An Algebraic Characterization of Inductive Soundness in Proof by Consistency

Kapur and Musser studied the theoretical basis for proof by consistency and ob-tained an inductive completeness result: p q if and only if p = q is true in everyinductive model. However, there is a loophole in their proof for the soundness part:p = q implies p = q is true in every inductive model. The aim of this paper is to give acorrect characterization of inductive soundness from an algebraic view by introducingstrong inductive models.