variable-length list of attribute sets bracketed by effective 
dates. 
Other researchers are also contributing to temporal GIS. 
Armstrong (1988) considered time in spatial databases, and 
developed a framework for incorporating temporality in 
spatial databases. Worboys (1990a, 1990b) discussed the 
role of modal logics in a GIS. Hunter and Williamson 
(1990) proposed a method of storing and processing tem- 
poral geographic data by addition of time-encoding attri- 
butes to data elements as required and developed a histori- 
cal digital cadastral database to demonstrate their method. 
Henrichsen (1986) studied Norwegian Socioeconomic 
Database which implements time encoding and handles 
administrative boundaries for the period 1770-1980. 
Since there is complexity in the time-semantic representa- 
tion, most GIS databases now in use do not model time 
attributes. Therefore, in order to retain historical geo- 
graphic information, a set of snapshot sequences (data ver- 
sions) are separately stored in the GIS database. This 
approach not only causes a tremendous amount of data 
duplication but also cannot support historical queries over 
time. Furthermore, most commercial GIS usually use the 
relational database system to store thematic and topological 
information, but use file systems to store geographic loca- 
tion information. Thus, semantic and data-granularity 
mismatches exist between the manipulation of the 
relational database and the manipulation of the file systems. 
A relational database system employs a set-oriented, 
declarative query language, in which the user requests a set 
of tuples without specifying the detailed steps to obtain this 
result. In contrast, the file systems usually use a tuple- 
oriented, procedural programming language, in which the 
problem solution is expressed as a sequence of detail 
operations on a global state. The crux of these problems is 
the lack of a sound temporal/historical spatial data model 
for GIS. 
This paper first reviews temporal/historical database 
research on both spatial and non-spatial applications. Two- 
level state topologies for geographic information are pro- 
posed. The state topologies are then viewed from the point 
of time of view, and two-level time topologies are defined. 
Finally, an approach for representation of the state topolo- 
gies and the time topologies with historical relations is 
developed. 
2. TWO-LEVEL STATE TOPOLOGIES FOR 
GEOGRAPHIC INFORMATION 
2.1 The State Topology for Geographic Objects 
The changes of a geographic object may be viewed as the 
changes of its states over time. The historical information 
of a geographic object may be represented by the collec- 
tion of its states. A mutation (or change) would transform 
the geographic object from one state to the next (Langran 
et al. 1988). A GIS database may be viewed as the collec- 
tion of the states of all the geographic objects concerned 
and transformed from version to version by any of the 
object mutations. 
The duration of a state, which started at time instant Ti, 
and ended at time instant Tj (not including Tj), is 
represented as [Ti, Tj). Ti is called start instant, and Tj is 
called end instant. The state is called a historical state. The 
duration of a state, which started at time instant Ti, and is 
now still active, is represented as [Ti, NOW). We consider 
"NOW" as a moving time variable, and the state as an 
active state. Historical states cannot change, only active 
states can change into historical states. Figure 2.1 shows 
the topology of states and mutations for geographic objects 
in a GIS database. 
Each state line in Figure 2.1 is punctuated by the object 
mutations, and represents the states of a geographic object 
over time. Two states which share a boundary may be 
viewed as contiguous neighbors. The states for all geo- 
graphic objects may be viewed as a topology comprised of 
these parallel state lines. 
2.2 The State Topology for a Geographic Object 
A mutation of a geographic object may be caused by spa- 
tial change or thematic change. Therefore, the states of a 
geographic object may be viewed as the composition of the 
Historical State Mutation Historical State Active State 
KY 
   
  
  
  
The States of Object A CL 
dau aul] Le Là 
Active State 
  
The States of Object B Cl 
The States of Object C 
'The Composition of | 
     
1 Active State 
  
Active State 
1 
I 
I 
I 
AM ri Se C ESS rn ANN) 
  
  
  
States in a GIS Database ESS 
World Time ; 
TO T1 
Figure 2.1 The Topology of Geographic Object States and Mutations 
NOW 
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