The present study is an extension of the topic introduced in Dr. Hailperin's Sentential Probability Logic, where the usual true-false semantics for logic is replaced with one based more on probability, and where values ranging from 0 to 1 are subject to probability axioms. Moreover, as the word "sentential" in the title of that work indicates, the language there under consideration was limited to sentences constructed from atomic (not inner logical components) sentences, by use of sentential connectives ("no," "and," "or," etc.) but not including quantifiers ("for all," "there is"). An initial introduction presents an overview of the book. In chapter one, Halperin presents a summary of results from his earlier book, some of which extends into this work. It also contains a novel treatment of the problem of combining evidence: how does one combine two items of interest for a conclusion-each of which separately impart a probability for the conclusion-so as to have a probability for the conclusion basedon taking both of the two items of interest as evidence? Chapter two enlarges the Probability Logic from the first chapter in two respects: the language now includes quantifiers ("for all," and "there is") whose variables range over atomic sentences, notentities as with standard quantifier logic. (Hence its designation: ontological neutral logic.) A set of axioms for this logic is presented. A new sentential notion-the suppositional-in essence due to Thomas Bayes, is adjoined to this logic that later becomes the basis for creating a conditional probability logic. Chapter three opens with a set of four postulates for probability on ontologically neutral quantifier language. Many properties are derived and a fundamental theorem is proved, namely, for anyprobability model (assignment of probability values to all atomic sentences of the language) there will be a unique extension of the probability values to all closed sentences of the language. The chapter concludes by showing the Borel's early denumerableprobability concept (1909) can be justified by its being, in essence, close to Hailperin's probability result applied to denumerable language. The final chapter introduces the notion of conditional-probability to a language having quantifiers of the kind

Authoritative account of the development of Boole's ideas in logic and probability theory ranges from The Mathematical Analysis of Logic to the end of his career. The Laws of Thought formed the most systematic statement of Boole's theories; this volume contains incomplete studies intended for a follow-up volume. 1952 edition.

Probability theory

The Fourth International Congress for Logic, Methodology, and Philos ophy of Science was held in Bucharest, Romania, on August 29-September 4, 1971. The Congress was organized, under the auspices of the Inter national Union for History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science, by the Academy of the Socialist Republic of Romania, the Academy of Social and Political Sciences of the Socialist Republic of Romania, and the Ministry of Education of Romania. With more than eight hundred participating scholars from thirty-four countries, the Congress was one of the major scientific events of the year 1971. The dedicated efforts of the organizers, the rich and carefully planned program, and the warm and friendly atmosphere contributed to making the Congress a successful and fruitful forum of exchange of scientific ideas. The work of the Congress consisted of invited one hour and half-hour addresses, symposia, and contributed papers. The proceedings were organized into twelve sections of Mathematical Logic, Foundations of Mathematical Theories, Automata and Programming Languages, Philos ophy of Logic and Mathematics, General Problems of Methodology and Philosophy of Science, Foundations of Probability and Induction, Methodology and Philosophy of Physical Sciences, Methodology and Philosophy of Biological Sciences, Methodology and Philosophy of Psychological Sciences, Methodology and Philosophy of Historical and Social Sciences, Methodology and Philosophy of Linguistics, and History of Logic, Methodology and Philosophy of Science.

Since its birth, the field of Probabilistic Logic Programming has seen a steady increase of activity, with many proposals for languages and algorithms for inference and learning. This book aims at providing an overview of the field with a special emphasis on languages under the Distribution Semantics, one of the most influential approaches. The book presents the main ideas for semantics, inference, and learning and highlights connections between the methods. Many examples of the book include a link to a page of the web application http://cplint.eu where the code can be run online. This 2nd edition aims at reporting the most exciting novelties in the field since the publication of the 1st edition. The semantics for hybrid programs with function symbols was placed on a sound footing. Probabilistic Answer Set Programming gained a lot of interest together with the studies on the complexity of inference. Algorithms for solving the MPE and MAP tasks are now available. Inference for hybrid programs has changed dramatically with the introduction of Weighted Model Integration. With respect to learning, the first approaches for neuro-symbolic integration have appeared together with algorithms for learning the structure for hybrid programs. Moreover, given the cost of learning PLPs, various works proposed language restrictions to speed up learning and improve its scaling.

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

This book is meant to be a primer, that is an introduction, to probability logic, a subject that appears to be in its infancy. Probability logic is a subject envisioned by Hans Reichenbach and largely created by Adams. It treats conditionals as bearers of conditional probabilities and discusses an appropriate sense of validity for arguments such conditionals, as well as ordinary statements as premises. This is a clear well written text on the subject of probability logic, suitable for advanced undergraduates or graduates, but also of interest to professional philosophers. There are well thought out exercises, and a number of advanced topics treated in appendices, while some are brought up in exercises and some are alluded to only in footnotes. By this means it is hoped that the reader will at least be made aware of most of the important ramifications of the subject and its tie-ins with current research, and will have some indications concerning recent and relevant literature.