It depends on what you man by "related to computer science". Undergraduate computer science "logic" books tend to focus more on computability, like
Hopcroft and Ullman, Introduction to Automata Theory, Languages, and Computation
Papadimitriou, Computational Complexity
Undergraduate mathematical "logic" books tend to focus on propositional logic and first-order logic but not things like computational complexity. One well-regarded book of that sort is
- Enderton, A Mathematical Introduction to Logic
That book does prove the unique readability (parsing) algorithm for propositional and first-order formulas.