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In conjunction with qualitative probability. (English) Zbl 0929.03029
Summary: Numerical probabilities (associated with propositions) are eliminated in favor of qualitative notions, with an eye to isolating what it is about probabilities that is essential to judgements of acceptability. A basic choice point is whether the conjunction of two propositions, each (separately) acceptable, must be deemed acceptable. Concepts of acceptability closed under conjunction are analyzed within Keisler’s weak logic for generalized quantifiers – or more specifically, filter quantifiers. In a different direction, the notion of a filter is generalized so as to allow sets with probability non-infinitesimally below 1 to be acceptable.

MSC:
03B48 Probability and inductive logic
03C80 Logic with extra quantifiers and operators
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