Language, Proof, and Logic
Second Edition
Distributed for Center for the Study of Language and Information
This textbook/software package covers first-order language in a method appropriate for first and second courses in logic. The unique on-line grading services instantly grades solutions to hundred of computer exercises. It is specially devised to be used by philosophy instructors in a way that is useful to undergraduates of philosophy, computer science, mathematics, and linguistics.
The book is a completely rewritten and much improved version of The Language of First-order Logic. Introductory material is presented in a more systematic and accessible fashion. Advanced chapters include proofs of soundness and completeness for propositional and predicate logic, as well as an accessible sketch of Godel's first incompleteness theorem. The book is appropriate for a wide range of courses, from first logic courses for undergraduates (philosophy, mathematics, and computer science) to a first graduate logic course.
The package includes four pieces of software:
Tarski's World 5.0, a new version of the popular program that teaches the basic first-order language and its semantics; Fitch, a natural deduction proof environment for giving and checking first-order proofs;
Boole, a program that facilitates the construction and checking of truth tables and related notions (tautology, tautological consequence, etc.);
Submit, a program that allows students to submit exercises done with the above programs to the Grade Grinder, the automatic grading service.
Grade reports are returned to the student and, if requested, to the student's instructor, eliminating the need for tedious checking of homework. All programs are available for Windows, Macintosh and Linux systems. Instructors do not need to use the programs themselves in order to be able to take advantage of their pedagogical value. More about the software can be found at lpl.stanford.edu.
The price of a new text/software package includes one Registration ID, which must be used each time work is submitted to the grading service. Once activated, the Registration ID is not transferable.
Introduction
I. Propositional Logic
1. Atomic Sentences
2. The Logic of Atomic Sentences
3. The Boolean Connectives
4. The Logic of Boolean Connectives
5. Methods of Proof for Boolean Logic
6. Formal Proofs and Boolean Logic
7. Conditionals
8. The Logic of Conditionals
II. Quantifiers
9. Introduction to Quantification
10. The Logic of Quantifiers
11. Multiple Quantifiers
12. Methods for Proof of Quantifiers
13. Formal Proofs and Quantifiers
14. More about Quantification
III. Applications and Metatheory
15. First-order Set Theory
16. Mathematical Induction
17. Advanced Topics in Propositional Logic
18. Advanced Topics in FOL
19. Completeness and Incompleteness
Summary of Formal Proof Rules
Glossary
File Index
Exercise Index
General Index
Language and Linguistics: Formal Logic and Computational Linguistics
Philosophy: Logic and Philosophy of Language
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