The Lefkas earthquake resistant technique has been studied and acknowledged by British Government.
I read two scientific papers (thanks to Pierre brc) : follow a brief summary of what i learnt.

General principles

Two-storey houses are built thus : ground floor is rough boulder masonry. Three lines of wooden posts (one along each long wall, and one in the middle of the room) support the first floor. This one is erected in wood-frame construction (cf. our Dajji).

Foundations

Foundations are laid on a three-layer round-poles mat, which could behave as a spring if a gap was left around. Since it is not the case, it is considered that the main benefit is outspread of the foundation surface.

Question of the benefit of the dual system regarding to earthquakes

On such multi-storey situation, one of the benefits is to lower the gravity centre of the building. That does not concern batar construction, unless people wanted to build a dajji house on top of a batar ground floor (i would recommend this option).
The principle is that if the stone wall fails with the earthquake, the wood posts carry more and more of the load. Actually, the hyperstatic aspect of the construction allows that the strongest structure takes the load.
Computer analysis and experience show that the dual system has better response that the upper "dajji" part. It might be due to an "elastic jump" from one type of resistance to the other, like jumping from one foot to the other instead of trying to remain standing (personal opinion).
Overall, it seems that the most important benefit of the dual-construction system is to combine two very different uncoupling fundamental periods (0.02 for masonry and 0.2 for wood-frame), thus allowing a very adaptative response.

Question of the bracing of the lower structure

Nothing is said about proper bracing of the ground floor (dual-system). I have two hypotheses :
1-Different wood reinforcement in the corners (detailed in the paper) allow a "strong but supple" resistance, in the likeness of our dajji principles, or
2-The strong posts take only vertical stress, whereas horizontal stress is taken by the masonry walls. That implies that in case a wall fails and collapses, floor works as a diaphragm.

To be continued...

One of the papers is very technical and computer-oriented. It will be read thoroughly by Pierre of the Belgian Red Cross (engineer) for further details and understanding.