This paper introduces a logical analysis of convex combinations within the framework of Lukasiewicz real-valued logic. This provides a natural, albeit as yet unexplored, link between the fields of many-valued logics and decision theory 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 Lukasiewicz 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-algebra, convexity, uncertainty measures, Anscombe-Aumann
Flaminio, T., H. Hosni, and S. Lapenta. 2017. “Convex MV-Algebras: Many-Valued Logics Meet Decision Theory.” Studia Logica (Online First ) DOI: 10.1007/s11225-016-9705-9.