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Analytic and Non-analytic Proofs

  • Frank Pfenning
Part of the Lecture Notes in Computer Science book series (LNCS, volume 170)

Abstract

In automated theorem Poving different kinds of proof systems have been used. Traditional proof systems, such as Hilbert-style proofs or natural deduction we call non-analytic, while resolution or mating proof systems we call analytic. There are many good reasons to study the connections between analytic and non-analytic proofs. We would like a theorem prover to make efficient use of both analytic and non-analytic methods to get the best of both worlds.

In this paper we present an algorithm for translating from a particular non-anMytic proof system to analytic proofs. Moreover, some results about the translation in the other direction are refornmlated and known algorithms improved, hnplementation of the algorithms presented for use in research and teaching logic is under way at Carnegie-Mellon University in the framework of TPS and its educational counterpart ETPS.

Finally we show how to obtain non-analytic proofs from resolution refutations. As an application, resolution refutations can be translated into comprehensible natural deduction proofs.

Keywords

Inference Rule Proof System Natural Deduction Expansion Term Analytic Proof 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Frank Pfenning
    • 1
  1. 1.Departnmnt of MathematicsCarnegie-Mellon UniversityPittsburgh

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