Implementing Semantics of Disjunctive Logic Programs Using Fringes and Abstract Properties

Many years of fruitful interaction between logic programming and non monotonic reasoning have resulted in the definition of an immense number of semantics for logic programs. Only recently, however, has there been spent considerable effort on how to implement these semantics efficiently. A particularly promising approach seems to be the notion of fringes [11] for semantics based on minimal models. It has been shown in [1] that the computation of fringes may be done efficiently by applying methods from integer programming. In this paper we shall report on results which have been obtained in the context of the first author's master's thesis [9]. We shall show how to use fringes to compute PERFECT and how to adapt them for the computation of STN [13]. We implemented the system Korf for computing various semantics for disjunctive logic programs. Building on and extending some work of the second author ([2, 3, 4]) we identify several abstract principles in the course of this implementation. These principles not only seem to be reasonable [3] but also are strongly related to the computational complexity of a semantics. Observing that the full generality of an algorithm for computing a semantics is only needed for certain islands of complcxity within a program one can reduce its cost by orders. The abstract principles which we shall present prove to be a valuable tool for pinpointing these regions and, in the typical case, improving the efficiency of computing a semantics.