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## Dolciani Mathematical Expositions No. 21: Logic as Algebra (Softcover)"This book is an introduction to modern logic, but it is quite different from other introductory books on the subject." — From the back cover ## $19.79 |

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Please contact us if you've got questions about this product.## Condition

**GOOD:** Except for a bend in the front cover and some of the first pages, this book is in excellent condition. There is no writing on the pages and the binding is tight.

## Description

From the back cover: The book’s “purpose, according to the preface, is ‘…to show that logic an (and perhaps should) be viewed from an algebraic perspective. When so viewed, many of its principal notions are seen to be old friends, familiar algebraic notions that were “disguised” in logical clothing. Moreover, the connection between the principal theorems of the subject and well-known theorems in algebra becomes clearer. Even the proofs often gain in simplicity.’

“The presentation is aimed at a broad audience—mathematics amateurs, students, teachers, philosophers, linguists, computer scientists, engineers, and professional mathematicians. Whether the reader’s goal is a quick glimpse of modern logic or a more serious study of the subject, the book’s fresh approach will bring novel and illuminating insights to beginners and professionals alike. All that is required of the reader is an acquaintance with some of the basic notions encountered in a first course in modern algebra. In particular, no prior knowledge of logic is assumed. The book could serve equally well as a fireside companion and as a course text.

“Propositional logic and nomadic predicate calculus—predicate logic with a single quantifier—are the principal topics treated. The connections between logic and algebra are carefully explained. The key notions and the fundamental theorems are elucidated from both a logical and an algebraic perspective. The final section gives a unique and illuminating algebraic treatment of the theory of syllogisms—perhaps the oldest branch of logic, and a subject that is neglected in most modern logic texts.”

**BRIEF CONTENTS**

**What is logic?**

- To count or to think
- A small alphabet
- A small grammar
- A small logic
- What is truth?
- Motivation of the small language
- All mathematics

**Propositional calculus**

- Propositional symbols
- Propositional abbreviations
- Polish notation
- Language as an algebra
- Concatenation
- Theorem schemata
- Formal proofs
- Entailment
- Logical equivalence
- Conjunction
- Algebraic Identities

**Boolean Algebra**

- Equivalence classes
- Interpretations
- Consistency and Boolean algebra
- Duality and commutativity
- Properties of Boolean algebras
- Subtraction
- Examples of Boolean algebras

**Boolean universal algebra**

- Subalgebras
- Homomorphisms
- Examples of homomorphisms
- Free algebras
- Kernels and ideals
- Maximal ideals
- Homomorphism theorem
- Consequences
- Representation theorem

**Logic via algebra**

- Pre-Boolean algebras
- Substitution rule
- Boolean logics
- Algebra of the propositional calculus
- Algebra of proof and consequence

**Lattices and infinite operations**

- Lattices
- Non-distributive lattices
- Infinite operations

**Monadic predicate calculus**

- Propositional functions
- Finite functions
- Functional monadic algebras
- Functional quantifiers
- Monadic algebras
- Free monadic algebras
- Modal logics
- Monadic logics
- Syllogisms

The book ends with an Index.

## Details

- SKU:
- 1924
- Author:
- Halmos, Paul and Steven Givant
- Publisher:
- The Mathematical Association of America
- Publish Date:
- 1998 (First Printing)
- Format:
- Softcover
- Weight (pounds):
- 0.46
- Dimensions (W”xL”xH”):
- 6″x9″x0.3″
- ISBN-13:
- 9780883853276
- ISBN-10:
- 0883853272
- Series:
- Dolciani Mathematical Expositions

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