One influential view of science focuses on the credibility that scientists attach to alternative theories and on the evolution of these credibilities under the impact of data. Interpreting credibility as probability leads to the Bayesian analysis of inquiry, which has helped us to understand diverse aspects of scientific practice. Eric Martin and Daniel N. Osherson take as their starting point a different set of intuitions about the variables to be retained in a model of inquiry. They present a theory of inductive logic that is built from the tools of logic and model theory. Their aim is to extend the mathematics of Formal Learning Theory to a more general setting and to provide a more accurate image of empirical inquiry. In particular, their theory integrates recent ideas in the theory of rational belief change. The formal results of their study illuminate aspects of scientific inquiry that are not covered by the Bayesian approach. – Exercises appear throughout the text; solutions are provided in an appendix. – Table of Contents : Preface. 1. Introduction (Modeling Inquiry; The Order Paradigm; Discussion of the Paradigm; Notes); 2. A Numerical Paradigm (Fundamentals; Solvability Characterized; Efficiency and Rationality; Memory Limitation; Computable Scientists; Functional Languages; Probabilistic Solvability; Transition to Chapter 3; Notes); 3. A First-Order Framework for Inquiry (Fundamentals; Solvability Characterized; Four Applications; Efficient Discovery; Computable Solvability; Probabilistic Solvability; Generalization to Arbitrary Structures; Notes); 4. Inquiry via Belief Revision (Belief Revision; Hypothesis Selection via Belief Revision; Augmenting the Background Theory; Efficient Inquiry via Belief Revision; Closure; Scientists Defined via Course-of-Values; Summary and Prospects; Notes).