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This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The selfcontained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving.Topics include propositional logic and its resolution, firstorder logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in firstorder logic; SLDresolution, logic programming, and the foundations of PROLOG; and manysorted firstorder logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.
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