Corrigendum to “Towards a probability theory for product logic: States, integral representation and reasoning” [Int. J. Approx. Reason. 93 (2018) 199–218]

•The class of states of a free product algebra is convex, but not closed.•Extremal states are in correspondence with Dirac measures and product logic valuations.•The class of Kolmogorov maps on the free n-generated product algebra is closed in the product topology. The aim of this short note is to r...

Full description

Saved in:
Bibliographic Details
Published in:International journal of approximate reasoning 2018-12, Vol.103, p.267-269
Main Authors: Flaminio, Tommaso, Godo, Lluis, Ugolini, Sara
Format: Article
Language:English
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:•The class of states of a free product algebra is convex, but not closed.•Extremal states are in correspondence with Dirac measures and product logic valuations.•The class of Kolmogorov maps on the free n-generated product algebra is closed in the product topology. The aim of this short note is to report on a counter-example by Stefano Aguzzoli (private communication) showing that a claim made in a recent paper of ours [2, Proposition 5.2], stating that the class of states of a free product algebra is closed, is in fact not true. That claim was used in turn in the proof of one of the main results of the same paper [2, Theorem 5.4]. However, we also provide in this note an alternative proof for that result, so that it keeps holding true.
ISSN:0888-613X
1873-4731
DOI:10.1016/j.ijar.2018.09.010