Unification in commutative theories

Authors:
Franz Baader
Affiliations:
Institut für Mathematische Maschinen und Datenverarbeitung (Informatik) 1, Universität Erlangen-Nürnberg, Martensstraβe 3,8520 Erlangen, F.R.G.
Venue:
Journal of Symbolic Computation
Year:
1989

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Abstract

A general framework for unification in ''commutative'' theories is investigated which is based on a categorical reformulation of theory unification. We thus obtain the well-known results for abelian groups, abelian monoids and idempotent abelian monoids as well as some new results as corollaries to a general theorem. In addition, it is shown that constant-free unification problems in ''commutative'' theories are either unitary or of unification type zero and we give an example of a ''commutative'' theory of type zero.