  The present paper investigates proof-theoretical and algebraic properties for
the probability logic FP(L,L), meant for reasoning on the uncertainty of
Lukasiewicz events. Methodologically speaking, we will consider a translation
function between formulas of FP(L,L) to the propositional language of
Lukasiewicz logic that allows us to apply the latter and the well-developed
theory of MV-algebras directly to probabilistic reasoning. More precisely,
leveraging on such translation map, we will show proof-theoretical properties
for FP(L,L) and introduce a class of algebras with respect to which FP(L,L)
will be proved to be locally sound and complete. Finally, we will apply these
previous results to investigate what we called "probabilistic unification
problem". In this respect, we will prove that Ghilardi's algebraic view on
unification can be extended to our case and, on par with the Lukasiewicz
propositional case, we show that probabilistic unification is of nullary type.
