Global Positioning System Reference
In-Depth Information
Table 6.
Formal defi nition of RLextA-A.
Let c
i
= (A
s
, M
i
, K
i
) be a class where c
i
∈ C. Let c
j
= (A
j
, M
j
, K
j
) be a class
A
i
where c
j
∈ C. Let A
s
= {a
s1
, .., a
sn
} be a set of attributes. Let A
t
= {a
t1
, ..,
a
tm
} be a set of attributes. Let REQSPAT defined as REQSPAT: OP
(ReqSpatP, ReqSpatP)
ReqSpatP : Geometry | OP (ReqSpatP ReqSpatF)
ReqSpatF: ′,′ ReqSpatP |
ε
Pre-conditions
: A
s
⊆ A
i
and A
t
⊆ A
j
and K
i
⊄ A
s
A RL of
RLextA-A (e-A_A->)
type between A
s
and A
t
is defined by:
e-A_A-> : C x REQSPAT x A x .. x A -> C x A x .. x A
(
c
i
,
reqspat,
a
s1
, .., a
sn
) = (
c
j
,
a
t1
, .., a
tm
)
Example 1 (1..* linked classes): From a tourist point of view, a user may
want to eat in a restaurant near a point of interest. It would be appropriate
to determine the types (e.g., international, French, Italian) and addresses
of Restaurants within a reasonable distance. The administrator defi nes
a RL between the spatial attribute “interestPoints” of the City class and
alphanumeric attributes “typeRestaurant” and “addressRestaurant”
of the Restaurant class. This RL is defi ned by: e-A_A-> (City, reqspat,
interestPoints) = (Restaurant, typeRestaurant, addressRestaurant), where
reqspat is a spatial query. This query is defi ned by the application of the √
operator: √(interestPoints, SR < 200) on the spatial attributes “interestPoints”
of the City class and “SR” of the Restaurant class.
Example 2 (independent classes): From a tourist point of view, a hotel
may have a park located in a wider green area. It would be appropriate
to determine the name and type of this green space. The administrator
defi nes a RL between the spatial attribute "park" of the Hotel class and
the alphanumeric attributes “nameGS” and “typeGS” of the GeenSpace
class. This RL is defi ned by: e-A_A-> (Hotel, reqspat, park) = (GreenSpace,
nameGS, typeGS), where reqspat is a spatial query. This query is defi ned
by the application of the
⊂
operator:
⊂
(park, SR) on spatial attributes Park
of the Hotel class and SR of the GreenSpace class.
Operational complexity is defi ned with two stages. The fi rst stage
concerns the complexity of the spatial operator. In a second stage, this
complexity can be modifi ed by the research of the potential instance(s) for
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