Data di Pubblicazione:
2018
Citazione:
Convex MV-algebras : many-valued logics meet decision theory / T. Flaminio, H. Hosni, S. Lapenta. - In: STUDIA LOGICA. - ISSN 0039-3215. - 106:5(2018 Oct), pp. 913-945. [10.1007/s11225-016-9705-9]
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
MV-algebras; convexity; uncertainty measures; Anscombe–Aumann
Elenco autori:
T. Flaminio, H. Hosni, S. Lapenta
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