Methods of Cut-Elimination
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The core of the book centers around the cut-elimination method CERES (cut elimination by resolution) developed by the authors. CERES is based on the resolution calculus and radically differs from the reductive cut-elimination methods. The book shows that CERES asymptotically outperforms all reductive methods based on Gentzen's cut-reduction rules. It obtains this result by heavy use of subsumption theorems in clause logic. Moreover, several applications of CERES are given (to interpolation, complexity analysis of cut-elimination, generalization of proofs, and to the analysis of real mathematical proofs). Lastly, the book demonstrates that CERES can be extended to nonclassical logics, in particular to finitely-valued logics and to G\"odel logic.
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Matthias Baaz is professor of logical foundations of computer science at the Vienna University of Technology. He obtained his Ph.D. in mathematical logic at the University of Vienna and habilitation at the Vienna University of Technology. His main field of research is proof theory in classical and nonclassical logics.
Alexander Leitsch is professor of mathematics and theoretical computer science at the Vienna University of Technology. He obtained his Ph.D. in mathematics at the University of Vienna and habilitation at the University of Linz. His research areas are automated deduction and computational proof theory.
