In the rest of this paper, we will use a simple set-based notation to describe the translation state of a page and all its linguistic alternatives. For example, given a particular page available in English, French, Spanish and German the following set of formulas, could be used to capture their state:

en_v3 = {e1, e2, e3}
fr_v1 = {e1, e2, e3}
de_v2 = {e1, e3}
es = None

These formulas simply state that the English page is currently at version 3, and includes 3 edits: e1, e2 and e3. The French version is at version 1, and includes the "same" three edits. The German version is at version 2 and only contains edits e1 and e3, and finally, the Spanish version simply does not exist yet.

It is important to note that this notation makes a few interesting assumption about how to best represent the status of a page and its linguistic alternatives.

Firstly, the state of a particular linguistic alternative is described as a set of edits, where edits are cross-linguistic. In other words, when a particular edit is made to a page in one language, and then translated to another language, both linguistic versions are deemed to include the "same" edit.

Secondly, the order in which edits were carried out is irrelevant. Because the state of the different linguistic variants is represent as sets of edits, it does not matter whether e1 was done before or after e2.

Thirdly, the translation state says nothing about which text segments are affected by a particular edit. Of course, if we are to help users translate an edit between languages, we need to be able to show what text needs to be translated. However as we shall see, this information can be retrieved using the standard page revision history present in all wikis, and for the purpose of tracking the translation state, we can ignore these details until that time when users actually get down to translating a particular edit.

As we will see, these three assumptions turn out to be important in turning an apparently complex problem of tracking edits in multiple languages at once, into a much simpler problem.