Computationally Improved Versions of Herbrand's Theorem

Abstract

Herbrand's Fundamental theorem is “the central theorem of predicate logic” that has a variety of applications of great importance. One of these applications is its use as a constructive tool for providing effective proof procedures, which in the beginning of the mid-50s has extensively been pursued in the field of Automated Theorem Proving (ATP). Herbrand's Fundamental theorem provides a straight forward mechanical proof procedure that is blown up with such redundancy that it is of no use in practice. The chapter presents a refined version of this theorem that from the computational point of view is substantially more efficient. The resulting proof method is superior to any other proof method. Some of the redundancies have been eliminated with the resolution proof method, developed by J. A. Robinson in the early 60s on the basis of various related results.