The SQL language of MapInfo Pro/MapBasic is some what limited when it comes to joins.
You can join multiple tables, but there is one basic rule that you need to follow, and looking at your SQL Select I doubt it's possible:
You need to "join" the first table to the second table, the second table to the third table, and so on.
From TABLEA, TABLEB, TABLEC, TABLED
Where TABLEA.ID = TABLEB.AID
And TABLEB.ID = TABLEC.BID
And TABLEC.ID = TABLED.CID
In your case you probably need to do the joins in two or three SQL Select statements and save each result into a temporary table and then join the result set to each other:
From Maladie, Malade, Ilot, Etat_Ilot
Where Maladie.ID_maladie = Malade.Maladie
And Malade.Ilot = Ilot.ID_Ilot
And Ilot.Etat_Ilot = Etat_Ilot.ID_Etat_Ilot
Commit Table TIAC_EXP_A As "C:\TIAC_EXP_A.tab"
Close Table TIAC_EXP_A
Open Table "C:\TIAC_EXP_A.tab"
From TIAC_EXP_A, Pauvreté
Where TIAC_EXP_A.Classe_Pauvreté = Pauvreté.Classe
Something like the above