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Complexity of translations from resolution to sequent calculus

Published online by Cambridge University Press:  16 January 2019

GISELLE REIS Open the ORCID record for GISELLE REIS [Opens in a new window]  and
BRUNO WOLTZENLOGEL PALEO
GISELLE REIS
Affiliation:
Carnegie Mellon University, Doha, Qatar Email: giselle@cmu.edu, bruno.wp@gmail.com
BRUNO WOLTZENLOGEL PALEO
Affiliation:
Carnegie Mellon University, Doha, Qatar Email: giselle@cmu.edu, bruno.wp@gmail.com
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Abstract

Resolution and sequent calculus are two well-known formal proof systems. Their differences make them suitable for distinct tasks. Resolution and its variants are very efficient for automated reasoning and are in fact the theoretical basis of many theorem provers. However, being intentionally machine oriented, the resolution calculus is not as natural for human beings and the input problem needs to be pre-processed to clause normal form. Sequent calculus, on the other hand, is a modular formalism that is useful for analysing meta-properties of various logics and is, therefore, popular among proof theorists. The input problem does not need to be pre-processed, and proofs are more detailed. However, proofs also tend to be larger and more verbose. When the worlds of proof theory and automated theorem proving meet, translations between resolution and sequent calculus are often necessary. In this paper, we compare three translation methods and analyse their complexity.

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Paper
Information
Mathematical Structures in Computer Science , Volume 29 , Special Issue 8: A special issue on structural proof theory, automated reasoning and computation in celebration of Dale Miller’s 60th birthday , September 2019 , pp. 1061 - 1091
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© Cambridge University Press 2019 

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