A Survey of Program Proof Technology

Cover A Survey of Program Proof Technology
A Survey of Program Proof Technology
Jacob T Schwartz
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For a substituted instance of C to appear in a minimal contradiction, P must precisely match the substituted negative of a unit formula P' appearing in some other clause C of S . We consider all such P, ', and for each of them we substitution is then applied to C and C, after which we go on to consider the still unmatched atomic subparts of (the appropriated substituted variants of) C and C* . Matches for each of these parts are worked out in turn; this generates a growing set C, C', C", ... Of... substituted variants of clauses taken from S, together with corresponding substitutions.
Whenever we encounter a set C, C', C", ... Of substituted clauses in which every unit subformula P. Is matched to at least one other P* as its J s - precise negative, we test the collection C, C', C", ... For prepositional consistency. According to Herb rand ' s fundamental theorem, this search process will eventually uncover a propositional inconsistency, provided that the given set S of predicate clauses is in fact logically inconsistent.


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