States on semi-divisible residuated lattices
Given a residuated lattice L, we prove that the subset M V (L) of complement elements x* of L generates an M V-algebra if, and only if L is semi-divisible. Riecan states on a semi-divisible residuated lattice L, and Riecan states on MV(L) are essentially the very same thing. The same holds for Bosbach states as far as L is divisible. There are semi-divisible residuated lattices that do not have Bosbach states.
residuated lattice wajsberg algebra mv-algebra probability theory