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date: 28 January 2020

Abstract and Keywords

This chapter presents axioms for comparative conditional probability relations. The axioms presented here are more general than usual. Each comparative relation is a weak partial order on pairs of sentences but need not be a complete order relation. The axioms for these comparative relations are probabilistically sound for the broad class of conditional probability functions known as Popper functions. Furthermore, these axioms are probabilistically complete. Arguably, the notion of comparative conditional probability provides a foundation for Bayesian confirmation theory. Bayesian confirmation functions are overly precise probabilistic representations of the more fundamental logic of comparative support. The most important features of evidential support are captured by comparative relationships among argument strengths, realized by the comparative support relations and their logic.

Keywords: Bayesian confirmation theory, comparative argument strength, comparative probability, conditional probability, qualitative probability, Popper function

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