A Tree Construction of the Preferable Answer Sets for Prioritized Basic Disjunctive Logic Programs

One of the most important works in the investigation of logic programming is to define the semantics of the logic programs and to find the preferable answer set of them. There are so far three methods can be used to establish the semantics of the logic programs, i.e., the means of model, fixpoint and proof theory. According to the form of the rules contained in a logic program, different logic program classes can be defined. Although well-defined semantics exist for some restricted classes of programs like Horn and stratified Programs, the declarative semantics of the more general program classes are still the subject of research. In this paper, the properties of the basic disjunctive logic programming are studied, and the notion of double prioritization is introduced, that is, the prioritization on both literals and clauses, by which the most preferable answer set of a basic disjunctive logic program is defined. In order to obtain the most preferable answer set of a basic disjunctive logic program explicitly, a recursion-theoretic construction called tree method is given.