Need help?  •  Forgot your password?
This web site will be decommissioned in June 2019. Visit our new site here.

Language, Proof and Logic

What's New in the Second Edition?


The main differences in the text book can be found in the chapters on Set Theory (15), and Mathematical Induction (16). Both of these chapters have been completely rewritten to improve the exposition. Many exercises have been added to these chapters, and these primarily involve the use of the software. Specifically, we encourage the use of the Lemma inference rule to complete more complex formal proofs in set theory, and the new Induction inference rules allow us to write more complex exercises involving formal induction proofs.

Chapter 10 also benefits from a discussion of the use of lemmas in completing proofs.

Changes to the Exercises

We have introduced many new exercises into the second edition, and others have been renumbered from their position in the first edition. Instructors should be aware of this when setting exercises from the textbook. The ideal situation is that you and all of your students are using the same edition of the book, and no confusion can arise. However it is unlikely that you will live in this Panglossian world. Instructors should be prepared to deal with situations where students have a mixture of first and second edition textbooks. Exercise changes are limited to four chapters:

The Grade Grinder recognizes which edition of the book a student is using by their registration id (see below).


The software accompanying the second edition of the text book has been completely rewritten since the first edition. We have previously released versions of the software which update the first edition software, but each of the applications released with the second edition of LPL differ from any previously released version.


The interfaces of the applications have been unified to use a new application toolbar which appears across the top of the application window. The tool bar contains controls for changing the font size and style, to print the current document and obtain help. In addition this toolbar contains controls for the critical application functions (E.g., checking steps in Fitch, checking truth values in Tarski's World, etc;) We hope this this will result in applications that are more intuitive for our users.

Each of the applications now allows users to specify preferences such as the size and style of text that they wish to use, whether to use step numbers and bold proof lines in Fitch, how to create blocks in Tarski's World, and so on.

New File Formats

Boole and Fitch both have new file formats. Both are implemented to be backward-compatible with the old format. This means that new versions of Boole and Fitch can read files created with earlier versions of the software. If such a file is read by the application and then saved, the new version will prompt for a new file name to allow the user to keep the old version of the file for use with the old file with earlier versions. Neither application is forward compatible, i.e. old versions application cannnot be used to read files produced by the new versions.