Splitting a CR-Prolog Program

CR-Prolog is an extension of A-Prolog, the knowledge representation language at the core of the Answer Set Programming paradigm. CR-Prolog is based on the introduction in A-Prolog of consistency-restoring rules (cr-rules for short), and allows an elegant formalization of events or exceptions that are unlikely, unusual, or undesired. The flexibility of the language has been extensively demonstrated in the literature, with examples that include planning and diagnostic reasoning. In this paper we hope to provide the technical means to further stimulate the study and use of CR-Prolog, by extending to CR-Prolog the Splitting Set Theorem, one of the most useful theoretical results available for A-Prolog. The availability of the Splitting Set Theorem for CR-Prolog is expected to simplify significantly the proofs of the properties of CR-Prolog programs.