2.2.5. An important consequence: transitivity of relatendness/unrelatedness
If we have proven unrelatedness of an x language belonging to X stock with y language that belongs to Y stock then, due to transitivity of unrelatedness, it means that x is not related with the whole Y stock.
2.3. Applying PAI method to some unsettled hypotheses
2.3.1. PAI against Nostratic hypothesis
Basing on comparison of lexis adepts of Nostratic hypothesis state that Indo-European stock, Kartvelian stock, Uralic stock and Turkic stock are relatives. Let’s see and test whether, for instance, Indo-European and Turkic stocks could be relatives.
PAI of Indo-European is about 0.5 (calculated after data represented in 2.1.4.2);
PAI of Turkic stock is about 0.012 (calculated after Yazyki mira. Tyurkskiye yazyki 1996).
Values of PAI differ more than tenfolds so these stocks evidently can’t be genetically related.
2.3.2. Whether Ainu belongs to Altaic stock?
Having compared some randomly chosen lexemes, Patrie states that Ainu is a relative of Japanese and Korean and thus belongs to Altaic stock (Patrie 1982).
Whether Japanese and Korean are part of Altaic stock is still a discussed issue and even relationship of Japanese and Korean is still actually questionable. However, let’s accept Patrie’s proposition and let’s look at PAI of these languages.
PAI of Ainu is 0.75 (calculated after Tamura 2000);
PAI of Japanese is 0.13 (see 2.1.6);
PAI of Korean is 0.13 (calculated after Mazur 2004).
Values of PAI of Ainu and Japanese/Ainu and Korean differ sixfold.
In the case of Coptic language and Semitic group values of PAI differ fourfold and if there were no firm structural evidences relationship of Coptic language and Semitic group would be very problematic.
In the case of Ainu and Altaic stock serious difference of PAI values is obviously proof of absence of relatedness. Ainu and Korean, Ainu and Japanese are completely unrelated like, for instance, Spanish and Basque.
Moreover, we should keep in mind that Japanese and Korean have probably the highest values of PAI among languages of Altai stock so if we compare Ainu with some “true” languages of Altaic stock the difference is much more striking.
And also the fact there is almost no structural correlation between Ainu and Japanese and between Ainu and Korean corroborates conclusion made with the use of PAI.
2.3.3. PAI suggests that Buyeo stock seems to be real
Japanese and Korean seem to be closer relatives than it has been thought usually, since their PAI values completely coincide (see 2.3.2). And this fact correlates well with their structural and material correlation.
Anyway after discovering closeness of PAI values proximity of grammar systems should be shown.
The question of Japanese and Korean relationship is considered in (5.2).
2.3.4. PAI against Mudrak’s hypotheses
Mudrak believes that such languages as: Ainu, Nivkh, Chukchi-Koryak, Itelmen and Eskimo-Aleut are genetically related (Mudrak 2013).
2.3.4.1. Whether Ainu and Nivkh could be relatives
According to Mudrak Ainu and Nivkh not just belong to that hypothetical stock but belong to same group inside the stock (pic. 4).
Pic. 4. Scheme representing genetic relationships of “Paleosiberian stock” languages accordingto Mudrak (source: [битая ссылка] http://polit.ru/article/2013/04/22/ps_mudrak_linguistics/ – accessed December 2015)
PAI of Nivkh is 0.07 (calculated after Gruzdeva 1997);
PAI of Ainu is 0.75.
Values differ more than tenfold.
Also grammars of Ainu and grammar of Nivkh show serious differences.