A critical question in unification theory is how to obtaina unification algorithm for the combination of non-disjointequational theories when there exists unification algorithmsfor the constituent theories. The problem is known to bedifficult and can easily be seen to be undecidable in thegeneral case. Therefore, previous work has focused onidentifying specific conditions and methods in which theproblem is decidable.We continue the investigation in this paper, building onprevious combination results and our own work.We are able to develop a novel approach to the non-disjointcombination problem. The approach is based on a new set ofrestrictions and combination method such that if the restrictionsare satisfied the method produces an algorithm for the unificationproblem in the union of non-disjoint equational theories.
Hierarchical Combination of Unication Algorithms (Extended Abstract)
