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Exploring infinitesimal events through MV-algebras and non-Archimedean states. (English) Zbl 1437.06020

Laurent, Anne (ed.) et al., Information processing and management of uncertainty in knowledge-based systems. 15th international conference, IPMU 2014, Montpellier, France, July 15–19, 2014. Proceedings. Part II. Cham: Springer. Commun. Comput. Inf. Sci. 443, 385-394 (2014).
Summary: In this paper we use tools from the theory of MV-algebras and MV-algebraic states to study infinitesimal perturbations of classical (i.e. Boolean) events and their non-Archimedean probability. In particular we deal with a class of MV-algebras which can be roughly defined by attaching a cloud of infinitesimals to every element of a finite Boolean algebra and for them we introduce the class of Chang-states. These are non-Archimedean mappings which we prove to be representable in terms of a usual (i.e. Archimedean) probability measure and a positive group homomorphism capable to handle the infinitesimal side of the MV-algebras we are dealing with. We also study in which relation Chang-states are with MV-homomorphisms taking value in a suitable perfect MV-algebra.
For the entire collection see [Zbl 1385.68006].

MSC:

06D35 MV-algebras
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