English

An analysis of the logic of Riesz Spaces with strong unit

Logic 2017-09-26 v3

Abstract

We study \L ukasiewicz logic enriched with a scalar multiplication with scalars taken in [0,1][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.

Keywords

Cite

@article{arxiv.1607.08030,
  title  = {An analysis of the logic of Riesz Spaces with strong unit},
  author = {Antonio Di Nola and Serafina Lapenta and Ioana Leustean},
  journal= {arXiv preprint arXiv:1607.08030},
  year   = {2017}
}