. We present a bottom-up algorithm for the computation of the well-founded model of non-disjunctive logic programs. Our method is based on the elementary program transformations studied by Brass and Dix [6, 7]. However, their "residual program" can grow to exponential size, whereas for function-free programs our "program remainder " is always polynomial in the size, i.e. the number of tuples, of the extensional database (EDB). As in the SLG-resolution of Chen and Warren [11, 12, 13], we do not only delay negative but also positive literals if they depend on delayed negative literals. When disregarding goal-directedness, which needs additional concepts, our approach can be seen as a simplified bottom-up version of SLG-resolution applicable to range-restricted Datalog programs. Since our approach is also closely related to the alternating fixpoint procedure [27, 28], it can possibly serve as a basis for an integration of the resolution-based, fixpoint-based, and transformation-based ev...

Abstract not found

. Tabling has become important to logic programming in part because it opens new application areas, such as model checking, to logic programming techniques. However, the development of new extensions of tabled logic programming is becoming restricted by the formalisms that underly it. Formalisms for tabled evaluations, such as SLG [3], are generally developed with a view to a specific set of allowable operations that can be performed in an evaluation. In the case of SLG, tabling operations are based on a variance relation between atoms. While the set of SLG tabling operations has proven useful for a number of applications, other types of operations, such as those based on a subsumption relation between atoms, can have practical uses. In this paper, SLG is reformulated in two ways: so that it can be parameterized using different sets of operations; and so that a forest of trees paradigm is used. Equivalence to SLG of the new formulation, Extended SLG or SLGX , is shown whe...

In this paper we will investigate the novel concept of clausal deductive databases (cd{databases), which are special normal deductive databases { i.e. deductive databases which may contain default negation in rule bodies { over a meta{language L with a xed set of predicate symbols, namely dis, con, and some built{in predicate symbols. The arguments of the literals in L are given by disjunctive and conjunctive clauses of a basic rst{order language L (which are considered as terms in L ). On the other hand, disjunctive deductive databases (dd{databases) extend normal deductive databases by allowing for disjunctions (rather than just single atoms or literals) in rule heads { next to default negation in rule bodies.

. The three most well-known semantics for negation in the logic programming framework are Clark's completion [Cla78], the stable semantics [GL88], and the well-founded semantics [vGRS91]. Clark's completion (COMP) was the first proposal to give a formal meaning to negation as failure. However, it is now accepted that COMP does not always captures the meaning of a logic program. Despite its computational and structural advantages, the well-founded semantics (WFS) is considered much too weak for real applications. The stable semantics (STABLE), on the other hand, is so strong that many programs become inconsistent. We present in this paper examples to support these claims, and we introduce a new semantics, called CWFS, which is as powerful as COMP in inferring positive literals and as powerful as WFS in inferring negative literals. Due to its particular construction, CWFS helps to understand the relationship among COMP, WFS, and STABLE. We also discuss some implementation issues of CWFS...

This paper investigates the novel concept of clausal deductive databases (cd{ databases), which are special normal deductive databases { i.e. deductive databases which may contain default negation in rule bodies { over a meta{language L with a xed set of predicate symbols, namely dis, con, and some built{in predicate symbols

Abstract. In this paper we present a novel methodology to compute stable models in Answer Set Programming. The process is performed with a bottom-up approach that does not require the preprocessing of the typical grounding phase. The implementation is completely in Prolog and Constraint Logic Programming over finite domains. 1