OI-implication: Soundness and Refutation Completeness

Weakening implication by assuming the object identity bias allows for both a model-theoretical and a proof-theoretical definition of a novel and more manageable ordering relationship over clausal spaces. In this paper, we give two important results, namely the soundness and the refutation completeness (through a subsumption theorem) of the underlying derivation procedure, that make this relationship particularly appealing for inducing a generalization model for clausal search spaces.