Mechanising partiality without re-implementation

  • Manfred Kerber
  • Michael Kohlhase
Nonclassical Logics
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1303)


Even though it is not very often admitted, partial functions do play a significant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using a three-valued logic decades ago. This approach allows rejecting certain unwanted formulae as faulty, which the simpler two-valued ones accept. We have developed resolution and tableau calculi for automated theorem proving that take the restrictions of the three-valued logic into account, which however have the severe drawback that existing theorem provers cannot directly be adapted to the technique. Even recently implemented calculi for many-valued logics are not well-suited, since in those the quantification does not exclude the undefined element. In this work we show, that it is possible to enhance a two-valued theorem prover by a simple strategy so that it can be used to generate proofs for the theorems of the three-valued setting. By this we are able to use an existing theorem prover for a large fragment of the language. For a more detailed discussion of the different approaches compare [Far90].


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Manfred Kerber
    • 1
  • Michael Kohlhase
    • 2
  1. 1.School of Computer ScienceThe University of BirminghamBirminghamEngland
  2. 2.Universität des Saarlandes, FB InformatikSaarbrückenGermany

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