Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010191236 | QA9 H343 1998 | Open Access Book | Book | Searching... |
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Summary
Summary
Here is an introduction to modern logic that differs from others by treating logic from an algebraic perspective. What this means is that notions and results from logic become much easier to understand when seen from a familiar standpoint of algebra. The presentation, written in the engaging and provocative style that is the hallmark of Paul Halmos, from whose course the book is taken, is aimed at a broad audience, students, teachers and amateurs in mathematics, philosophy, computer science, linguistics and engineering; they all have to get to grips with logic at some stage. All that is needed to understand the book is some basic acquaintance with algebra.
Reviews 1
Choice Review
Logicians typically devise formal systems to model or reform the processes by which we reason; mathematical logicians typically start with the formal systems logicians devise in order to ferret out their structural properties, particularly their limitations. The theory of Boolean algebra provides a semantic interpretation for unquantified propositional calculus and monadic algebras; these algebras with certain extra structure interpret quantifiers as well. Halmos and Givant offer an exposition of classical logic suitable for beginners, arriving as quickly as possible at Boolean algebras. These standard mathematical tools--homomorphisms, ideals, universal mapping properties--lead quickly to major theorems of logic. In the first chapters the authors carry on a background conversation with experts, defending their approach, but the cross talk represents a potential distraction for those readers who really come with no prior knowledge of formal logic. Beginners also might not know how to take the authors' expressions of impatience for the care required to set everything up right in conventional treatments. The book would benefit from at least a passing mention of nonclassical logics, Heyting algebras, and toposes as important directions for further reading. Recommended. Undergraduates through faculty. D. V. Feldman; University of New Hampshire
Table of Contents
| 1 What is logic? |
| 2 Propositional calculus |
| 3 Boolean algebra |
| 4 Boolean universal algebra |
| 5 Logic via algebra |
| 6 Lattices and infinite operations |
| 7 Monadic predicate calculus |
