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.
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]
Convex MV-algebras : many-valued logics meet decision theory
H. Hosni;
2018
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.File | Dimensione | Formato | |
---|---|---|---|
10.1007_s11225-016-9705-9.pdf
accesso riservato
Tipologia:
Publisher's version/PDF
Dimensione
677.96 kB
Formato
Adobe PDF
|
677.96 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Flaminio2018_Article_ConvexMV-AlgebrasMany-ValuedLo.pdf
accesso riservato
Tipologia:
Publisher's version/PDF
Dimensione
673.33 kB
Formato
Adobe PDF
|
673.33 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.