De Finetti’s coherence and exchangeability in infinitary logic. (English) Zbl 07537324
Summary: We continue the investigation towards a logic-based approach to statistics within the infinitary conservative extension of Łukasiewicz logic \(\mathcal{IRL}\) and prove versions of de Finetti’s theorems on coherence and exchangeability. In particular we will prove a coherence criterion for a subclass of the variety of \(\sigma\)-complete Riesz MV-algebras in the conditional and unconditional case, and discuss de Finetti’s exchangeability in a special case.
MSC:
| 68T37 | Reasoning under uncertainty in the context of artificial intelligence |
Keywords:
de Finetti; coherence criterion; exchangeability; random variables; Baire functions; infinitary logicReferences:
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