Amalgamating NAF and NAI

We deene a new logic language with negation by introducing existential and universal quantiiers in the queries. We call ??general programs and ??general goals the programs and the goals in this language. Negation is handled by using two rules: the NAF rule for universally quantiied negative queries and the NAI rule for existentially quantiied negative queries. We formalize this amalgamation in terms of NAIF-resolution (SLD-resolution with Negation As In-stantiation and Failure), and we prove its correctness w.r.t. the completion semantics. We also show how extended programs and goals, i.e. programs and goals whose body is an arbitrary rst-order formula ((11]), can be transformed into ??general programs and goals and then evaluated using our system.