### A New Class of Automated Theorem-Proving AlgorithmsA New Class of Automated Theorem-Proving Algorithms

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 Author Overbeek, Ross A. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1974 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract A procedure is defined for deriving from any statement $\textit{S}$ an infinite sequence of statements $\textit{S}0,$ $\textit{S}1,$ $\textit{S}2,$ $\textit{S}3,$ ··· such that: (a) if there exists an $\textit{i}$ such that $\textit{Si}$ is unsatisfiable, then $\textit{S}$ is unsatisfiable; (b) if $\textit{S}$ is unsatisfiable, then there exists an $\textit{i}$ such that $\textit{Si}$ is unsatisfiable; (c) for all $\textit{i}$ the Herbrand universe of $\textit{Si}$ is finite; hence, for each $\textit{i}$ the satisfiability of $\textit{Si}$ is decidable. The new algorithms are then based on the idea of generating successive $\textit{Si}$ in the sequence and testing each $\textit{Si}$ for satisfiability. Each element in the class of new algorithms is complete. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1974-04-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 21 Issue Number 2 Page Count 10 Starting Page 191 Ending Page 200

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Source: ACM Digital Library