An analysis of the logic of Riesz spaces with strong unit

We study Łukasiewicz logic enriched by a scalar multiplication with scalars in [0,1]. Its algebraic models, called Riesz MV-algebras, are, up to isomorphism, unit intervals of Riesz spaces with strong unit endowed with an appropriate structure. When only rational scalars are considered, one gets the class of DMV-algebras and a corresponding logical system. Our research follows two objectives. The first one is to deepen the connections between functional analysis and the logic of Riesz MV-algebras. The second one is to study the finitely presented MV-algebras, DMV-algebras and Riesz MV-algebras, connecting them from logical, algebraic and geometric perspective.