Logic with a Probability Semantics [Hardcover]

There are some original features in the treatment given to the subject by the author, which make it an interesting reading also for people well acquainted with other work on probabilistic logics.Anyone interested in the history and philosophy of logic will find this work intriguing. Amateur logicians will find it challenging but will appreciate the progression toward expressing quantified probability logic in a richer formal structure, thus broadening the book's range of possible applications.The book extends the development of probability logica logic using probability, not verity (true, false) as the basic semantic notion. The basic connectives not, and, and or are described in depth to include quantified formulas. Also discussed is the notion of the suppositional and resolution of the paradox of confirmation.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 based on 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 lÄ