Journal of Automated Reasoning

, Volume 2, Issue 3, pp 277–281 | Cite as

Unification under associativity and idempotence is of type nullary

  • Manfred Schmidt-Schauss


It is shown, that there exist a unification problem〈s=t〉 AI , for which the set of solutions under associativity and idempotence is not empty. But\(\mu U\sum _{Al} \left( {s,t} \right)\), the complete and minimal subset of this set of solutions does not exist, i.e.A+I is of type nullary. This is the first known standard first order theory with this unpleasant feature.

Key words

Unification Equational Theories Idempotent Semigroups 


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Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • Manfred Schmidt-Schauss
    • 1
  1. 1.Universität KaiserslauternKaiserslauternGermany

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