MV-modules

Nola, Antonio Di; Flondor, Paul; Leustean, Ioana

doi:10.1016/s0021-8693(03)00332-6

Cited by 36 publications

(33 citation statements)

References 6 publications

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“…By Theorem 3.17, Riesz MV-algebras are exactly the MV-modules [10] over [0,1]. Hence some basic properties follow from the general theory of MVmodules developed in [10,21].…”

Section: Riesz Mv-algebrasmentioning

confidence: 93%

“…Hence some basic properties follow from the general theory of MVmodules developed in [10,21]. One of the most important results is the categorical equivalence between Riesz MV-algebras and unital Riesz spaces.…”

Section: Riesz Mv-algebrasmentioning

confidence: 99%

“…Other results are proved in a more general setting in [10,12,21]. For the sake of completeness we sketched the proofs that we consider important for the present development.…”

Section: Introductionmentioning

confidence: 99%

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Łukasiewicz logic and Riesz spaces

Nola

Leustean

2014

Soft Comput

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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 ℓ-groups, we prove that Riesz MV-algebras are categorically equivalent with unit intervals in Riesz spaces with strong unit. Moreover, the subclass of norm-complete Riesz MV-algebras is equivalent with the class of commutative unital C * -algebras. The propositional calculus RL that has Riesz MV-algebras as models is a conservative extension of Lukasiewicz ∞-valued propositional calculus and it is complete with respect to evaluations in the standard model [0, 1]. We prove a normal form theorem for this logic, extending McNaughton theorem for Lukasiewicz logic. We define the notions of quasi-linear combination and quasi-linear span for formulas in RL and we relate them with the analogue of de Finetti's coherence criterion for RL.

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“…By Theorem 3.17, Riesz MV-algebras are exactly the MV-modules [10] over [0,1]. Hence some basic properties follow from the general theory of MVmodules developed in [10,21].…”

Section: Riesz Mv-algebrasmentioning

confidence: 93%

Section: Riesz Mv-algebrasmentioning

confidence: 99%

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Łukasiewicz logic and Riesz spaces

Nola

Leustean

2014

Soft Comput

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“…Note that RMV-algebras are particular MVmodules, structures defined in [6]. Consequently, some results presented in this paper are obtained from general results proved in [6,14].…”

Section: Introductionmentioning

confidence: 92%

“…Consequently, some results presented in this paper are obtained from general results proved in [6,14].…”

Section: Introductionmentioning

confidence: 99%