On the logic of nonmonotonic conditionals and conditional probabilities: Predicate logic [Book Review]

Journal of Philosophical Logic 27 (1):1-34 (1998)

James Hawthorne
University of Oklahoma
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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Reprint years 2004
DOI 10.1023/A:1004264305582
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References found in this work BETA

Logic, Meaning, and Conceptual Role.Hartry Field - 1977 - Journal of Philosophy 74 (July):379-409.

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Conditional Probability and Defeasible Inference.Rohit Parikh - 2005 - Journal of Philosophical Logic 34 (1):97 - 119.

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