Global Positioning System Reference
In-Depth Information
Notations: The following notations and conventions are used throughout
the chapter. {} denotes the set constructor and () denotes the list constructor.
Let C = {c
1
,..., c
p
} be a set of classes. Let A = {a
1
,..., a
m
} be a set of attributes.
Let M = {m
1
,..., m
n
} be a set of methods. For each class c
i
∈
C, we denote
c
i
= (A
i
, M
i
) a class with A
i
⊆
A and M
i
⊆
M. Let K
i
be a set containing the
attribute(s) defi ning a key for a given class c
i
with K
i
⊆
A
i
. The defi nition of a
class c
i
becomes c
i
= (A
i
, M
i
, K
i
). The list (p
1
, .., p
q
) denotes the parameters of a
method m
k
as m
k
∈
M. OP denotes the available set of spatial operators (e.g.,
orthometric distance noted √, inclusion noted
⊂
). FD denotes a Functional
Dependency. RL denotes a Relevant Link.
This section is organized into fi ve parts. In the fi rst part, we present
the concept of functional dependency and its weaknesses. In the following
three sections, we present the three types of proposed Relevant Links.
Finally, we conclude this section by giving in a fi fth part a summary of our
proposals.
Functional Dependencies
Functional Dependencies (FDs) are one of the key concepts of relational
database schema defi nition.
Defi nition
The fi rst semantic link introduced in the design of a relational database
schema is the functional dependency. It expresses a dependency between
two (sets of) attributes at the functional level. The formal defi nition in the
relational database context is the following: X functionally determines Y if,
whatever relation r is the current value for R (a relation), it is not possible
that r (an instance of R) has two tuples that agree in the components for all
attributes in the set X yet disagree in one or more components for attributes
in the set Y (Ullman 1995). Table 3 presents a representation of Functional
Dependencies in a class context.
Table 3.
Formal defi nition of a functional dependency.
Let c
i
= (A
i
, M
i
, K
i
) be a class where c
i
∈ C. Let A
s
= {a
s1
,..., a
sn
} be a set
of attributes. Let A
c
= {a
c1
,..., a
cm
} be a set of attributes
Pre-conditions
: A
s
⊂ A
i
and A
c
⊂ A
i
and A
s
∩ A
c
= ∅
There is a Functional Dependency between A
s
et A
c
noted A
s
Æ
A
c
then:
and A
c
noted A
s
Æ
A
c
then:
∀ I
1
, I
2
two instances of c
i
,
(I
1
.a
s1
, ..., I
1
.a
sn
) = (I
2
.a
s1
, .., I
2
.a
sn
) == > (I
1
.a
c1
, .., I
1
.a
cm
) = (I
2
.a
c1
, .., I
2
.a
cm
)
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