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.

It depends on what you mean 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.