Pure Inductive Logic

A self-contained guide to pure inductive logic, the study of rational probability treated as a branch of mathematical logic.

Jeffrey Paris (Author), Alena Vencovská (Author)

9781107042308, Cambridge University Press

Hardback, published 2 April 2015

354 pages, 1 b/w illus.
22.9 x 15.2 x 2.1 cm, 0.64 kg

'The monograph should prove an invaluable reference for researchers keen to embark on working in this area …' Eric A. Martin, MathSciNet (www.ams.org/mathscinet)

Pure inductive logic is the study of rational probability treated as a branch of mathematical logic. This monograph, the first devoted to this approach, brings together the key results from the past seventy years plus the main contributions of the authors and their collaborators over the last decade to present a comprehensive account of the discipline within a single unified context. The exposition is structured around the traditional bases of rationality, such as avoiding Dutch Books, respecting symmetry and ignoring irrelevant information. The authors uncover further rationality concepts, both in the unary and in the newly emerging polyadic languages, such as conformity, spectrum exchangeability, similarity and language invariance. For logicians with a mathematical grounding, this book provides a complete self-contained course on the subject, taking the reader from the basics up to the most recent developments. It is also a useful reference for a wider audience from philosophy and computer science.

Part I. The Basics: 1. Introduction to pure inductive logic
2. Context
3. Probability functions
4. Conditional probability
5. The Dutch book argument
6. Some basic principles
7. Specifying probability functions
Part II. Unary Inductive Logic: 8. Introduction to unary pure inductive logic
9. de Finetti's representation theorem
10. Regularity and universal certainty
11. Relevance
12. Asymptotic conditional probabilities
13. The conditionalization theorem
14. Atom exchangeability
15. Carnap's continuum of inductive methods
16. Irrelevance
17. Another continuum of inductive methods
18. The NP-continuum
19. The weak irrelevance principle
20. Equalities and inequalities
21. Principles of analogy
22. Unary symmetry
Part III. Polyadic Inductive Logic: 23. Introduction to polyadic pure inductive logic
24. Polyadic constant exchangeability
25. Polyadic regularity
26. Spectrum exchangeability
27. Conformity
28. The probability functions $u^{overline{p},L}$
29. The homogeneous/heterogeneous divide
30. Representation theorems for Sx
31. Language invariance with Sx
32. Sx without language invariance
33. A general representation theorem for Sx
34. The Carnap–Stegmüller principle
35. Instantial relevance and Sx
36. Equality
37. The polyadic Johnson's sufficientness postulate
38. Polyadic symmetry
39. Nathanial's invariance principle, NIP
40. NIP and atom exchangeability
41. The functions $u_{overline{E}}^{overline{p},L}$
42. The state of play
Bibliography
Index
Glossary.

Subject Areas: Artificial intelligence [UYQ], Mathematical logic [PBCD], Philosophy: logic [HPL]