Customer Reviews

Logic for Mathematics and Computer Science

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I found this book to be an excellent reference for automated reasoning. It covers resolution and unification in great detail. It also covers Knuth-Bendix procedure for equational logic. I used this book as a starting point to learning about automated reasoning and logic in AI.

I recommend this book for anyone who is just beginning to learn about automated reasoning.

The one suggestion that I have to anyone reading this book is to review your abstract algebrea and set theory. Although this books does introduce and cover abstract algebra basics, anohter reference is useful. As for set theory, try Schaum's Outline on Set Theory as an intro or a refresher.

In terms of the coverage of logic for mathematics and computer science, the target here is really the area of automated theorem proving. The book is split into two sections:

*) Quantifier-free logics
*) Logic with quantifiers

While the basic coverage of the propositional and predicate calculi is typical of what is done in other logic books, chapter three deals with equational logic and there is some coverage of abstract algebra. In particular, the representation of algebraic structures such as groups and fields. There is also extensive coverage of term rewrite systems (TRSs), which are constructed using replacement rules that resemble those of formal grammars.
If you are looking for a text in a course in basic mathematical logic, in my opinion this one is unsuitable. The extensive coverage of representations of structures including graphs takes you down a path not normally taken in a course in mathematical logic. In terms of computer science, it would have been helpful if more effort were spent in tying the logic into more mainstream areas covered in the computer science major. I also would not consider using this book as a text in a course in computation theory.

I used this book as a course book and I can say that it is quite difficult to follow the book. All the proofs are either intuitive or very short without much explanation or example. So, if you want to take this book as a guide for this field think twice!