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Mathematical Logic for Computer Science

Mathematical Logic for Computer Science by Mordechai Ben-Ari
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Semantic tableaux are used because they are theoretically sound and easy to understand 

The Third Edition has new chapters on SAT solvers and model checking 

Supplementary materials: Prolog source code for the algorithms and answers to the exercises (available to qualified instructors)

Springer London; June 2012
350 pages; ISBN 9781447141297
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Title: Mathematical Logic for Computer Science
Author: Mordechai Ben-Ari
 
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