# Introduction to Logic: Propositional Logic, Revised Edition, 3rd edition

• Howard Pospesel

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## Overview

Designed to make logic interesting and accessible—without sacrificing content or rigor—this classic introduction to contemporary propositional logic explains the symbolization of English sentences and develops formal-proof, truth-table, and truth-tree techniques for evaluating arguments. An accompanying computer tutorial program, PropLogic, is available on CD-ROM in two versions: one version can be installed and run off a hard drive; one (identical) “portable” version can be run off the CD-ROM itself (allowing students/instructors flexibility on when/where they use the program). An appendix in the text describes program details. KEY TOPICS: Tutors readers on formula construction, symbolization, formal proofs, full and brief truth tables, and truth trees. Also provides additional practice exercises. Content organized around natural-deduction formal-proof procedures, truth tables, and truth trees. Gradual presentation of logical statement connectives. Shows students how to symbolize sentences containing the connective and how to use proof rules involving that connective before introducing additional connectives. Examples of actual arguments similar to those readers encounter, and to which they can readily relate. Draws examples and exercises from newspapers, magazines, television, books, textbooks, term papers, posters, comic strips, television programs, films, records, and conversations. Increases students' awareness of the arguments they read and hear every day. Extensive exercise sets throughout provide solutions to about one-quarter of the exercises (in an appendix). Provides ample opportunities for assignments and practice.

1. Logic.

Introduction. Key Terms. Exercises.

2. If.

Compound Statements. Symbolizing Conditionals. Arrow Out. Exercises.

3. And.

Symbolizing Conjunctions. Ampersand In. Ampersand Out. Exercises.

4. If (Again).

Symbolizing Puzzling Conditionals. Arrow In. Exercises.

5. Not.

Symbolizing Negations. Dash In. Dash Out. Exercises.

6. Iff.

Symbolizing Biconditionals. Double Arrow In and Out. Exercises.

7. Or.

Symbolizing Disjunctions. Wedge In. Wedge Out. Exercises.

8. Résumé.

Summary. Proof Strategy. Definitions. Exercises.

9. Derived Rules.

Derived Rules 1. Exercises. Derived Rules 2. Exercises.

10. Truth Tables.

Full Truth Tables. Exercises. Brief Truth Tables. Exercises.

11. Truth Trees.

Constructing Trees. Testing Arguments. Exercises.

12. Statements.

Logical Truths. Contradictions. Contingent Statements. Exercises.

13. Logical Relations.

Entailment. Logical Equivalence. Exercises.

14. Natural Arguments.

Argument Identification. Formalization. Evaluation. Exercises.

Appendix 1. Metatheory: Soundness and Completeness of the System PL.

Appendix 2. Is Propositional Logic Reliable?

Appendix 3. Alternative Symbols.

Appendix 4. One-Sided Truth Trees.

Appendix 5. Using Proplogic.

Appendix 6. Solutions to Starred Exercises.

Index.

Proof Rules.

Truth-Tree Rules.