Three Views of Logic

This book offers a comprehensive exploration of logic's roles in various disciplines. Three Views of Logic is ideal for upper-level undergraduate courses.

In Three Views of Logic, the interplay of logic across computer science, mathematics, and philosophy is explored in depth. This concise undergraduate textbook delves into proof theory, computability theory, and nonclassical logic, providing a comprehensive overview that balances accessibility with rigor. The structure is designed for a single semester, making it an ideal resource for upper-level undergraduates looking to enhance their understanding of logic.

The proof theory section introduces classical propositional logic and first-order logic through a computer-oriented resolution formal system. By connecting linear resolution to the programming language Prolog, the book offers practical insights into the application of logic in computational contexts. The computability theory segment presents both a machine model and a mathematical model for computation, highlighting the equivalence of these approaches while addressing famous decision problems that are unsolvable by algorithms.

The discussion of nonclassical logic critiques the limitations of classical logic in handling implications, introducing Anderson and Belnap's relevance logic as a more effective alternative. Each section includes applications to reinforce the concepts presented, and for the first time, the four-valued semantics for relevance logic is laid out in textbook form. Three Views of Logic is a valuable addition to any classroom setting, providing a broad perspective on traditional and modern logic.