Rational Models of Normal Logic

In general, the application of the meaning function T P to a normal logic program P results in innnite expressions and, hence, is infeasible in practice. On the other hand, the iteration of T P is of interest for several elds in AI. Therefore, we introduce a new representation of interpretations and adopt T P to this. The resulting function always results in nite expressions of tractable length and overcomes some limitations of usual model generating systems. 1 Motivation Model generation is of interest for several elds in AI. For example, the computation of the extensions of a default logic 7] is a generation of models, and P. N. Johnson{Laird assumes that the human way of reasoning corresponds to the generation of models 3]. Wrt. logic programming, the iteration of the meaning function T P corresponding to a logic program P is the basic method of model generation 1. In general, the application of the meaning function T P corresponding to a normal logic program P results in innnite interpretations of P and is, hence, infeasible in practice. For this reason, model generating systems like SATCHMO 5] can be applied only to range restricted programs 2 : T P (I) is nite if I is a nite interpretation and P is a range restricted program. As stated in 5], every program can easily be transformed into a range restricted program. But, however, T P 0 does not reach a xed point in nite time if P 0 results from such a transformation of a not range restricted program P, even if T P reaches a xed point in nite time. Hence, model generating systems like SATCHMO can not compute complete minimal models of not range restricted programs in nite time. We therefore introduce a nite representation of interpretations, viz. so{called rational interpretations, and adopt T P to this. The resulting function S P always yields nite expressions of tractable length. By this, we solve the problem mentioned above: By the iteration of S P a nite representation of a complete minimal model of P is computed in nite time if T P reaches a xed point in nite number of steps. This paper is organized as follows. We introduce the concept of rational interpretations Section 2. In Section 3 we map T P to a function S P which yields rational interpretations representing the results of T P , and …