A Bottom-up Semantics for Constructive Negation

The constructive negation rule has been introduced by Chan 5, 6] to overcome the main drawbacks of the negation-as-failure rule: the unsoundness of oundering programs and, consequently , the inability of providing answers for non-ground negative queries. In this paper we deene a bottom-up semantics for constructive negation which we prove sound and complete with respect to the three-valued completion of the program. The semantics describes answers as well as undeened computations for both positive and negative queries. Its construction closely follows the basic idea of constructive negation whereby answers to a negative query are obtained by negating a frontier of the computation tree for the corresponding positive query. Therefore, the proposed semantics can be considered as a natural base for reasoning on the operational semantics for constructive negation deened in the literature. Moreover, we show how the semantics can be eeectively used to perform a bottom-up computation of the answers of a normal query.