portada Methods of Cut-Elimination (en Inglés)

Formato

Libro Físico

Autor

Alexander Leitsch

Matthias Baaz

Editorial

Springer

Idioma

Inglés

N° páginas

290

Encuadernación

Tapa Blanda

Dimensiones

23.4x15.6x1.6 cm

Peso

0.42 kg.

ISBN13

9789400734975

Categorías

Lógica matemática
Programación informática/desarrollo de software
Ciencias de la computación

Methods of Cut-Elimination (en Inglés)

Alexander Leitsch (Autor) · Matthias Baaz (Autor) · Springer · Tapa Blanda

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Reseña del libro "Methods of Cut-Elimination (en Inglés)"

This is the first book on cut-elimination in first-order predicate logic from an algorithmic point of view. Instead of just proving the existence of cut-free proofs, it focuses on the algorithmic methods transforming proofs with arbitrary cuts to proofs with only atomic cuts (atomic cut normal forms, so-called ACNFs). The first part investigates traditional reductive methods from the point of view of proof rewriting. Within this general framework, generalizations of Gentzen's and Sch\"utte-Tait's cut-elimination methods are defined and shown terminating with ACNFs of the original proof. Moreover, a complexity theoretic comparison of Gentzen's and Tait's methods is given.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.