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This book provides a good hands-on introduction to mathematical logic for computer science - the basics in quantified and non-quantified logic, modal logics etc. The CS-specific part would be the applications to databases (formulation of logical Datalog queries), and the set of ready-made translations of the proof systems into pseudocode.
This is a self-contained book for an introductory course in logic for computer science. Thus far it does what it says on the tin.
However, if you are expecting a more thorough treatment of the subject, or a look from a mathematical viewpoint, you would be advised to check out eg The Handbook of Logic in Computer Science (Gabbay et al, series ed), or "Topoi - The categorial analysis of logic" (Goldblatt). Ben-Ari's book is a good, practical introduction, but it doesn't dwell on the algebraic structures, or explain eg Kripke semantics particularly well.
