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Author Wos, Lawrence ♦ Robinson, George A. ♦ Carson, Daniel F. ♦ Shalla, Leon
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1967
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract In many fields of mathematics the richness of the underlying axiom set leads to the establishment of a number of very general equalities. For example, it is easy to prove that in groups $(\textit{x}-1)-1$ = $\textit{x}$ and that in rings $-\textit{x}$ · - $\textit{y}$ = $\textit{x}$ · $\textit{y}.$ In the presence of such an equality, each new inference made during a proof search by a theorem-proving program may immediately yield a set of very closely related inferences. If, for example, $\textit{b}·\textit{a}$ = $\textit{c}$ is inferred in the presence of $(\textit{x}-1)-1$ = $\textit{x},$ substitution immediately yields obviously related inferences such as $(\textit{b}-1)-1$ · $\textit{a}$ = $\textit{c}.$ Retention of many members of each such set of inferences has seriously impeded the effectiveness of automatic theorem proving. Similar to the gain made by discarding instances of inferences already present is that made by discarding instances of repeated application of a given equality. The latter is achieved by use of demodulation. Its definition, evidence of its value, and a related rule of inference are given. In addition a number of concepts are defined the implementation of which reduces both the number and sensitivity to choice of parameters governing the theorem-proving procedures.
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 1967-10-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 14
Issue Number 4
Page Count 12
Starting Page 698
Ending Page 709


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Source: ACM Digital Library