
Logic with a Probability Semantics (Hardback)
Theodore Hailperin (author)
£62.00
Hardback
126 Pages /
Published: 16/12/2010
- We can order this from the publisher
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 includes quantifiers ("for all," and "there is") whose variables range over atomic sentences, not entities 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 any probability 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.
Publisher: Lehigh University Press
ISBN: 9781611460100
Number of pages: 126
Weight: 358 g
Dimensions: 241 x 162 x 15 mm
MEDIA REVIEWS
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. * Mathematical Reviews *
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. * Mathematics Teacher *
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. * Mathematics Teacher *
You may also be interested in...
Please sign in to write a review
Sign In / Register
Not registered? CREATE AN ACCOUNTCREATE A plus ACCOUNT
Sign In
Download the Waterstones App
Would you like to proceed to the App store to download the Waterstones App?
Click & Collect
Reserve online, pay on collection
Alternatively, for multiple items you may find it easier to add to basket, then pay online and collect in as little as 2 hours, subject to availability.
Alternatively, for multiple items you may find it easier to add to basket, then pay online and collect in as little as 2 hours, subject to availability.
Thank you for your reservation
Your order is now being processed and we have sent a confirmation email to you at
When will my order be ready to collect?
Following the initial email, you will be contacted by the shop to confirm that your item is available for collection.
Call us on or send us an email at
Unfortunately there has been a problem with your order
Please try again or alternatively you can contact your chosen shop on or send us an email at