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Matt Duckham and Mike Worboys
Second, developing ad hoc fusion rules, such as illustrated above, may not always lead to an associative and commutative fusion system. Thus, we could add
further rules to our reasoning system that would result in different fusion products,
depending on what order we input data into the system. This is clearly undesirable.
To be well formed we would expect a fusion process to produce a unique fusion
product for a set of inputs irrespective of the order in which they are fused. As a parallel, GIS would be considerably less useful if the overlay operator were defined in
such a way that the order in which source data sets were overlaid affected the output
results of the overlay operation.
An important result of [22] is to formalize geographical information fusion in
such a way that
1. the taxonomy associated with a data set can be represented as a lattice;
2. the fusion process is represented as an associative and commutative binary operator;
3. the fusion process is closed, in the sense that the fusion product is itself a valid
geographical data set that can be used in subsequent fusion operations.
Formally, [22] shows that the geographical data sets (represented as a partition of
space, a lattice, and an extension function) combined with the fusion operator form
a fusion algebra with the properties of a commutative semigroup (closed, associative, commutative). The reader is referred to [22] for more detail on this topic; the
remainder of this chapter turns to issues of reliability and uncertainty rather than
formalization of fusion systems.
6.4 Reliability
The rosetta system outlined above is simple, effective, and has a clear theoretical
basis. However, in developing practical automated geographical information fusion
systems, there are two main issues that must be addressed: unreliability and uncertainty in the fusion process. In this section, we first examine the issue of the unreliability of inductive inference.
6.4.1 Deductive Validity
An inherent limitation of the extensional approach to geographical information fusion is that inductive inference is not deductively valid. In general, an inference is
said to be deductively valid if, given that all the premises are true, the conclusion is
also true. Using inductive inference, it is entirely possible to formulate deductively
invalid inferences. For example, given the premise that all the birds I have ever seen
can fly, I might inductively infer the conclusion that all birds can fly. Clearly, this
conclusion is not necessarily valid, even though the premise may be. A similar problem can occur with a rosetta system. In the example in Fig. 6.1, it might be that if
we had used data sets with greater spatial extents, we would have discovered a region
of built-up area in data set A that overlapped a region of Woodland in data set B. In
Matt Duckham and Mike Worboys
Second, developing ad hoc fusion rules, such as illustrated above, may not always lead to an associative and commutative fusion system. Thus, we could add
further rules to our reasoning system that would result in different fusion products,
depending on what order we input data into the system. This is clearly undesirable.
To be well formed we would expect a fusion process to produce a unique fusion
product for a set of inputs irrespective of the order in which they are fused. As a parallel, GIS would be considerably less useful if the overlay operator were defined in
such a way that the order in which source data sets were overlaid affected the output
results of the overlay operation.
An important result of [22] is to formalize geographical information fusion in
such a way that
1. the taxonomy associated with a data set can be represented as a lattice;
2. the fusion process is represented as an associative and commutative binary operator;
3. the fusion process is closed, in the sense that the fusion product is itself a valid
geographical data set that can be used in subsequent fusion operations.
Formally, [22] shows that the geographical data sets (represented as a partition of
space, a lattice, and an extension function) combined with the fusion operator form
a fusion algebra with the properties of a commutative semigroup (closed, associative, commutative). The reader is referred to [22] for more detail on this topic; the
remainder of this chapter turns to issues of reliability and uncertainty rather than
formalization of fusion systems.
6.4 Reliability
The rosetta system outlined above is simple, effective, and has a clear theoretical
basis. However, in developing practical automated geographical information fusion
systems, there are two main issues that must be addressed: unreliability and uncertainty in the fusion process. In this section, we first examine the issue of the unreliability of inductive inference.
6.4.1 Deductive Validity
An inherent limitation of the extensional approach to geographical information fusion is that inductive inference is not deductively valid. In general, an inference is
said to be deductively valid if, given that all the premises are true, the conclusion is
also true. Using inductive inference, it is entirely possible to formulate deductively
invalid inferences. For example, given the premise that all the birds I have ever seen
can fly, I might inductively infer the conclusion that all birds can fly. Clearly, this
conclusion is not necessarily valid, even though the premise may be. A similar problem can occur with a rosetta system. In the example in Fig. 6.1, it might be that if
we had used data sets with greater spatial extents, we would have discovered a region
of built-up area in data set A that overlapped a region of Woodland in data set B. In