Hawthorne, James and Makinson, David C,
(2007)
The quantitative/qualitative watershed for rules of uncertain inference.
Studia Logica, 86 (2).
pp. 247-297.
ISSN 0039-3215
Abstract
We chart the ways in which closure properties of consequence relations for uncertain inference take on different forms according to whether the relations are generated in a quantitative or a qualitative manner. Among the main themes are: the identification of watershed conditions between probabilistically and qualitatively sound rules; failsafe and classicality transforms of qualitatively sound rules; non-Horn conditions satisfied by probabilistic consequence; representation and completeness problems; and threshold-sensitive conditions such as `preface' and `lottery' rules.
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