Logic for applications

This book aims to provide a first course in mathematical logic that aligns with the recent surge in logic applications within computer science. While it covers traditional topics such as syntax, semantics, soundness, completeness, and compactness, it also emphasizes less conventional subjects. Resolution theorem proving is a central focus, particularly regarding its relevance to Logic Programming and PROLOG, with a thorough exploration of the mathematical foundations of these areas. Additionally, two chapters are dedicated to nonclassical logics—modal and intuitionistic—which are gaining traction in computer science. The book develops the essential syntax and semantics for these logics using Kripke frames. The approach to formal proofs, soundness, and completeness employs a modified tableau method initially introduced for classical logic, adaptable to various modal logics. Advanced topics, including nonmonotonic logic, are also briefly introduced in both the nonclassical logic chapters and the sections on Logic Programming and PROLOG. Overall, the text is designed to be more relevant and practical for students interested in the intersection of logic and computer science.