. In A.U. Frank, editor, Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, Lecture Notes in Computer Science, 639, pp. 22-64, Heidelberg Berlin: Springer-Verlag. Van Assche, F., Layzell, P.J., Loucopoulos, P. and Spelltinex, G. 1988. Information systems: a rule-based approach. Journal of Knowledge Based Systems, 1(4). Williams, G.J. 1995. Templates for spatial reasoning in responsive geographical information systems. International Journal of Geographical Information Systems, 9(2): 117-131. Worboys, M.F. 1992. A generic model for planar geographic objects. International Journal of Geographical Information Systems, 6: 353-372. Worboys, M.F. 1994. Object-oriented approaches to geo-referenced information. International Journal of Geographical Information Systems, 8(4): 385-399. 11
Accepted for publication in book of ESF GISDATA Conference on Modelling Change in Socio-Economic Units, Napthlion, Greece, 1998 Worboys, M.F. 1996. An approach to object modelling of a ‘navigable’ database. Proceedings of the NCGIA/CALTRANS Conference on Navigable Databases. NCGIA, University of California, Santa Barbara, CA.
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