Where can I learn more about automated Reasoning?

The Handbook of Automated Reasoning http://www.cs.man.ac.uk/~voronkov/handbook-ar/ presents overviews of the fundamental notions, techniques, ideas, and methods developed and used in automated reasoning and its applications, which are used in many areas of computer science, including software and hardware verification, logic and functional programming, formal methods, knowledge representation, deductive databases, and artificial intelligence.
Unfortunately, it is published by Elsevier so is rather expensive to purchase
http://www.amazon.com/exec/obidos/ASIN/0262182238/002-6631692-7348053

Alan Bundy's "Computer Modelling of Mathematical Reasoning" provides a fairly comprephensive survey of the more mathematical end of automated reasoning. Although this is no longger in print, second hand
copies are fairly easy to obtain.
http://isbn.nu/0121412504

ORA Canada have a comprehensive bibliography of articles in automated deduction. The bibliography cites over 3,000 reports and papers related to automated deduction. The bibliography focuses on the years 1970 to 1995, but it also includes nearly 250 references to early classic work in the field.
http://www.ora.on.ca/biblio/biblio-prover-welcome.html

You may also wish to join the Association for Automated Reasoning.
http://www-unix.mcs.anl.gov/AAR/
It is free and there is a regular newsletter which contains news and
articles.

 

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Automated Reasoning