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Introduction to logic. (Einführung in die Logik.) (German) Zbl 1149.03001
Urban-Taschenbücher 402. Grundkurs Philosophie 18. Stuttgart: Kohlhammer (ISBN 978-3-17-015460-5/pbk). 272 p. (2008).
This is a well-written elementary introduction to logic, particularly suitable for students in the humanities, but also accessible for interested high school students. Always there are lots of examples and exercises.
The book starts with a broad propaedeutics focussing on aspects of the extraction of the logical content of common language sentences. The main part presents propositional as well as first-order logic, including identity logic and definite descriptions, but also an interesting discussion of syllogisms. At the end there is a concise explanation of logics of modalities: alethic, deontic, and also epistemic ones.
For each logic a tableau method is explained and a Hilbert-type calculus sketched. For classical logic, additionally, a natural deduction system is given. All the necessary details are provided, but general results are only mentioned and not proved.
03-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations
03B05 Classical propositional logic
03B10 Classical first-order logic
03B45 Modal logic (including the logic of norms)