Probability Theory and Probability Semantics / / Hughes Leblanc, Peter Roeper.

• Superior document: Title is part of eBook package: De Gruyter University of Toronto Press eBook-Package Archive 1933-1999
• VerfasserIn: Leblanc, Hughes,; Roeper, Peter,
• Place / Publishing House: Toronto : : University of Toronto Press, , [2016]; ©1999
• Year of Publication: 2016
• Language: English
• Series: Toronto Studies in Philosophy
• Physical Description: 1 online resource (252 p.)

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.

Table of Contents

Frontmatter -- Contents -- Acknowledgments -- Part One: Probability Theory -- Introduction -- Chapter 1. Probability Functions for Prepositional Logic -- Chapter 2. The Probabilities of Infinitary Statements and of Quantifications -- Chapter 3. Relative Probability Functions and Their T-Restrictions -- Chapter 4. Representing Relative Probability Functions by Means of Classes of Measure Functions -- Chapter 5. The Recursive Definability of Probability Functions -- Chapter 6. Families of Probability Functions Characterised by Equivalence Relations -- Part Two: Probability Logic -- Introduction -- Chapter 7. Absolute Probability Functions Construed as Representing Degrees of Logical Truth -- Chapter 8. Relative Probability Functions Construed as Representing Degrees of Logical Consequence -- Chapter 9. Absolute Probability Functions for Intuitionistic Logic -- Chapter 10. Relative Probability Functions for Intuitionistic Logic -- Appendix I -- Appendix II -- Notes -- Bibliography -- Index -- Index of Constraints