S. Yu. Maslov. Theory of deductive systems and its applications. English translation by Michael Gelfond and Vladimir Lifschitz of Téoriá déduktivnyh sistém i éé priménéniá. Foundations of computing. The MIT Press, Cambridge, Mass., and London, 1987, x + 151 pp.

Abstract

In a fluent, clear, and lively style this translation by two of Maslov's junior colleagues brings the work of the late Soviet scientist S. Yu. Maslov a wider audience. Maslov was considered by his peers be a man of genius who was making fundamental contributions in the fields of automatic theorem proving and computational logic. He published little, and those few papers were regarded as notoriously difficult. This book, however, was written for a broad audience of readers and describes elegant examples of applications in such fields as computer science, artificial intelligence, operations research, economic modeling, and biological modeling, among others.The book also brings light the work by the American mathematician E. L. Post, which inspired Maslov's own work in the development of a general theory and which has been long neglected by mathematicial logicians and systems theorists in the United States.The book's first chapter introduces the Rules of the Game. Part I, Mathematics of Calculi, covers E. L. Post's canonical systems, deductive systems and algorithms, and probabilistic calculi and deductive information. Part II, Horizonal Modeling, takes up a toy economy, the calculi of technological possibilities, and the development of rules. Part III, Vertical Modeling, deals with the topics of to fight and search and the consequences of the asymmetry of cognitive mechanisms.Vladimir Lifschitz is affiliated with the Department of Computer Science at Stanford University, and Michael Gelfond with the Department of Electrical Engineering and Computer Science at the University of Texas, El Paso. Theory of Deductive Systems and Its Applications is included in the Foundation of Computing Series, edited by Michael Garey.