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Nonresolution theorem proving
 Artificial Intelligence
, 1977
"... This talk reviews those efforts in automatic theorem proving, during the past few years, which have emphasized techniques other than resolution. These include: knowledge bases, natural deduction, reduction, (rewrite rules), typing, procedures, advice, controlled forward chaining, algebraic simplific ..."
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This talk reviews those efforts in automatic theorem proving, during the past few years, which have emphasized techniques other than resolution. These include: knowledge bases, natural deduction, reduction, (rewrite rules), typing, procedures, advice, controlled forward chaining, algebraic simplification, builtin associativity and commutativity, models, analogy, and manmachine systems. Examples are given and suggestions are made for future work. 1.
SET VARIABLES
"... ABSTRACT: A procedure is described that gives values to set variables in automatic theorem proving. The result is that a theorem is thereby reduced to first order logic, which is often much easier to prove. This procedure handles a part of higher order logic, a small but important part. It is not as ..."
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ABSTRACT: A procedure is described that gives values to set variables in automatic theorem proving. The result is that a theorem is thereby reduced to first order logic, which is often much easier to prove. This procedure handles a part of higher order logic, a small but important part. It is not as general as the methods of Huet, Andrews, Pietrzykowski, and Haynes and Henschen, but it seems to be much faster when it applies. It is more in the spirit of J.L. Darlington's FMatching. This procedure is not domain specific: results have been obtained In intermediate analysis (the intermediate value theorem), topology, logic, and program verification (finding internal assertions). This method is a &quot;maximal method&quot; in that a largest (or maximal) set is usually produced if there is one. A preliminary version has been programmed for the computer and run to prove several theorems.
Using Message Passing Instead of the GOTO Construct
, 1978
"... This paper advocates a programming methodology using message passing. Efficient programs are derived for fast exponentiation, merging ordered sequences, and path existence determination in a directed graph. The problems have been proposed by John Reynolds as interesting ones to investigate because t ..."
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This paper advocates a programming methodology using message passing. Efficient programs are derived for fast exponentiation, merging ordered sequences, and path existence determination in a directed graph. The problems have been proposed by John Reynolds as interesting ones to investigate because they. illustrate significant issues in programming. The methodology advocated here is directed toward the production of programs that are intended to execute efficiently in a computing environment with many processors. The absence of the COTO construct does not seem to be constricting in any respect in the development of efficient programs using the programming methodology advocated here.
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"... This paper describes a new method for determining the validity of certain formulas from Presburger Arithmetic, namely those with only universally quantified variables. To do this the notion of a Presburger formula, is generalized slightly to that of a quasilinear formula. This so called "s ..."
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This paper describes a new method for determining the validity of certain formulas from Presburger Arithmetic, namely those with only universally quantified variables. To do this the notion of a Presburger formula, is generalized slightly to that of a quasilinear formula. This so called &quot;suplnf &quot; method seems particularly suited for proving certain verification conditions that arise from program validation, especially those in which &quot;proof by cases &quot; is required. It also eliminates the need for proof by enumeration, inherent in some methods described earlier In the literature, which sometimes require a search through a large number of consecutive Integers. These algorithms have been programmed and used extensively as a part of an automatic theorem proving system.