Method of automated proving for unrestricted first-order logic

摘要

A method of automated proving for unrestricted first-logic to test the satisfiability of clause sets describing an industrial system which applies the instance generation rule $\mathop{\mathrm{image}}$ \left(\mathrm{IG}\right)\⁢\text{\ }\⁢\frac{\mathrm{\Ψ}}{\mathrm{\Ψ}\⁢\text{\ }\⁢\mathrm{\σ}}$$;where &PSgr; is a term, &sgr; a substitution and &PSgr;&sgr; an instance of &PSgr; yielded by the substitution &sgr;, and is characterized in that, instance subtraction is defined as the substraction of the instance &PSgr;&sgr; from &PSgr; resulting in a generalized term which is a triplet &PSgr;, &sgr;, &Lgr; where &Lgr; is a finite set of standard substitutions {&lgr;₁, . . . , &lgr;_n} and defined by; $PTEXTHILITALICPDATGE/PDAT/ITALIC/HILPDAT(\&PSgr;,\; \&sgr;,\; \&Lgr;)\=/PDATHILITALICPDATGE/PDAT/ITALIC/HILPDAT(\&PSgr;\&sgr;)\−/PDATHILITALICPDATGE/PDAT/ITALIC/HILPDAT(\{\&PSgr;\&lgr;/PDATHILSBPDAT1/PDAT/SB/HILPDAT,\; .\; .\; .\; ,\; \&PSgr;\&lgr;/PDATHILSBPDATn/PDAT/SB/HILPDAT\})/PDAT/PTEXT$ ;the method further applies an instance subtraction combined with said instance generation rule to get an instance extraction rule defined by; $PTEXTPDAT(/PDATHILITALICPDATIE/PDAT/ITALIC/HILPDAT)\&Sgr;\→(\&Sgr;\−\{\&PSgr;\&sgr;,\&Lgr;\})\∪\{\&PSgr;\&sgr;\&mgr;,\&Lgr;*\&sgr;\&mgr;,\; \&PSgr;\&sgr;,\&Lgr;\∪\{\&sgr;\&mgr;\})/PDAT/PTEXT$ ;where &Sgr; is a set of clauses and &mgr; is a substitution valid for the generalized term &PSgr;&sgr;, &Lgr;, whereby the set &Sgr; can be proven unsatisfiable.