The methods presented in this chapter are based on the use of constrained formulae, and are devoted to the principle of simultaneous search for refutations and models (respectively proofs and countermodels). They are extensions of proof procedures (resolution and tableaux) obtained by adding new rules, so-called disinference rules, to the standard inference rules. The purpose of these new rules is to discard redundant instances of formulae or of clauses. The expression of these redundant instances (by constraints) prevents some further applications of inference rules and thus leads to a reduction of the search space. In some cases, the method may produce Herbrand models, represented by sets of constrained literals. By the principle of lazy unification, constraint-based inference is efficient and useful also in ordinary refutational theorem proving without features of model building.
KeywordsEquational Problem Ground Term Ground Instance Equational Formula Deletion Rule
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