Global Positioning System Reference
In-Depth Information
Table 1.
Example of geographic classes.
ܥݑ݊ݐݎݕൌ൏ሼ݊ܽ݉݁ǣܵݐݎ݅݊݃ǡܿݑ݊ݐݎݕܥ݀݁ǣܫ݊ݐ݁݃݁ݎǡݎ݁ݏ݅݀݁݊ݐǣܵݐݎ݅݊݃ǡ݂݈ܽ݃ǣܵݐݎ݅݊݃ሽǡሼ݈ݕ݃݊ሽ
ܴ݁݃݅݊ൌ൏ሼ݈ܾ݈ܽ݁ǣݐݎ݅݊݃ǡ݄݈݁ܽݐ݄ܥ݁݊ݐ݁ݎǣܵݐݎ݅݊݃ǡݎ݁ݏ݅݀݁݊ݐǣܵݐݎ݅݊݃ሽǡሼ݈ݕ݃݊ሽ
ܵݐܽݐ݁ൌ൏ሼݐܽ݃ǣܵݐݎ݅݊݃ǡܿݑ݊ݐݎݕܥ݀݁ǣܫ݊ݐ݁݃݁ݎǡ݃ݒ݁ݎ݊ݎǣܵݐݎ݅݊݃ሽǡሼ݈ݕ݃݊ሽ
ܦ݁ܽݎݐ݉݁݊ݐൌ൏ሼݐܽ݃ǣܵݐݎ݅݊݃ǡܿݑ݊ݐݎݕܥ݀݁ǣܫ݊ݐ݁݃݁ݎǡ݃ݒ݁ݎ݊ݎǣܵݐݎ݅݊݃ሽǡሼ݈ݕ݃݊ሽ
ܲݎݒ݅݊ܿ݁ൌ൏ሼ݊ܽ݉݁ǣܵݐݎ݅݊݃ǡݎ݂݁݁ܿݐݑݎ݁ǣܵݐݎ݅݊݃ǡ݈݈ܿܽܧ݀ݑܿݐܱ݂݂݅݊݅ܿ݁ǣܵݐݎ݅݊݃ሽǡሼ݈ݕ݃݊ሽ
ܯݑ݈݊݅ܿ݅ܽ݅ݐݕൌ
൏ሼ݅݀݁݊ݐ݅ݐݕǣܵݐݎ݅݊݃Ǣܿݑ݈݊ܿ݅ܪ݁ܽ݀ǣܵݐݎ݅݊݃ǡܿݑ݊ݐݎݕܥ݀݁ǣܫ݊ݐ݁݃݁ݎǡ݄ܾ݅݊ܽ݅ݐܽ݊ݐǣܵݐݎ݅݊݃ǡܽݎ݁ܽǣܫ݊ݐ݁݃݁ݎሽǡ
ሼ݅݊ݐǡ݈ݕ݃݊ሽ
ܥݑ݊ݐݕൌ൏ሼܿݑ݊ݐݕܫܦǣܫ݊ݐ݁݃݁ݎǡݑ݈ܽݐ݅݊ǣܫ݊ݐ݁݃݁ݎǡݏݑݎ݂ܽܿ݁ǣܫ݊ݐ݁݃݁ݎሽǡሼ݈ݕ݃݊ሽ
as a partition hierarchy. In this fi gure,
Country
is partitioned according
to different administrative organizations, i.e.,
Region
,
State
,
Department,
which correspond to the territorial subdivision of Italy, USA, and France,
respectively. Similarly,
Region
and
State
are partitioned again into
Province
and
County
, respectively, and are related to
Region
and
State
by a partial
order relationship. Analogously,
Province
into
Municipality
.
Defi nition
4: Given a geographic knowledge base
K
E
=
(
C, A, Cls
), let
S
i
N
A
,
i =
1, ...,
n
, be sets of synonyms according to a lexical database for the
English language. Then,
SynSet
K
is a (possibly empty)
set of synonyms
for
the geographic knowledge base
K
E
if:
SynSet
K
=
{
S
1
, ...,
S
n
},
n
≥ 0, and
S
i
∩
∪
(
C
∪
A
) for
i
= 1, ...,
n
.
Example
4: The set of synonyms for the geographic knowledge
GeoKB,
shown
in Table 1 (i.e.,
SynSet
GeoKB
), defi ned according to WordNet, are (for the sake
of illustration we consider the following set):
SynSet
GeoKB
=
{{
name, label, identity, mark
}, {
surface, area
},
{
inhabitant, indweller, denizen, dweller, population
}}
Weight Assignment Methods
In this section, we investigate the problem of assigning weights to a
reference ontology (or
H
)
of geographic classes. We address a simplifi ed
notion of hierarchy,
H
, consisting of a set of concepts organized according
to essentially
Is-A
or
Part-of
relations, here referred to as
R
.
Defi nition
5: Let
R
be a relation.
H
is a
taxonomy
defi ned by the pair
H
=<
C, H
>, where
C
is a set of concepts and
H
is the set of pairs of concepts of
C
that are in
R
relation as follows:
H
= {(
c
i
, c
j
) ¢
C × C|R
(
c
i
, c
j
)}
Note that, given two concepts,
c
i
, c
j
¢
C
, the
least upper bound
of
c
i
, c
j
,
lub
(
c
i
,
c
j
), is always uniquely defi ned in
C
(we assume the hierarchy is a lattice).
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