On the logic of nonmonotonic conditionals and conditional probabilities: Predicate logic [Book Review]
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Philosophical Logic 27 (1):1-34 (1998)
In a previous paper I described a range of nonmonotonic conditionals that behave like conditional probability functions at various levels of probabilistic support. These conditionals were defined as semantic relations on an object language for sentential logic. In this paper I extend the most prominent family of these conditionals to a language for predicate logic. My approach to quantifiers is closely related to Hartry Field's probabilistic semantics. Along the way I will show how Field's semantics differs from a substitutional interpretation of quantifiers in crucial ways, and show that Field's approach is closely related to the usual objectual semantics. One of Field's quantifier rules, however, must be significantly modified to be adapted to nonmonotonic conditional semantics. And this modification suggests, in turn, an alternative quantifier rule for probabilistic semantics
|Keywords||Conditionals Nonmonotonic Logic Popper Functions Probability Semantics|
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James Hawthorne (2014). A Primer on Rational Consequence Relations, Popper Functions, and Their Ranked Structures. Studia Logica 102 (4):731-749.
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