2016/07/27 by Di Nola, Antonio, Lapenta, Serafina, Leustean, Ioana
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1607.08030
We study Łukasiewicz logic enriched with a scalar multiplication with scalars taken in [0,1]. Its algebraic models, called \em Riesz MV-algebras, are, up to isomorphism, unit intervals of Riesz spaces with a strong unit endowed with an appropriate structure. When only rational scalars are considered, one gets the class of \em 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.