Author’s note to the English-language edition

Mechanical theorem proving (MTP) is a traditional topic of mathematical logic. In contrast to the usual approaches to MTP by mathematical logic, approaches using algebraic methods seem to be originated in the paper by the present writer (Wu 1978). In 1984 appeared the present book “Basic Principles of Mechanical Theorem Proving in Geometries” devoted to a systematic exposition of such algebraic methods for MTP. The book, written in Chinese and published in China, was little known beyond China. The method became widely known owing to papers by Wu (1978, 1984a) and Chou (1984) published in the anthology edited by Bledsoe and Loveland (1984). Since that time the algebraic methods of treating MTP have been developed rapidly and vigorously in various directions. For example, in 1986 there appeared several papers on MTP based on Grobner basis method and others (e.g., Kutzler and Stifter 1986, Kapur 1986). In this note we shall give a brief review of the achievements of MTP in recent years restricted, however, to the methods as exhibited in the present book alone. Thus it may serve merely as complement and addendum to the original version of the book.