[FOM] A textbook on logic with natural deduction

Sara L. Uckelman S.L.Uckelman at uva.nl
Wed Dec 2 11:30:36 EST 2009

Andrej Bauer wrote:
> I am teaching a freshman course in logic and set theory. The formalism
> is kept very low, indeed, I never really explain the difference
> between syntax and semantics, I am just trying to teach the students
> what a (real-life) proof is. However, we did learn natural-deduction
> style proofs as trees. There are several foreign students who asked me
> for an English textbook on the topic. They seem very happy with "Naive
> set theory" by Halmos, but I couldn't really find an _introductory_
> textbook that would cover logic in natural deduction style. Can
> someone recomment a good textbook or available lecture notes that are
> written in natural-deduction style (trees, not proof boxes, I know I
> should have used boxes... but it is too late for this year)? This is
> for a freshman course.

If I understand you correctly, you're looking for a tableaux-style
natural deduction system (rather than, e.g., a Fitch-style one), right?
If so, I can recommend Graham Priest's _Introduction to Non-Classical
Logic_.  While the majority of the book is on non-classical logic, the
first chapter covers classical logic, and the presentation of tableaux
in \S 1.4 is clear and concise.  (However, it covers only propositional
logic, not predicate logic).


Dr. Sara L. Uckelman
Institute for Logic, Language, & Computation
Universiteit van Amsterdam

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