The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beiiins.2008 
intersection matrix represents always the true intersections of 
the interiors and boundaries of regions. That way the 
interpretation of the set of H R relations has to be done by an 
algorithm of the application itself. Consequently the algorithm 
interprets the respective relation correctly. For example the 
intersection-matrix for the situation between operational area 1 
and 2 is presented in equation 13. 
(13) 
The meaning of this matrix is that the intersection of the interior 
is empty. However, the intersection of the closure between both 
is non-empty. A common point on the closure is existent and 
the respective relation is touch. But the algorithm identifies this 
set of intersections as disjoint, because the intersections 
between the interior and the closure as well as the interiors of 
both are empty. 
For the application in the disaster domain using the IM and an 
algorithm that is able to identify the set of H R relations correctly 
has two advantages. The first one is that the IM is widely 
implemented in GIS and spatial databases. The second one is 
that this GIS component can then also be used for visualization 
and user feedback. 
2.3 Types of Reasoning 
The spatial reasoning process has to provide the needed 
information based on the present information state of the 
database as well as general and context knowledge. An example 
for such reasoning is the query for all operational areas which 
are in a damage site containing a fire (cf. Figure 1). For solving 
this problem two approaches are possible. 
The first one is the geometric approach which is compulsory for 
GIS. A spatial query algorithm checks if a point location with 
the attribute fire is inside the closure of a region with the 
attribute damage site. The next step is to find all operational 
areas, which are also inside this damage site. 
The second approach is a more elegant way of processing this 
question on the level of the ontology. The knowledge base 
contains general knowledge about the domain as well as 
specific knowledge about a situation. The general domain 
knowledge is defined a-priori by modeling the ontology 
accordingly (cf. chapter 2.1). For example the part of relation in 
the ontology between the two classes damage site and 
operational area corresponds to the topological relation inside. 
Such relations are universally valid in the whole domain. The 
disjoint relation between several operational areas as well as the 
contained relation between an operational area and an event are 
modeled in a similar manner (cf. Figure 5). In contrast dynamic 
knowledge, which is also given by the knowledgebase, is only 
valid for a specific situation at a specific moment. For the 
example the specific fire event is related to operational area 3 
by the inside relation. 
All relations which are given by the knowledge base for the 
situation of Figure 1, are represented in Figure 5 by solid lines. 
That way answering the query for all operational areas which 
are in the damage site of the fire is possible. The fire is inside 
operational area 3 which is also inside the damage site. Again 
all operational areas of this damage site can be provided. The 
advantage of this type of reasoning is that the relations are 
always present and do not have to be evaluated geometrically. 
Figure 5. Ontology based inference net for topological relations 
of the spatial scene in Figure 1 (used shortcuts of the H R cf. 
Figure 4) 
Figure 6. GIS supported inference net for the special scene of 
Figure 1 (used shortcuts of the fI R cf. Figure 4) 
Another advantage of the reasoning process lies in conditions of 
plausible combinations of relations, so called compositions 
(dashed lines in Figure 5). A plausible combination is given, 
when the relation can be identified unambiguous. For example 
when the fire is inside the operational area 3 and operational