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

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