Undecidable properties of syntactic theories

  • Francis Klay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 488)


Since we are looking for unification algorithms for a large enough class of equational theories, we are interested in syntactic theories because they have a nice decomposition property which provides a very simple unification procedure. A presentation is said resolvent if any equational theorem can be proved using at most one equality step at the top position. A theory which has a finite and resolvent presentation is called syntactic. In this paper we give decidability results about open problems in syntactic theories: unifiability in syntactic theories is not decidable, resolventness of a presentation and syntacticness of a theory are even not semidecidable. Therefore we claim that the condition of syntacticness is too weak to get unification algorithms directly.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Francis Klay
    • 1
  1. 1.INRIA LorraineVillers les Nancy

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