Unification of concept terms is a new kind of inference problem for description logics, which extends the equivalence problem by allowing one to replace certain concept names by concept terms before testing for equivalence. We show that this inference problem is of interest for applications, and present first decidability and complexity results for a small concept description language.

Since about 1971, much research has been done on Thue systems that have properties that ensure viable and efficient computation. The strongest of these is the Church-Rosser property, which states that two equivalent strings can each be brought to a unique canonical form by a sequence of length-reducing rules. In this paper three ways in which formal languages can be defined by Thue systems with this property are studied, and some general results about the three families of languages so determined are studied.

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