On the dynamic increase of multiplicities in matrix proof methods for classical higher-order logic

  • Authors:

  • Serge Autexier

  • Affiliations:

  • Saarland University & German Research Center for Artificial Intelligence (DFKI GmbH), Saarbrücken, Germany

  • Venue:
  • TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
  • Year:
  • 2005

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Abstract

A major source of the undecidability of a logic is the number of instances—the so-called multiplicities—of existentially quantified formulas that are required in a proof. We consider the problem in the context of matrix proof methods for classical higher-order logic and present a technique which improves the standard practice of iterative deepening over the multiplicities. We present a mechanism that allows to adjust multiplicities on demand during matrix-based proof search and not only preserves existing substitutions and connections, but additionally adapts them to the parts that result from the increase of the multiplicities.