Logic

Abstract

higher-order intuitionistic Some torsion-free Applying automated reasoning technology to research: our experiences; logical problems of programming Fixed-point theorems in a general Early work in automated theorem proving characterized by wild enthusiasm and modest results. These experiences, in addition to insights concerning the computational complexity of general-purpose algorithms, resulted in a widespread skepticism concerning the potential of general-purpose theorem proving systems based on the first-order predicate calculus. the early expectations were not achieved, the reaction against general-purpose systems was excessive. 1977, researchers Argonne exploring the possibility of utilizing automated theorem provers to aid in attacking open questions in mathematics. We experienced many disappointments and some successes. Open questions have been successfully answered in areas such as finite semigroups, ternary Boolean algebras, and equivalential calculus. Current work includes problems from a variety of other areas in mathematics. Our automated reasoning system has been used both to prove theorems and to derive counterexamples. In this talk, I will try to convey a sense of what types of problems have been successfully addressed, how they were solved, what we have learned from the experiences, and what we anticipate in the near future.