You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format. However, this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the Department of Computer Science of the University of Maryland at College Park under terms that include this permission. All other rights are reserved by the author(s).
Dietmar Seipel. Jack Minker. Carolina Ruiz. Model Generation and State Generation for Disjunctive Logic Programs. October 1995.
This paper investigates two fixpoint approaches for minimal model reasoning with disjunctive logic programs DB. The first one, called model generation [4], is based on an operator TI defined on sets of Herbrand interpretations, whose least fixpoint is logically equivalent to the set of minimal Herbrand models of the program. The second approach, called state generation [12], uses a fixpoint operator TS based on hyperresolution. It operates on disjunctive Herbrand states and its least fixpoint is the set of logical consequences of DB, the so--called minimal model state of the program. We establish a useful relationship between hyperresolution by TS and model generation by TI. Then we investigate the problem of continuity of the two operators TS and TI. It is known that the operator TS is continuous [12], and so it reaches its least fixpoint in at most omega steps. On the other hand, the question of whether TI is continuous has been open. We show by a counterexample that TI is not continuous. Nevertheless, we prove that it converges towards its least fixpoint in at most omega steps too, as follows from the relationship that we show exists between hyperresolution and model generation. We define an iterative version of TI that computes the perfect model semantics of stratified disjunctive logic programs. On each stratum of the program, this operator converges in at most omega steps. Model generations for the stable semantics and the partial stable (and so the well--founded semantics) are respectively achieved by using this iterative operator together with the evidential transformation [3] and the 3-S transformation [16]. (Also cross-referenced as UMIACS-TR-95-99) University of Maryland Institute for Advanced Computer Studies, Dept. of Computer Science, Univ. of Maryland,
Computing Stable and Partial Stable Models of Extended Disjunctive. Carolina Ruiz. Jack Minker. April 1995.
In [Prz91], Przymusinski introduced the partial (or 3-valued) stable model semantics which extends the (2-valued) stable model semantics defined originally by Gelfond and Lifschitz [GL88]. In this paper we describe a procedure to compute the collection of all partial stable models of an extended disjunctive logic program. This procedure consists in transforming an extended disjunctive logic program into a constrained disjunctive program free of negation-by-default whose set of 2-valued minimal models corresponds to the set of partial stable models of the original program. (Also cross-referenced as UMIACS-TR-95-49) University of Maryland Institute for Advanced Computer Studies, Dept. of Computer Science, Univ. of Maryland,
Last Generated Fri Aug 11 04:01:01 EDT 2000