Convex MV-Algebras: Many-Valued Logics Meet Decision Theory |
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Authors: | T. Flaminio H. Hosni S. Lapenta |
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Affiliation: | 1.Dipartimento di Scienze Teoriche e Applicate,Univesità degli Studi dell’Insubria,Varese,Italy;2.Dipartimento di Filosofia,Università degli Studi di Milano,Milano,Italy;3.Dipartimento di Matematica,Università degli Studi di Salerno,Fisciano,Italy |
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Abstract: | This paper introduces a logical analysis of convex combinations within the framework of ?ukasiewicz 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 ?ukasiewicz 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. |
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