Semantic Model for Induction of First Order Theories

This paper presents an extension of the inverse resolution framework, which is a logical model of theory induction in first order logic. We first propose a definition of completeness for inductive procedures and exhibit some limitations of inverse resolution with respect to this definition. We then propose our model of inversion of logical entailment that extends inverse resolution with regard to these limitations. Two operators are formalized that implement this formal framework and we prove that they arc complete. In the last part of the paper, we propose two possible controls for these operators, to restrict the search for an acceptable theory. These two controls express some semantic properties of the theory that the system is searching for.