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.
Titolo: | Convex MV-algebras : many-valued logics meet decision theory | |
Autori: | ||
Parole Chiave: | MV-algebras; convexity; uncertainty measures; Anscombe–Aumann | |
Settore Scientifico Disciplinare: | Settore M-FIL/02 - Logica e Filosofia della Scienza Settore MAT/01 - Logica Matematica | |
Data di pubblicazione: | ott-2018 | |
Rivista: | ||
Tipologia: | Article (author) | |
Data ahead of print / Data di stampa: | 23-feb-2017 | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s11225-016-9705-9 | |
Appare nelle tipologie: | 01 - Articolo su periodico |
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