Global Positioning System Reference
In-Depth Information
Note that in the sequel, the term
concept
will be used to denote a class,
an attribute, or a type name. Before introducing the notion of
geographic
knowledge base
, the notion of
partial order on partitions
is given below.
∪
Defi nition
2: Let
E
be a subset of the plane, and
P
a partition of
E
, i.e.,
P
= E
, and
p, p'
¢
P, p
p' =
. Let
P
(
E
) be a set of partitions of
E
, and
P,
P'
¢
P
(
E
)
.
The partial order,
⊑
, on
P
(
E
), indicated as (
P
(
E
),
⊑
), is given as
follows:
P
⊑
P'
iff
p
¢
P, p'
¢
P', p
p' =
{
p,
}
Example
2: Let
E
be a subset of the plane called
Country
, and let
P
(
Country
)
=
{
Region, State, Department, Province, County, Municipality
} be a set of
partitions. The partial order
⊑
on the above partitions is the following, as
shown in Fig. 2:
Department
⊑
Country
Municipality
⊑
Province
Province
⊑
Region
Region
⊑
Country
County
⊑
State
State
⊑
Country
Defi nition
3: Let
E
be a subset of the plane and (
P
(
E
),
⊑
) be a partial order on
the set of partitions of
E
. A
geographicknowledge base
K
E
=
(
C, A, Cls
) consists
of fi nite sets
C
N
, A
A
and a fi nite set
Cls
of geographic classes such
that, for each
n
¢
C,
n
is the name of precisely one geographic class in
Cls
,
and
Cls
also contains a class expression of name
E
. Thus
C
=
P
(
E
), and (
P
(
E
),
⊑
) is referred to as
Part-of
hierarchy.
Example
3: Let us consider the partitions of the class
Country
of Example 2.
A geographic knowledge, called
GeoKB
, can be defi ned by the geographic
classes shown in Table 1. In Fig. 2, these geographic classes are organized
Country
Region
State
Department
Province
County
Municipality
Fig. 2.
Illustration of a partition hierarchy.
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