On the Dynamic Increase of Multiplicities in Matrix Proof Methods for Classical Higher-Order Logic

  • Serge Autexier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3702)


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.


Modal Logic Proof Search Expansion Tree Extensionality Rule Secondary Type 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Serge Autexier
    • 1
  1. 1.Saarland University & German Research Center for Artificial Intelligence (DFKI GmbH)SaarbrückenGermany

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