First-Order Logic

First-Order Logic presents a comprehensive introduction to mathematical logic through Smullyan's signature method of analytic tableaux. The book progresses from propositional logic to predicate calculus while maintaining mathematical rigor throughout. The text includes extensive practice problems and exercises that build in complexity. Smullyan develops the logical systems step by step, with each chapter adding new concepts and rules while reinforcing previous material. Core topics covered include truth tables, validity, formal proofs, quantification, and the completeness theorem. The book uses clear notation and precise definitions to establish fundamental concepts before advancing to more complex applications. This groundbreaking work stands as both a textbook and a reference guide, demonstrating the power and elegance of formal logical systems. The material presents logic as a tool for precise reasoning while highlighting connections to mathematics, computer science, and philosophy.

Readers describe this logic textbook as rigorous but clear in its step-by-step presentation. Students and professors cite its detailed coverage of formal proofs and systematic approach to first-order logic. Likes: - Clear explanations of complex concepts - Gradual buildup from basics to advanced topics - Precise definitions and notation - Useful exercises with varying difficulty levels Dislikes: - Dense mathematical notation can overwhelm beginners - Some sections require multiple re-readings - Limited real-world examples - Few solutions provided for exercises Ratings: Goodreads: 4.2/5 (32 ratings) Amazon: 4.5/5 (12 ratings) One professor on Mathematics Stack Exchange noted: "Smullyan's approach through tableaux gives students a concrete method to work with." A graduate student reviewer wrote: "The tree method made more sense to me than resolution-based proofs." Several readers mentioned the book works better as a supplement to a course rather than for self-study.

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⚡ Raymond Smullyan was not only a logician but also a concert pianist, magician, and prolific puzzle creator who wrote over 30 books combining logic with entertainment 🎯 First-Order Logic (1968) introduced a groundbreaking proof method called the "analytic tableau," which simplified complex logical proofs through an elegant tree-based system 📚 The book bridges the gap between informal mathematical reasoning and formal logical systems, making it influential in both mathematics and computer science education 🧩 Smullyan's unique teaching approach in the book uses "Knights and Knaves" puzzles (where knights always tell truth and knaves always lie) to illustrate logical principles 🔄 The methods presented in First-Order Logic later influenced automated theorem proving and artificial intelligence, particularly in developing logical reasoning systems for computers