Łukasiewicz logic and Riesz spaces

@article{Nola2014ukasiewiczLA,
  title={Łukasiewicz logic and Riesz spaces},
  author={Antonio di Nola and Ioana Leustean},
  journal={Soft Comput.},
  year={2014},
  volume={18},
  pages={2349-2363}
}
We initiate a deep study of Riesz MV-algebras which are MV-algebras endowed with a scalar multiplication with scalars from [0, 1]. Extending Mundici’s equivalence between MV-algebras and -groups, we prove that Riesz MValgebras are categorically equivalent to unit intervals in Riesz spaces with strong unit. Moreover, the subclass of normcomplete Riesz MV-algebras is equivalent to the class of commutative unital C∗-algebras. The propositional calculus RL that has Riesz MV-algebras as models is a… CONTINUE READING

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