The use of a many sorted logic for theorem proving carries many advantages over a traditional unsorted logic. By placing restrictions on the search space, a many sorted logic can significantly reduce the amount steps in the resolution process. However, as a logic becomes more efficient, it increases in complexity.

One of these efficient log ics is Cohn's Many Sorted Logic, LLAMA. It uses complex data structures such as the sort lattice and sort arrays to maintain information about the sorts. Recasting LLAMA into Bürckert's constrained logic will keep the functionality of LLAMA while using a format that reduces the complexity and maintains a more traditional resolution rule.