Method of automated proving for unrestricted first-order logic

Details Method of automated proving for unrestricted first-order logic Method of automated proving for unrestricted first-order logic

G - Physics

06

F

G06F 9/44 (2006.01) G06F 15/18 (2006.01) G06N 5/00 (2006.01)

Patent

CA 2133699

The method of automated proving for unrestricted first-logic to test the satisfiability of clause sets describing an industrial system applies the instance generation rule (IG)~~ ~.sigma. where ~ is a term, .sigma. a substitution and ~.sigma. an instance of ~ yielded by the substitution .sigma., and is characterized in that, defining an instance subtraction as the subtraction of the instance ~.sigma. from ~ resulting in a generalized term which is a triplet <~, .sigma., ~> where ~ is a finite set of standard substitutions {.lambda.1, ..., .lambda.n} and defined by GE(<~, .sigma., ~>) = GE (~.sigma.)~ - GE ({~.lambda.1, ..., ~.lambda.n}) the method further applies an instance subtraction combined with said instance generation rule to get an instance extraction rule defined by (IE) .SIGMA. ~ (.SIGMA. - {~<.sigma.,~>})~{~<.sigma.µ, ~*.sigma.µ>, ~<.sigma., ~~{.sigma.µ}>) where .SIGMA. is a set of clauses and µ is a substitution valid for the generalized term ~<.sigma., ~>, whereby the set .SIGMA. can be proved unsatisfiable.

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