Chiswell Ian (EN) — Mathematical Logic

Тут можно читать онлайн книгу Chiswell Ian (EN) - Mathematical Logic - бесплатно полную версию (целиком). Жанр книги: Иностранная литература. Вы можете прочесть полную версию (весь текст) онлайн без регистрации и смс на сайте Lib-King.Ru (Либ-Кинг) или прочитать краткое содержание, аннотацию (предисловие), описание и ознакомиться с отзывами (комментариями) о произведении.

Автор: Chiswell Ian (EN)
Язык книги: Английский
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Mathematical Logic краткое содержание

Mathematical Logic - описание и краткое содержание, автор Chiswell Ian (EN), читать бесплатно онлайн на сайте электронной библиотеки Lib-King.Ru.

Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can andcan't be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter,assuming Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguisticsand computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students inLogic, Mathematics, Philosophy, and Computer Science.

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Mathematical Logic - читать книгу онлайн бесплатно, автор Chiswell Ian (EN)

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