8 citations · 37 across the 12 of their papers we have counts for
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Infinitary logic and basically disconnected compact Hausdorff spaces
Antonio Di Nola, Serafina Lapenta, Ioana Leustean
We extend Łukasiewicz logic obtaining the infinitary logic whose models are algebras , where is a basically disconnected compact Hausdorff space. Eq…
An analysis of the logic of Riesz Spaces with strong unit
Antonio Di Nola, Serafina Lapenta, Ioana Leustean
We study Łukasiewicz logic enriched with a scalar multiplication with scalars taken in . Its algebraic models, called {\em Riesz MV-algebras}, are, up to isomorphism, unit i…
Notes on divisible MV-algebras
Serafina Lapenta, Ioana Leustean
In these notes we study the class of divisible MV-algebras inside the algebraic hierarchy of MV-algebras with product. We connect divisible MV-algebras with -vector latt…
Mutually exclusive nuances of truth in Moisil logic
Denisa Diaconescu, Ioana Leustean
Moisil logic, having as algebraic counterpart Łukasiewicz-Moisil algebras, provide an alternative way to reason about vague information based on the following principle: a many-val…
Towards understanding the Pierce-Birkhoff conjecture via MV-algebras
Serafina Lapenta, Ioana Leustean
Our main issue was to understand the connection between Łukasiewicz logic with product and the Pierce-Birkhoff conjecture, and to express it in a mathematical way. To do this we de…
A general view of the algebraic semantics of Łukasiewicz logic with product
Serafina Lapenta, Ioana Leustean
This paper aims at connecting the various classes that provide an algebraic semantics for three different conservative expansions of Lukasiewicz logic, using algebraic and category…
The Riesz hull of a semisimple MV-algebra
Denisa Diaconescu, Ioana Leustean
MV-algebras and Riesz MV-algebras are categorically equivalent to abelian lattice-ordered groups with strong unit and, respectively, with Riesz spaces (vector-lattices) with strong…
Scalar extensions for algebraic structures of Lukasiewicz logic
Serafina Lapenta, Ioana Leustean
In this paper we study the tensor product for MV-algebras, the algebraic structures of Łukasiewicz -valued logic. Our main results are: the proof that the tensor product is…
Stochastic independence for probability MV-algebras
Serafina Lapenta, Ioana Leustean
We prove that any MV-algebra has a faithful state can be embedded in an \em{f}MV-algebra of integrable functions. As consequence, we prove Hölder's inequality and Hausdorff moment…
Lukasiewicz logic and Riesz spaces
Antonio Di Nola, Ioana Leustean
We initiate a deep study of {\em Riesz MV-algebras} which are MV-algebras endowed with a scalar multiplication with scalars from . Extending Mundici's equivalence between MV…