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The present paper investigates proof-theoretical and algebraic properties forthe probability logic FP(L,L), meant for reasoning on the uncertainty ofLukasiewicz events. Methodologically speaking, we will consider a translationfunction between formulas of FP(L,L) to the propositional language ofLukasiewicz logic that allows us to apply the latter and the well-developedtheory of MV-algebras directly to probabilistic reasoning. More precisely,leveraging on such translation map, we will show proof-theoretical propertiesfor 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 theseprevious results to investigate what we called "probabilistic unificationproblem". In this respect, we will prove that Ghilardi's algebraic view onunification can be extended to our case and, on par with the Lukasiewiczpropositional case, we show that probabilistic unification is of nullary type.

Encoding de Finetti's coherence within Lukasiewicz logic and MV-algebras