Computing Protected Circumscription

ABSTRACT: This paper deals with computing circumscription in the case of Horn data with additional protection (indefinite data), an intermediate investigation between Reiter’s result on predicate completion and Lifschitz’s efforts to make general (formula) circumscription more efficient as a computational tool. Reiter has shown a close tie between McCarthy’s circumscription and Clark’s predicate completion. Here we investigate a similar tie between an extended version of circumscription involving protected data, and an extended version of predicate completion. When we have a fully ground atomic protected theory, we show that an extension to the relational algebra can be used to obtain all (and only) correct answers. When general Horn axioms are added to the protected theory, we show that Horn axioms also can be used to compute sound answers; however, some correct answers will not be found.