Universal (meta-)logical reasoning: Recent successes

Abstract

Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is suitable as a foundation for the development of a universal logical reasoning engine. Such an engine may be employed, as already envisioned by Leibniz, to support the rigorous formalisation and deep logical analysis of rational arguments on the computer. A respective universal logical reasoning framework is described in this article and a range of successful first applications in philosophy, artificial intelligence and mathematics are surveyed.