On the convergence with fixed regulator in residuated structures. (English)
Sossai, Claudio (ed.) et al., Symbolic and quantitative approaches to reasoning with uncertainty. 10th European conference, ECSQARU 2009, Verona, Italy, July 1‒3, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-02905-9/pbk). Lecture Notes in Computer Science 5590. Lecture Notes in Artificial Intelligence, 899-910 (2009).
Summary: The convergence with a fixed regulator has been studied for lattice-ordered groups and MV-algebras. In this paper we present some particular results for the case of perfect MV-algebras using Di Nola-Lettieri functors and we extend the notion of convergence with a fixed regulator for residuated lattices. The main results consist of proving that any locally Archimedean MV-algebra has a unique $v$-Cauchy completion and that in an Archimedean residuated lattice the $v$-limit is unique.
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