The Problem of Inductive Logic

Logic is a field studied mainly by researchers and students of philosophy, mathematics and computing. Inductive logic seeks to determine the extent to which the premisses of an argument entail its conclusion, aiming to provide a theory of how one should reason in the face of uncertainty. It has applications to decision making and artificial intelligence, as well as how scientists should reason when not in possession of the full facts. In this book, Jon Williamson embarks on a quest to find a general, reasonable, applicable inductive logic (GRAIL), all the while examining why pioneers such as Ludwig Wittgenstein and Rudolf Carnap did not entirely succeed in this task. Along the way he presents a general framework for the field, and reaches a new inductive logic, which builds upon recent developments in Bayesian epistemology (a theory about how strongly one should believe the various propositions that one can express). The book explores this logic in detail, discusses some key criticisms, and considers how it might be justified. Is this truly the GRAIL? Although the book presents new research, this material is well suited to being delivered as a series of lectures to students of philosophy, mathematics, or computing and doubles as an introduction to the field of inductive logic

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

An introductory 2001 textbook on probability and induction written by a foremost philosopher of science.

Inductive Logic is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. - Chapter on the Port Royal contributions to probability theory and decision theory - Serves as a singular contribution to the intellectual history of the 20th century - Contains the latest scholarly discoveries and interpretative insights

This book constitutes the refereed proceedings of the 8th International Conference on Inductive Logic Programming, ILP-98, held in Madison, Wisconsin, USA, in July 1998. The 27 revised full papers presented together with the abstracts of three invited talks were carefully reviewed and selected for inclusion in the book. All relevant aspects of inductive logic programming are covered ranging from theory to implementations and applications.

This book constitutes the refereed proceedings of the 10th International Conference on Inductive Logic Programming, ILP 2000, held in London, UK in July 2000 as past of CL 2000. The 15 revised full papers presented together with an invited paper were carefully reviewed and selected from 37 submissions. The papers address all current issues in inductive logic programming and inductive learning, from foundational aspects to applications in various fields like data mining, knowledge discovery, and ILP system design.

Inductive logic programming is a new research area emerging at present. Whilst inheriting various positive characteristics of the parent subjects of logic programming an machine learning, it is hoped that the new area will overcome many of the limitations of its forbears. This book describes the theory, implementations and applications of Inductive Logic Programming.

The 18th International Conference on Inductive Logic Programming was held in Prague, September 10–12, 2008. ILP returned to Prague after 11 years, and it is tempting to look at how the topics of interest have evolved during that time. The ILP community clearly continues to cherish its beloved ?rst-order logic representation framework. This is legitimate, as the work presented at ILP 2008 demonstrated that there is still room for both extending established ILP approaches (such as inverse entailment) and exploring novel logic induction frameworks (such as brave induction). Besides the topics lending ILP research its unique focus, we were glad to see in this year’s proceedings a good n- ber of papers contributing to areas such as statistical relational learning, graph mining, or the semantic web. To help open ILP to more mainstream research areas, the conference featured three excellent invited talks from the domains of the semantic web (Frank van Harmelen), bioinformatics (Mark Craven) and cognitive sciences (Josh Tenenbaum). We deliberately looked for speakers who are not directly involved in ILP research. We further invited a tutorial on stat- tical relational learning (Kristian Kersting) to meet the strong demand to have the topic presented from the ILP perspective. Lastly, Stefano Bertolo from the European Commission was invited to give a talk on the ideal niches for ILP in the current EU-supported research on intelligent content and semantics.

1 “Change is inevitable.” Embracing this quote we have tried to carefully exp- iment with the format of this conference, the 15th International Conference on Inductive Logic Programming, hopefully making it even better than it already was. But it will be up to you, the inquisitive reader of this book, to judge our success. The major changes comprised broadening the scope of the conference to include more diverse forms of non-propositional learning, to once again have tutorials on exciting new areas, and, for the ?rst time, to also have a discovery challenge as a platform for collaborative work. This year the conference was co-located with ICML 2005, the 22nd Inter- tional Conference on Machine Learning, and also in close proximity to IJCAI 2005, the 19th International Joint Conference on Arti?cial Intelligence. - location can be tricky, but we greatly bene?ted from the local support provided by Codrina Lauth, Michael May, and others. We were also able to invite all ILP and ICML participants to shared events including a poster session, an invited talk, and a tutorial about the exciting new area of “statistical relational lea- ing”. Two more invited talks were exclusively given to ILP participants and were presented as a kind of stock-taking—?ttingly so for the 15th event in a series—but also tried to provide a recipe for future endeavours.