Logic In Three Books

Forever Undecided is the most challenging yet of Raymond Smullyan’s puzzle collections. It is, at the same time, an introduction—ingenious, instructive, entertaining—to Gödel’s famous theorems. With all the wit and charm that have delighted readers of his previous books, Smullyan transports us once again to that magical island where knights always tell the truth and knaves always lie. Here we meet a new and amazing array of characters, visitors to the island, seeking to determine the natives’ identities. Among them: the census-taker McGregor; a philosophical-logician in search of his flighty bird-wife, Oona; and a regiment of Reasoners (timid ones, normal ones, conceited, modest, and peculiar ones) armed with the rules of propositional logic (if X is true, then so is Y). By following the Reasoners through brain-tingling exercises and adventures—including journeys into the “other possible worlds” of Kripke semantics—even the most illogical of us come to understand Gödel’s two great theorems on incompleteness and undecidability, some of their philosophical and mathematical implications, and why we, like Gödel himself, must remain Forever Undecided!

This safari will send students on an expedition that will result in hours of good thinking and unbridled enthusiasm. As enthusiasm soars, so do the levels of thinking skills engaged. Students love these deductive logic puzzles so much that they beg to do them, little realizing that they are building important reading comprehension and thinking skills. Teachers love these puzzles because of their ease of use in multicurricular parallels and their effortlessness in fitting into pullout programs of limited duration. Each motivating puzzle includes an introduction with student-related topics, clues, a grid, and an illustration. The goal in Logic Safari is to hunt down the clues, sort, analyze, and combine them into the correct solution. Each book represents an ever-increasing challenge to students while scenarios remain fresh, evoking renewed eagerness. The size of the grids is an indication of difficulty. This is the first book in a three-part series of deductive logic puzzles. For more advanced puzzles, see Logic Safari Book 2 and Logic Safari Book 3. Grades 2-3

Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses

"The best introduction to logic you will find."—Martin Gardner "Professor Bennett entertains as she instructs," writes Publishers Weekly about the penetrating yet practical Logic Made Easy. This brilliantly clear and gratifyingly concise treatment of the ancient Greek discipline identifies the illogical in everything from street signs to tax forms. Complete with puzzles you can try yourself, Logic Made Easy invites readers to identify and ultimately remedy logical slips in everyday life. Designed with dozens of visual examples, the book guides you through those hair-raising times when logic is at odds with our language and common sense. Logic Made Easy is indeed one of those rare books that will actually make you a more logical human being.

This leading text for symbolic or formal logic courses presents all techniques and concepts with clear, comprehensive explanations, and includes a wealth of carefully constructed examples. Its flexible organization (with all chapters complete and self-contained) allows instructors the freedom to cover the topics they want in the order they choose.

"Beautifully written."—Publishers Weekly, starred review The martial Sainnites have occupied Shaftal for fifteen years. Every year the cost of resistance rises. Emil, an officer and scholar; Zanja, a diplomat and last survivor of her people; and Karis, a metalsmith, half-blood giant, and an addict, can only watch as their country falls into lawlessness and famine. Together, perhaps they can change the course of history. Laurie J. Marks' first two Elemental Logic novels (Fire Logic and Earth Logic) both won the Gaylactic Spectrum Award and received multiple starred reviews. She lives in Boston, Massachusetts, and teaches at the University of Massachusetts.