Compact Propositionalizations of First-Order Theories

We present new insights and algorithms for converting reasoning problems in monadic First-Order Logic (includes only 1place predicates) into equivalent problems in propositional logic. Our algorithms improve over earlier approaches in two ways. First, they are applicable even without the unique-names and domain-closure assumptions, and for possibly infinite domains. Therefore, they apply for many problems that are outside the scope of previous techniques. Secondly, our algorithms produce propositional representations that are significantly more compact than earlier approaches, provided that some structure is available in the problem. We examined our approach on an example application and discovered that the number of propositional symbols that we produced is smaller by a factor of than traditional techniques, when those techniques can be applied. This translates to a factor of about increase in the speed of reasoning for such structured problems.