Unification in many-sorted equational theories

  • Manfred Schmidt-Schauss
Unification Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 230)


Unification in many-sorted equational theories is of special interest in automated deduction. It combines the work done on unification in unsorted equational theories and unification in many-sorted signatures without equational theories. The sort structure considered in this paper may be an arbitrary finite partially ordered set, the equational theory may be arbitrary. Combining them, however, requires some natural restrictions, one of which is that equal terms have equal sorts.

Given a unification algorithm A for an unsorted equational theory the corresponding unification algorithm for the many-sorted equational theory is obtained by simply postprocessing the substitutions generated by A with a uniform algorithm to be presented in this paper.

The results obtained concern the decidability of unification as well as the existence and the cardinality of complete and minimal sets of unifiers. The most useful results are obtained for a combination of finitary matching theories with a polymorphic signature.

Key words

Unification Many-Sorted Logics Heterogeneous Algebras Equational Theories 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Manfred Schmidt-Schauss
    • 1
  1. 1.Fachbereich Informatik, Universität KaiserslauternKaiserslauternFRG

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