Convex MV-Algebras: Many-Valued Logics Meet Decision Theory

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Abstract

This paper introduces a logical analysis of convex combinations within the framework of Łukasiewicz real-valued logic. This provides a natural link between the fields of many-valued logics and decision theory under uncertainty, where the notion of convexity plays a central role. We set out to explore such a link by defining convex operators on MV-algebras, which are the equivalent algebraic semantics of Łukasiewicz logic. This gives us a formal language to reason about the expected value of bounded random variables. As an illustration of the applicability of our framework we present a logical version of the Anscombe–Aumann representation result.

Keywords

MV-algebras Convexity Uncertainty measures Anscombe–Aumann 

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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Dipartimento di Scienze Teoriche e ApplicateUnivesità degli Studi dell’InsubriaVareseItaly
  2. 2.Dipartimento di FilosofiaUniversità degli Studi di MilanoMilanoItaly
  3. 3.Dipartimento di MatematicaUniversità degli Studi di SalernoFiscianoItaly

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