Книга “Mathematical Logic” является всеобъемлющим и доступным для пользователя руководством по использованию логики в математических рассуждениях. Она представляет собой всеобъемлющее введение в формальные методы логики и их использование в качестве надежного инструмента для дедуктивного мышления. Благодаря своему удобному подходу, эта книга успешно обучает читателей ключевым понятиям и методам формулирования обоснованных математических аргументов, которые можно использовать для обнаружения истин в различных областях знаний, таких как математика, информатика и философия. Книга развивает логические инструменты для написания доказательств, направляя читателей как в общепринятый стиль написания доказательств “Хайльберса”, так и в новый стиль, который развивается в компьютерных науках и инженерных приложениях. Главы были организованы в две тематические области: булева логика и предикатная логика. Техники, не связанные с формальной логикой, используются для иллюстрации и демонстрации важных фактов о силе и ограничениях логики, таких как: Логика может подтверждать истины и только истины. Логика может подтвердить все абсолютные истины (теоремы полноты)
This comprehensive manual for mathematicians, computer scientists, students of logic and philosophy should provide teachers and learners alike with a wealth of understanding and confidence in using formal logics. The J.P. Burgess and C.A. Hooker research team have provided in Mathematical Logic a user friendly introduction to logic as a tool for truth seeking across diverse areas. This book evolved around two well covered chapters on Boolean and Predicate logics plus two more on logic system including Hilbert style and equational style. Mathematical Logic also includes useful information and techniques achieved as illustrations of power and limitations out side formal logic. Some major lessons learnt include the fact that formal logic can validate all absolute mathematical truths but it does not necessarily validate conditional mathematical truths as evidenced by the incompleteness theory of Godel declared earlier this century. In essence, no formal logic proves technically every lemma or theorem or statement which can or cannot exist theoretically. Here, the authors describe some useful examples gathered from difficult theoretic dilemmas and problems. They also link the subject with actual computation through Tarski’s model and explain their treatment of these worlds in great detail. Generally, a comprehensive and practical guide for users of a logical bent, learners of advanced mathematics and subjects who would obviously find this to be a useful resource and learning experience to grasp their true potential.
Электронная Книга «Mathematical Logic» написана автором Группа авторов в году.
Минимальный возраст читателя: 0
Язык: Английский
ISBN: 9781118030691
Описание книги от Группа авторов
A comprehensive and user-friendly guide to the use of logic in mathematical reasoning Mathematical Logic presents a comprehensive introduction to formal methods of logic and their use as a reliable tool for deductive reasoning. With its user-friendly approach, this book successfully equips readers with the key concepts and methods for formulating valid mathematical arguments that can be used to uncover truths across diverse areas of study such as mathematics, computer science, and philosophy. The book develops the logical tools for writing proofs by guiding readers through both the established «Hilbert» style of proof writing, as well as the «equational» style that is emerging in computer science and engineering applications. Chapters have been organized into the two topical areas of Boolean logic and predicate logic. Techniques situated outside formal logic are applied to illustrate and demonstrate significant facts regarding the power and limitations of logic, such as: Logic can certify truths and only truths. Logic can certify all absolute truths (completeness theorems of Post and Gödel). Logic cannot certify all «conditional» truths, such as those that are specific to the Peano arithmetic. Therefore, logic has some serious limitations, as shown through Gödel's incompleteness theorem. Numerous examples and problem sets are provided throughout the text, further facilitating readers' understanding of the capabilities of logic to discover mathematical truths. In addition, an extensive appendix introduces Tarski semantics and proceeds with detailed proofs of completeness and first incompleteness theorems, while also providing a self-contained introduction to the theory of computability. With its thorough scope of coverage and accessible style, Mathematical Logic is an ideal book for courses in mathematics, computer science, and philosophy at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who wish to learn how to use logic in their everyday work.
