This title explains how to use the English language with logical responsibility, how to define and use formal language, and how to reason correctly. Specific issues include propositional and predicate logic, logic networks, logic programming, proof of correctness, semantics, syntax, and theorems of Herbrand and Kalman. TOC:Preliminaries of "Naive" Mathematical Logic. Propositional Logic: The Formal Language of Propositional Logic. The Truth Structure on Lo in Semantic Version. The Truth Structure of Lo in Syntactic Version. Other Syntactic Versions of the Truth Structure on Lo. Elements of Fuzzy Propositional Logic. Applications in Computer Science. Exercises. Predicate Logic: Introductory Considerations. The Formal Language Predicate Logic. The Semantic Truth Structure on the Language L of Predicate Logic. The Syntactic Truth Structure on the Language L of Predicate Logic. Elements of Fuzzy Predicate Logic. Applications in Computer Science. Exercises. Boolean Algebras. MV-Algebras. General Considerations about Fuzzy Sets. Index.