Abstract
Kapur and Musser studied the theoretical basis for proof by consistency and obtained an inductive completeness result:p≡q if and only ifp=q is true in every inductive model. However, there is a loophole in their proof for the soundness part:p≡q impliesp=q is true in every inductive model. The aim of this paper is to give a correct characterization of inductive soundness from an algebraic view by introducing strong inductive models.
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