## Theory of deductive systems and its applicationsIn 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 to a wider audience. Maslov was considered by his peers to 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 to 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 to 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 Applicationsis included in the Foundation of Computing Series, edited by Michael Garey. |

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### Contents

Rules of the Game | 1 |

Posts Canonical Systems | 19 |

Deductive Systems and Algorithms | 44 |

Copyright | |

6 other sections not shown

### Common terms and phrases

admissible rules ah+1 allows apparatus application arbitrary auxiliary axiom c-local C-rules called canonical calculus cells chapter cognitive mechanism complete concept consider construct a calculus contain creative process cut elimination cut-elimination theorems deductive systems defined derivable objects derivation search described discussed economic systems encoding evolution example finite number formal function given hemisphere hypothesis idea important indeterminacy inference rules infinite initial instance integration by substitution inverse method iterative method language left-hemisphere lemma length letters mathematical logic method of metavariables Michael Garey Minsky machine modeling monotonicity natural numbers normal calculus occurrences possible Post's Post's theorem precisely probabilistic calculus probability problem proof propositional calculus prove r.e. set recursive enumerability right-hemisphere rules of inference satisfies selection sequence sequent set of words theorem theory of deductive tion TP-rules TP-system transformation undecidable units of resource variables word derivable