De Finetti's coherence and exchangeability in infinitary logic

Abstract

We continue the investigation towards a logic-based approach to statistics within the infinitary conservative extension of Łukasiewicz logic 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 σ-complete Riesz MV-algebras in the conditional and unconditional case, and discuss de Finetti's exchangeability in a special case.