## 4 Inference Rules for Matching Geographic Ontologies in Different Languages
### Conceptual Framework
#### 4.1.6 Toponyms and Located Toponyms  
One can define a homology relationship for toponyms. For instance, the various cities in the word Sevilla are also called Seville in French and \(\frac{\lambda}{\lambda}\frac{\lambda}{\lambda-\lambda}\) (transliterated into Ishibilyya) in the Arabic language:  
\[\begin{array}{l}\text{Sevilla}\quad\text{\small$\mathfrak{a}$ \mathfrak{a}  
Monaco Munegu  
However, in the Italian language, the German city of Munich (Munchen, in German) is also called Monaco. Therefore, we can write:  
Monaco Munich  
It is obvious that \"Munich\" and \"Munegu\" have nothing in common except their names in Italian. In this case, when necessary to disambiguate, Italians say \"Monaco di Baviera\" and \"Principato di Monaco\". In the U.S., when speaking about a place named Washington, generally it is followed by the name of the state.  
Regarding the multiplicity of languages, in some cases, it is important to get the endonym of a place. As previously mentioned, sometimes there are several possible endonyms: in this case, one will prefer the name as used by local people in a well-established language. For instance, in Canada, the French toponym \"Quebec\" will be the endonym of the English toponym \"Quebec\". Therefore, let Endonym denote a function transforming any toponym into its corresponding exonym. For example:  
\[\text{Venezia = Endonym (Venice)}\]  
Back to the example of Granada, in order to disambiguate those homonyms, a solution is to use a hyperonym, for instance the name of the country as a topological prefix \(\supset\) in which \(\mathit{A}\supset\mathit{B}\) can be read \"\(\mathit{A}\) contains \(\mathit{B}\)\", \"\(\mathit{B}\) inside \(\mathit{A}\)\" or \(\mathit{A}\) is the hyperonym of \(\mathit{B}\). Therefore, we can write ES \(\supset\) Granada, US \(\supset\) California \(\supset\) Granada, US \(\supset\) Kansas \(\supset\) Granada, MX \(\supset\) Granada, _etc._, in which MX stands for Mexico, ES for Spain. Let us call them located toponyms. As a consequence, if there is no ambiguity, we can define relationships in another mode:  
\[\mathit{LocTopo}_{1}\ \mathit{RelationX\,LocTopo}_{2}\]  
As the previous solution is interesting to distinguish designated human settlements or administrative subdivisions, it cannot be used directly to disambiguate natural features, such as rivers, mountains, _etc._, which can spread over several cities, provinces, regions and even countries. Indeed US \(\supset\) Mississippi can relate to both the state and the river.  
Let us define Earth as a toponym with its homologous \"planet\", \"our planet\", _etc._ Any located toponym can derive from Earth by a sort of inclusion path. For instance:  
\[\text{ENG.Earth }\supset\text{``Pacific Ocean''}\]  
\[\text{ENG.Earth }\supset\text{America }\supset\text{``North America'' }\supset\text{California }\supset\text{Granada}\]  
\[\text{ENG.Earth }\supset\text{America }\supset\text{``North America'' }\supset\text{``Lake Erie''}.\]  
For the path description of Hawaii, there are two possibilities:  
* country inclusion: ENG.Earth \(\supset\) \"U.S.A.\" \(\supset\) Hawaii;
* location inclusion: ENG.Earth \(\supset\) \"Pacific Ocean\" \(\supset\) Hawaii.