Christophe Claramunt
email: christophe.claramunt@dgr.epfl.ch

Marius Thériault
email: marius.theriault@ggr.ulaval.ca

Toward Semantics for Modelling Spatio-temporal Processes within GIS

Keywords: Temporal GIS, Events, Processes, Modelling, Spatial dynamics

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INTRODUCTION

Time is a fundamental dimension for understanding and modelling evolution of geographic phenomena. Previous papers propose temporal models and query languages for GIS applications [START_REF] Hazelton | [END_REF], Langran 1992and 1993[START_REF] Cheylan | [END_REF], Frank 1994, Peuquet 1994and 1995, Worboys 1994a]. Many of them use a linear scale to model time. However, time is too complex to be reduced to a simple collection of time-stamps [Peuquet 1994, Frank 1994]. A temporal GIS (TGIS) must be able to monitor and analyse successive states of spatial entities, and also be equipped to study dependencies between linked entities [START_REF] Claramunt | [END_REF]]. This implies formal representation of spatio-temporal processes in order to fully describe their topological networks, which involve both temporal and spatial dimensions.

In a previous paper, we have proposed a model to describe basic spatio-temporal processes using an eventoriented approach [START_REF] Claramunt | [END_REF]]. It provides a topological framework for representing entity-based events and processes. It describes basic processes of evolution, distinguishes between the metric and topological dimensions of time, and suggests temporal query operators. The purpose of this paper is to develop a taxonomy of spatio-temporal processes that retain the original meaning of events and processes while they are represented within a GIS database. The approach allows for complete representation of processes involving both space and time, and the encoding of known relationships between entities that produces complex spatiotemporal evolution. It is based on the Event Pattern Language (EPL) described by [START_REF] Gehani | [END_REF] and [START_REF] Motakis | [END_REF]. EPL is already used for active database applications and provides logical constructors for complex event specifications. The proposed model takes advantage of EPL's expressiveness to summarise complex spatio-temporal processes.

In section 2, we present the temporal ontology used to define the framework. Section 3 concerns modelling of spatio-temporal objects. Identification and classification of basic processes follow in section 4. A summary of the necessary EPL constructs is presented in section 5. Section 6 addresses the semantic specification of composite processes. Section 7 concludes with a summary about capabilities and the usefulness of this approach and outlines further research issues.

TEMPORAL ONTOLOGY

The proposed process-oriented TGIS model combines the quantitative concept of time (measured dates and durations) [Langran 1992] with a qualitative temporal reasoning involving topologically ordered events [Frank 1994, Peuquet 1994]. An event is defined as a set of processes (emphasis on global result) while a process is an action which modifies entities (emphasis on the mechanisms) [START_REF] Bestougeff | [END_REF]]. The model represents local and discrete spatial dynamism and retains the Kowalski's principle of local event representation [Kowalski 1986]. It is not oriented toward global changes which are rather described by space and time series (E.g. statistical or numerical analysis of spatio-temporal behaviour) [Peuquet 1994[START_REF] Thériault | [END_REF] or by temporal logics dealing with global event descriptions [McCarthy 1969].

To respond adequately to scientific needs, a TGIS should explicitly preserve known or possible links (the temporal topology) between events and their consequences, the facts [Beller 1991]. 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 search for causal links that associate entities through influence and transformation processes. Recording known relationships between entities is an essential requirement for scientific TGIS because these facts are the basic constructs used in the research.

We define an entity as a real-world abstraction of an existing feature while␣'object' means its database representation. Object versions correspond to successive states of a specific entity. Additionally, we will use the term 'instance' to designate versions that are linked by a spatio-temporal process and that do not concern the same entity. Various metaphors represent complementary dimensions of time: linear time, cyclical time, branching time (inter-entity time dependencies) and multidimensional time (valid-time, transaction-time, user-time) [START_REF] Jensen | [END_REF]. The model is built using valid-time to decribe real-world events occurrence and duration, as opposed to transaction-time and user-time that are used for management and user purposes [START_REF] Jensen | [END_REF]]. The time range of any process or entity is represented by its lifespan [Segev 1994]. The quantitative attributes of time may be represented as an instant or a period. An instant is generally modelled as a time-stamp [START_REF] Navathe | [END_REF]]. A period is defined by a composite attribute involving two time-stamps with an order constraint [Snodgrass 1995]. The chronon describes the shortest duration of time that can be represented in the computer system [START_REF] Jensen | [END_REF]], and the time granularity represents the time line partitioning related to application needs (E.g., geologic, historic or annual scales) [Snodgrass 1995].

SPATIO-TEMPORAL ENTITIES MODELLING

Recent thinking about integrating time into GIS has shown that it is a complementary facet of spatial and thematic domains [Peuquet 1994and 1995[START_REF] Claramunt | [END_REF]. This paper retains the triad representational framework proposed by Peuquet (1994) and uses an object-oriented model to define the data structure. Objectoriented models provide a natural method for describing real-world spatial entities [Worboys 1994a and1994b], avoids data fragmentation, and enables useful capabilities for managing time (E.g., inheritance of time properties) [Snodgrass 1994]. We represent an entity class as a set of objects (A) of the same type. These objects share common attribute sets. The object type (A i ) of a spatial entity is defined by three attribute sets:

• The temporal domain (A i Temp) represents entities' temporal data {Valid time, Transaction time, Last Process, Next Process}. Last Process and Next Process attributes link each version of an entity to the processes that generate and replace it. The Valid time attribute describes the total duration of each version; thus the lifespan of an entity is the total duration of its successive versions. • The thematic domain (A i Them) describes the thematic attributes {Them 1 , ..., Them j }.

• The spatial domain (A i Spat) conveys the geographical representation of entities {Spat 1 , ..., Spat j }.

Object versions use this triad structure to describe evolution manageable at the domain level. Successive object versions can refer to the same spatial attribute set if the mutation is thematic, or to the same thematic attribute set if the mutation is only spatial. This behaviour specialisation allows for asynchronous value changes of a same object within the thematic or the spatial domain without affecting the other one. When needed, time-stamps (Valid time and Lifespan) may be used to take a snapshot of the contents of the database at a specific instant or during a period. Specifying time granularity enables simultaneous use of many temporal scales within the same database. Rules for inheritance of temporal attributes depend on the characteristics and semantics of abstraction mechanisms. Generalisation and aggregation are the main abstractions generally identified for spatial applications. Generalisation assembles objects with common behaviours and properties while aggregation groups different objects into a composite object. We define temporal inheritance as follows:

• Each object member of a generalisation hierarchy has its set of temporal attributes (A i Temp) declared at the highest supertype object level.

• Each object member of an aggregation hierarchy has its set of temporal attributes (A i Temp) defined at its own type level. An aggregated object has a set of temporal attributes that is a composite of the constituent subtype objects. For example, the lifespan of a flooded parcel has to be an intersection of the parcel's and the flood area's respective lifespans. These consistency rules may change according to the entities' characteristics and to the composition type. Moreover, object hierarchies introduce temporal constraints. The existence of a subtype object depends on the previous existence of the appropriate supertype object [START_REF] Wachowicz | [END_REF]]. Conversely, there is no fixed rule for transaction-time composition since it is independent of any order constraints (E.g., the second process of a sequence may be registered in the database before the first one).

BASIC SPATIO-TEMPORAL PROCESSES

Events are defined through processes that transform entities. We distinguish between evolving and mutating entities [Langran 1992] to define three main classes of basic spatio-temporal processes (Figure 1):

• Evolution of a single entity represents basic changes (appearance, disappearance, etc.), transformations and movements of that entity. • Functional relationships involve spatio-temporal processes between several entities (replacement and diffusion processes). They convey known dependence links that need to be modelled explicitly in the temporal domain. The range of phenomena that can be processed in a TGIS is probably inexhaustible. Therefore, a rule must be provided to distinguish between relationships with predominant temporal incidence (which must be modelled within the temporal structure) and relationships in which time plays a secondary role. Certain events are ordered in an unchanging sequence (E.g., an ancestor must live before his descendants) that dates alone cannot always reproduce. A review of the principal types of temporal relationships studied in geography leads us to set forth the following rule: functional processes that involve a dependence link between entities, while they impose a precedence constraint, must be modelled on the temporal structure in order to clarify the topological relationships they convey. Furthermore, processes with only one time-period overlap may be described in the thematic domain without creating confusion [START_REF] Claramunt | [END_REF]].

III -Evolution of spatial structures involving several entities (restructuring processes)

( • Evolution of spatial structures describes spatio-temporal processes involving several land-based entities. Restructuring processes are used to model changes that affect the way a given piece of land is partitioned according to a system of mutually exclusive zones (E.g., counties, municipalities, census tracts, land parcels). This involves a mix of simultaneous transformation, appearance and disappearance of interrelated entities with an obvious precedence constraint. However, evolving spatial patterns of independent entities in a population conveys overall tendencies that can be modelled using aggregation mechanisms. This typology identifies three main classes of spatio-temporal processes that allows for the hierarchic decomposition of real-world phenomena (E.g., a displacement is a movement and a movement is an evolution). Although we postulate that these basic processes are mutually exclusive and their number is finite, the model can further integrate other basic processes defined with the same rules.

We also model processes as objects. This provides a homogeneous representation structure for both entities and processes. Process objects have to be kept distinct from those describing entity characteristics and behaviour. Thus, entity objects may use process objects (through methods) to describe their evolution and link their respective versions or instances (Figure 2). A basic process type (P) represents a class of spatio-temporal processes with the same attribute set. Each process class (P i ) has a temporal (P i Temp) and thematic (P i Them) attribute set:

• The temporal domain (P i Temp) is a set of temporal attributes {Valid time, Transaction time, Entities lists}. The entities lists are used to reference active entities generating the process, passive entities being modified by the process and other entities directly involved during the process. These lists contain versions related to only one object when they describe the evolution of a single entity.

For multiple-entity relationships, they refer to the appropriate instances of each entity involved. Links between the active, passive and involved entities define a relation, taking the form:

Process_Type{set(s) of related instances or versions}.

• The thematic domain (P i Them) is a set of thematic attributes {Process type, Attribute 1, ..., Attribute j } which describes and qualifies the process. The Process type represents the basic processes shown in Figure 1. Spatial properties of processes are inferred from the entities included in the process, thereby avoiding the need for a spatial domain to locate it. On the other hand, temporal topologic relationships between successive entities (versions or instances) are inferred through the process that produces the modifications. Spatio-temporal processes describing the evolution of a single entity (Figure 3) are:

• Appearance (Appearance{0;X}) occurs when an object version of X has no preceding version (0 is the null set). • Disappearance (Disappearance{X;0}) occurs when an object version of X has no subsequent version. • Stability (Stability{X;X}) occurs when an object version of X has the same state for a certain period. This process is needed to handle the case of an entity that changes in the thematic domain without corresponding evolution of its spatial properties. Functional spatio-temporal processes are:

• Succession (Succession{X;Y;A}) occurs when an instance of entity Y is the immediate successor of an instance of X at the position A. Both instances may survive the replacement (Figure 4), instance of X being permuted to another location tracked with the appropriate evolution process. We represent the succession process as a relationship of one-to-one entities over one position. This process built networks showing the succession of individuals or groups holding a given position. The position is a real (E.g., a parking place) or a virtual (E.g., a set of coordinates) entity with a spatial domain that is used to define a spatial link between a set of succeeding owner entities. In Figure 4, the ownership link expresses the relationship between one owner entity and the position during a given period of time, whilst the temporal link is used to model the succession of owners for a same position. • Permutation (Permutation{X;Y;A;B}) occurs when an instance of Y is the immediate successor of an instance of X at position A, and when this same instance of X is the immediate successor of the instance of Y at position B,during the same instant or period. This is a relationship of one-to-one entities over one-to-one positions (Figure 5). The Permutation{X;Y;A;B} expression is not strictly equivalent to the combination of Succession{X;Y;A} and Succession{Y;X;B} because the simultaneity of the process is an essential property of the changes occurring. For example, this process is needed to model two hockey teams (X and Y) exchanging their goals (A and B) at the end of a period, because this change must be simultaneous when it occurs and there is a complementary relationship between entities A and B. • Production (Production{X 1 ...X n ;B 1 ...B p; A 1 ...A q }) occurs when a set of entities (X) produce a set of entities (B) while consuming a third set of involved entities (A). The production process is modelled as a relationship of many-to-many entities using many component entities (Figure 6). The producers, the involved components and the products must be entities of different classes. The production process implies the disappearance or tranformation of involved components and the appearance of produced entities. However, it is more meaningful than Disappearance{A 1 ;0} and Appearance{0;B 1 } because it describes the linkages between entities and the mechanisms involved (via the process thematic attributes). The Disappearance{A 1 ;0} and Appearance{0;B 1 } are used only when the mechanism involved is missing (E.g., disappearance and appearance in unknown circumstances). For example, this process can model a plant (producer) using pieces (components) to manufacture cars (product). The relationship between the involved components is needed to model the exchange of products between firms and describe complex industrial networks.

Production {set of producing entities set of produced entities; set of consumed entities} The reproduction process is modelled as a many-to-many entities relationship (Figure 7). It shares the linkage capabilities of the production process while restricting the parent and the child entities to the same class. It is valid only for life phenomena, and the need to specify the contributed material is not obvious. Successive reproduction involving grandparents, parents and children may be used to model complex reproduction networks needed in biology or genealogy. • Transmission (Transmission{X 1 ...X n ;Y 1 ...Y p; A 1 ...A q ) occurs when a set of entities (Y) has its attributes modified by some contact with a set of entities (X) with the collaboration of a third set of involved entities (A). The third set of entities (A) acts as a vector of transmission (Figure 8). The main difference with the production and reproduction processes is that the Y entities existed prior to transmission. Their previous histories are tracked through evolution processes. We represent the transmission process as a network of many-to-many entities using many vector entities. This type is needed to model diffusion mechanisms for telecommunications and innovations, as well as contagion processes in epidemiology. In both fields there is an obvious need to make the relation with the transmission medium explicit (the communication network or the virus).

Time line

Production process

Process

Transmission {set of transmitting entities; set of receiving entities; set of involved entities}

Time line

Transmission process

Process Temporal topologic links

Set of entities

ACTIVE ENTITIES PASSIVE ENTITIES set of transmitting entities

Entity x1 Version i set of involved entities

Entity a1 Version k set of receiving entities

Entity y1 Version j set of transmitting entities

Entity x1 Version i+1 set of involved entities

Entity a1 Version k+1 set of receiving entities

Entity y1 Version j+1

Figure 8. Syntactic graph of a transmission functional process

Spatial restructuring processes (Figure 9) are:

• Land subdivision (Split{X;Y 1 ...Y n }) occurs when a spatial entity (X) is replaced by a set of distinct entities (Y) of the same class. It is a one-to-many entities relationship that implies a simultaneous Disappearance{X;0} and Appearance{0;Y 1 } ... Appearance{0;Y n } while adding a functional link between all those simultaneous events. • Land union or fusion (Union{X 1 ...X n ;Y}) occur when a set of spatial entities (X) is replaced by another spatial entity (Y). It is a many-to-one entities relationship that implies a simultaneous Disappearance{X 1 ;0} ... Disappearance{X n ;0} and Appearance{0;Y} plus the simultaneous functional meaning. • Territory re-allocation (Re-allocation{X 1 ...X n ;Y 1 ...Y p }) occurs when a set of spatial entities (Y)

is the immediate successor of a distinct set of entities (X), overlapping the same common territory. It is a many-to-many entities relationship (Figure 9). Figure 10 illustrates a re-allocation of land parcels: Re-allocation{(A,B,R1,C1);(D,E,F,G,H,R2,C2)}. This re-allocation cannot be modelled as a land union followed by a land subdivision for many reasons. Firstly, entities C and R survived the process. Secondly, original parcels are split among many new parcels which may themselves be formed by the union of parts of various original ones. Thirdly, one original parcel (R) extends its territory over contemporaneous parcels (A, B and C) while giving some part of its previous area to form a new parcel (H). Fourthly, parcel C has shrunk during the operation. We get a complex mix of simultaneous related (one process involved) appearance, disappearance, expansion, contraction and land exchange. Therefore, representing this process as many distinct processes is inadequate because it hides the underlying common cause. Land subdivision and land union processes are related to administrative procedures, like day-to-day surveying operations. Territory re-allocation is needed to model a comprehensive change involving many entities caused, for example, by a law. It is also the appropriate process for modelling borderline change between two or more existing spatial entities.

Evolution processes are generally sufficient to operate with the adjacent versions of an object, even if timestamps are missing or corrupted. The other basic processes are mandatory for time-dependent applications in many fields, including industry (production), biology or genealogy (reproduction), communications or epidemiology (transmission). Temporal integrity constraints are enforced by appropriate controls on versions' or instances' lifespans (E.g., the begin-time of a produced instance must be compatible with the respective lifespan of its parent instances) and transitive rules to maintain consistent temporal networks (E.g., an ancestor cannot be the child of one of its descendants).

EVENT PATTERN LANGUAGE CONSTRUCTS

Composite processes enable description of complex natural phenomena by reproducing their dynamics (epidemiology, mobile entities, fire evolution, innovation diffusion, etc.). A knowledge representation of composite processes requires a formal language to understand and describe their semantics. Although temporal logics propose different theories to describe evolving systems, the issue of formally specifying the semantics of complex events is only partially solved [Long 1989].

The proposed approach uses event-oriented constructs [START_REF] Gehani | [END_REF][START_REF] Motakis | [END_REF] to represent such complex processes. The expressive power of the Event Pattern Language (EPL) is efficient for modelling complex spatio-temporal processes. A composite process is defined as an expression formed through processes and operators. The thematic attributes of a composite process are embodied in its constituents.

Let us introduce some basic notions and operations of the Event Pattern Language:

• P is a basic or a composite process.

• *:P is a sequence of zero or more consecutive occurrences of P.

• !P is the exclusion and indicates that there is no occurrence of P.

• (P 1 ,P 2 ,...,P n ) is a sequence of processes consisting of an occurrence of P 1, immediately followed by an occurrence of P 2 , ..., immediately followed by an occurrence of P n .

• (P 1 &P 2 &...&P n ) is a conjunction of processes occurring simultaneously (at a same instant or period). • {P 1 ,P 2 ,...,P n } is a disjunction of processes. It happens when at least one process among P 1 , P 2 , ..., P n occurs.

• [P 1 ,P 2 ,...,P n ] is a relaxed sequence consisting of an occurrence of P 1, followed later by an occurrence of P 2 , ..., followed later by an occurrence of P n . It is logically equivalent to (P 1 ,*:any,P 2 ,...,*:any,P n ), where *:any means a sequence of zero or more other processes. We introduce a cycle operator which is formed by the recursive repetition of the same sequence of processes using the ⊕: operator. It can be combined with sequences (⊕:(P 1 ,P 2 ,...,P n )), conjunctions (⊕:(P 1 &P 2 &...&P n )), disjunctions (⊕:{P 1 ,P 2 ,...,P n }), and relaxed sequences (⊕:[P 1 ,P 2 ,...,P n ]). This operator is requested to model recurrent natural and human phenomena (E.g., seasons in climatology or cultural rotations in agriculture). The cycle operator is significantly different than the sequence operator (*:): there are at least two occurrences of the sequence; the recurrence is regular on the time line (I.e., equally spaced events); and the successive instances may be separated by any other events.

COMPOSITE PROCESSES

Dynamic phenomena involving real-world entities may be represented by composite process expressions. Let us develop a few representative examples:

• A boat trip described successively by a stability position, a casting off and a sailing: Transition graphs [START_REF] Gertz | [END_REF]] express the structure of composite processes and may improve users' comprehension of the underlying system with explicit mapping of relevant constraints. Figure 11 shows a proposal for presenting composite processes in graphical form. This example presents a composite process (P=[P1,P2,P3]) involving two cars (entities A and B) arriving successively (relaxed sequence P1) at a ferryboat (entity C), a ferryboat trip to another port (process P2), and a simultaneous landing of cars (processes conjunction P3): The ferry trip is implicitly transmitted to the cars using the positional link defined by the succession processes. The ferry's storage capacity limits the number of cars it can move. Such semantics provides a language for describing processes with an object-oriented database model. The process decomposition principle offers a way to represent different time granularities or user point of views. The model allows for representation of ordered, linear and cyclic temporal processes. A regular composite process is defined by a constant granularity (i.e., regular data points). The lifespan of each composite process depends on the set of involved processes. Composite processes enable snapshot generation of historic states (using time-stamps).

The described processes connect entities and define the necessary lineages to discover the causal relationships that produce the observed events. Although temporal query languages provide operators that allows to compare time intervals [Snodgrass 1995], there is a need for a new class of topological operators to efficiently access the explicit links between evolving or mutating entities [Wuu 1992[START_REF] Claramunt | [END_REF]. The method outlined in this paper may be applied in many fields. It provides basic constructors for defining concepts specific to each discipline. In a paper dealing with temporal and spatial patterns of vegetation, [START_REF] Miles | [END_REF] defined many concepts related to ecology that can be modelled through formal semantics. They can distinguish between the local and the global extinction of a species. The first is related to an entity disappearance while the latter involves the disappearance of all the members of a class (defined through the generalisation mechanism). The permanence of a vegetative species (A) may be defined as !Disappearance{A;0}; its absolute regression as [Contraction{A;A}, !Expansion{A;A}]; its global progression as [Expansion{A;A}, !Contraction{A;A}]; its replacement by species B in locality L with Succession{A;B;L}; etc. Using the concept of time granularity to study the rhythms of change, it is also possible to distinguish between fluctuations (rapid and cyclical temporary changes) and trends (slow and permanent modifications). Moreover, in many scientific fields, it is only possible to measure time through indirect methods like C14. These measures include a factor of inaccuracy (E.g., 3200 years before present ± 75 years) that must be stored in the database to define the time granularity. In many fields of natural sciences there is a clear need to handle fuzzy time-stamps and to define the time line as a sequence of ordered and related events.

CONCLUSION

Studies of spatial dynamics need formal semantics to decompose and represent the characteristics of spatiotemporal processes. Scientists seeking causal links need qualitative models that describe functional links between entities and improve analysis of event sequences. These models must represent spatial entities as well as processes involved in their evolution. The semantics outlined in this paper enable homogeneous and flexible representation of spatio-temporal processes and related spatial entities. The framework is based on a classification of basic processes combined with an object-oriented formalism and the EPL language. Representation of processes and spatial entities enable specialised temporal, spatial and thematic behaviours, thereby allowing object versions to be managed

Figure 2 .

 2 Figure 2. Temporal topology

Figure 3 .

 3 Figure 3. Syntactic graph of single entity spatial evolution processes

Figure 4 .

 4 Figure 4. Syntactic graph of a succession functional process

Figure 5 .

 5 Figure 5. Syntactic graph of a permutation functional process

Figure 6 .

 6 Figure 6. Syntactic graph of a production functional process • Reproduction (Reproduction{X 1 ...X n ;Y 1 ...Y p }) occurs when a first set of entities (X) creates a new set of entities (Y) of the same class.The reproduction process is modelled as a many-to-many entities relationship (Figure7). It shares the linkage capabilities of the production process while restricting the parent and the child entities to the same class. It is valid only for life phenomena, and the need to specify the contributed material is not obvious. Successive reproduction involving grandparents, parents and children may be used to model complex reproduction networks needed in biology or genealogy.

Figure 9 .Figure 10 .

 910 Figure 9. Syntactic graph of land restructuring processes

(

  Stability{A;A}, Displacement{A;A}, *:{Displacement{A;A}, Rotation{A;A}}, Stability{A;A}). • A forest fire as it evolves: (Appearance{0;A}, *:(Expansion{A;A} & Displacement{A;A}), Contraction{A;A}, Disappearance{A;0}). • An epidemic phenomenon involving a virus (V) and many individuals (A, B, C 1 ...C 5 , D 1 ...D 45 ): [Transmission{A;B;V}, Transmission{B;C 1 ...C 5; V}, Transmission{C 1 ...C 5 ;D 1 ...D 45; V}]. • An industrial plant (A) producing cars (B) and industrial rejects (C) using M 1 ...M 35 components: *:(Production{A;B;M 1 ...M 35 } & Production{A;C;M 1 ...M 35 }). • Two boats (A and B) exchanging their dockyard positions (C and D) while transmitting radio information (I and J): (Permutation{A;B;C;D} & Transmission{A;B;I} & Transmission{B;A;J}). • The genealogical tree of an individual (X): [Reproduction{(A,B);(C,D)}, Reproduction{(M,N);O}, Reproduction{(D,O);X}]. In this example, there is a pair of twins in the first generation. • A cyclic three-year rotation of three crops (W: Wheat, G: Grass, V: Vegetables) on a farm divided into three parcels (A, B, C): ⊕:((Succession{W;G;A} & Succession{G;V;B} & Succession{V;W;C}),

Figure 11 .

 11 Figure 11. Diagram of composite processesThis diagram uses few constructors, which enhances understanding of composite process sequences and structure.

  • Transformation processes involve changes in entity's size or shape. They are Expansion (Expansion{X;X}), Contraction (Contraction{X;X}) and Deformation (Deformation{X;X}).• Movement processes convey location changes related to Displacement (Displacement{X;X}) and Rotation (Rotation{X;X}). The {X;X} operands link any given version of X with the immediately succeeding version of the same entity after the event occurs.

	Spatial evolution processes
	Appearance{} Disappearance{} Stability{}		Evolution process		Process
	Expansion{} Contraction{} Deformation{}	Entity x		Entity x	Entity versions
	Displacement{} Rotation{}	Version i previous version	Time line	Version i+1 next version	Temporal topologic links
					Evolution process
					{previous version;
					next version}

ACKNOWLEDGEMENTS

We are indebted to anonymous reviewers for their useful comments and suggestions. We also acknowledge Christine Parent for stimulating discussions about several issues of this paper. We thank Yves Brousseau and Sylvie Saint-Jacques for designing the graphics and Patricia Dyksterhuis for carefully revising preliminary versions of this paper. This research has been developed with the support of the Spatial Information System Institute of the Swiss Federal Institute of Technology in Lausanne, and the Planning and Development Research Centre, Laval University, Quebec, Canada. It is partly funded by the Social Sciences and Humanities Research Council of Canada (410-93-1097) and the Tri-Council Secretariat (Social Sciences and Humanities Research Council, Natural Sciences and Engineering Research Council and Medical Research Council) of Canada (922-94-0015).

Seventh International Symposium on Spatial Data Handling, SDH'96. Delft August 12-16, 1996 11 by domains in an asynchronous mode. The language developped can model complex spatial processes. It includes an order syntax, coordinating rules and a graphical presentation proposal.

The model provides formal support for representing evolving phenomena via database and for developing simulation models. Since the proposed semantics are oriented toward spatio-temporal applications, they could be used for TGIS and other temporal applications involving qualitative reasoning. Further research perspectives include specifying spatio-temporal operators to interact with the database. Spatio-temporal process analysis may also be extended by integrating non-spatial processes related to geographic phenomena (e.g., non-spatial successions or permutations). Implementation in real case studies is an essential validation perspective. Applications to study soil dynamics and ecological impacts in Canada and Switzerland are currently in development.