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Abstract

We present a sound and complete calculus for an expressive sorted first-order logic. Sorts are extended to the semantic and pragmatic use of unary predicates. A sort may denote an empty set and the sort structure can be created by making use of the full first-order language. Technically spoken, we allow sort declarations to be used in the same way than ordinary atoms. Therefore we can compile every first-order logic formula into our logic.\\ The extended expressivity implies an extended sorted inference machine. We present a new unification algorithm and show that the declarations the unification algorithm is built on have to be changed dynamically during the deduction process. Deductions in the resulting resolution calculus are very efficient compared to deductions in the unsorted resolution calculus. The approach is a conservative extension of the known sorted approaches, as it simplifies to the known sorted calculi if we apply the calculus to the much more restricted input formulas of these calculi.