A Many-Sorted Calculus Based on Resolution and Paramodulation

The f i rst-order calculus whose well formed formulas are clauses and whose sole inference rules are factor izat ion, resolution and paramodulation is extended to a many-sorted calculus. As a basis for Automated Theorem Proving, this many-sorted calculus leads to a remarkable reduction of the search space and also to simpler proofs. The soundness and completeness of the new calculus and the Sort-Theorem, which relates the many-sorted calculus to i t s one-sorted counterpart, are shown. In addition results about term rewrit ing and uni f icat ion in a many-sorted calculus are obtained. Practical examples and a proof protocol of an automated theorem prover based on the many-sorted calculus are presented.