Decidability of finiteness properties

  • Leszek Pacholski
Applications to Logic Programming, Normalization Strategies and Unification
Part of the Lecture Notes in Computer Science book series (LNCS, volume 656)


We are going to survey decidability results concerning finiteness of sets of terms or formulas that arise in investigations of equational bases of abstract algebras, axiomatisations of propositional logics, unifications theory, database theory, and logic programming.

In particular we are going to provide an unified treatment of finiteness properties that lead to several undecidability results, including for example the old result by Linial and Post solving a problem of Tarski and the recent theorem by Marcinkowski and Pacholski on the undecidability of the Horn clause implication problem.

The methods are based on a thorough analysis of the structure of derivation trees in “logics” based on one rule of inference.

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Leszek Pacholski
    • 1
    • 2
  1. 1.Institute of MathematicsPolish Academy of SciencesPoland
  2. 2.Institute of Computer ScienceUniversity of WrocławPoland

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