Probability Theory and Probability Logic

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University of Toronto Press, 1999 - Philosophy - 240 pages
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As a survey of many technical results in probability theory and probability logic, this monograph by two widely respected scholars offers a valuable compendium of the principal aspects of the formal study of probability.

Hugues Leblanc and Peter Roeper explore probability functions appropriate for propositional, quantificational, intuitionistic, and infinitary logic and investigate the connections among probability functions, semantics, and logical consequence. They offer a systematic justification of constraints for various types of probability functions, in particular, an exhaustive account of probability functions adequate for first-order quantificational logic. The relationship between absolute and relative probability functions is fully explored and the book offers a complete account of the representation of relative functions by absolute ones.

The volume is designed to review familiar results, to place these results within a broad context, and to extend the discussions in new and interesting ways. Authoritative, articulate, and accessible, it will interest mathematicians and philosophers at both professional and post-graduate levels.

 

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Contents

Probability Theory
3
The Probabilities of Infinitary Statements and of Quantifications
26
Relative Probability Functions and Their TRestrictions
45
Probability Logic
111
Absolute Probability Functions for Intuitionistic Logic
167
Relative Probability Functions for Intuitionistic Logic
182
191
191
Appendix II223
223
Bibliography
231
Index of Constraints
239
Copyright

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About the author (1999)

Peter Roeper is a Senior Lecturer in the Department of Philosophy at Australian National University. Hugues Leblanc is retired Research Professor at l'Universit du Qubec Montral and the author of numerous books and articles on subjects related to logic and probability.

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