The most general notion of canonical model for a logic program with negation is the one of stable model [9]. In [7] the stable models of a logic program are characterized by the well-supported Herbrand models of the program, and a new fixed point semantics that formalizes the bottom-up truth maintenance procedure of [4] is based on that characterization. Here we focus our attention on the abstract notion of well-supportedness in order to derive sufficient conditions for the existence of stable models. We show that if a logic program \Pi is positive-order-consistent (i.e. there is no infinite decreasing chain w.r.t. the positive dependencies in the atom dependency graph of \Pi) then the Herbrand models of comp(\Pi) coincide with the stable models of \Pi. From this result and the ones of [10] [17] [2] on the consistency of Clark's completion, we obtain sufficient conditions for the existence of stable models for positive-order-consistent programs. Then we show that a negative cycle free ...

The paper is a general overview of an approach to the semantics of logic programs whose aim is finding notions of models which really capture the operational semantics, and are therefore useful for defining program equivalences and for semantics-based program analysis. The approach leads to the introduction of extended interpretations which are more expressive than Herbrand interpretations. The semantics in terms of extended interpretations can be obtained as a result of both an operational (top-down) and a fixpoint (bottom-up) construction. It can also be characterized from the model-theoretic viewpoint, by defining a set of extended models which contains standard Herbrand models. We discuss the original construction modeling computed answer substitutions, its compositional version and various semantics modeling more concrete observables. We then show how the approach can be applied to several extensions of positive logic programs. We finally consider some applications, mainly in the area of semantics-based program transformation and analysis.

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We present a new and general approach of defining semantics for disjunctive logic programs. Our framework consists of two parts: (1) a semantical , where semantics are defined in an abstract way as the weakest semantics satisfying certain properties, and (2) a procedural, namely a bottom-up queryevaluation method based on operators working on conditional facts (introduced independently by Bry and Dung/Kanchansut for nondisjunctive programs). As to (1), we concentrate in this paper on a particular set of abstract properties (the most important being the unfolding or partial evaluation property GPPE) and define a new semantics D-WFS. Our semantics coincides for normal programs with the well-founded semantics WFS. For positive disjunctive programs D-WFS coincides with the generalized closed world semantics GCWA. As a byproduct, we get new characterizations of WFS and GCWA. D-WFS is strongly related to Przymusinski's STATIC semantics: we conjecture that they coincide w.r.t. to the derivati...

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Recently, considerable interest and research e#ort has been given to the problem of finding a suitable extension of the logic programming paradigm beyond the class of normal logic programs. In order to demonstrate that a class of programs can be justifiably called an extension of logic programs one should be able to argue that: . the proposed syntax of such programs resembles the syntax of logic programs but it applies to a significantly broader class of programs; . the proposed semantics of such programs constitutes an intuitively natural extension of the semantics of normal logic programs; . there exists a reasonably simple procedural mechanism allowing, at least in principle, to compute the semantics; . the proposed class of programs and their semantics is a special case of a more general non-monotonic formalism which clearly links it to other well-established non-monotonic formalisms. In this paper we propose a specific class of extended logic programs which will be (modestly) called super logic programs or just super-programs. We will argue that the class of super-programs satisfies all of the above conditions, and, in addition, is su#ciently flexible to allow various application-dependent extensions and modifications. We also provide a brief description of a Prolog implementation of a query-answering interpreter for the class of super-programs which is available via FTP and WWW. Keywords: Non-Monotonic Reasoning, Logics of Knowledge and Beliefs, Semantics of Logic Programs and Deductive Databases. # An extended abstract of this paper appeared in the Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning (KR'96), Boston, Massachusetts, 1996, pp. 529--541. + Partially supported by the National Science Fou...

. There are three most prominent semantics defined for certain subclasses of disjunctive logic programs: GCWA (for positive programs), PERFECT (for stratified programs) and STABLE (defined for the whole class of all disjunctive programs). While there are various competitors based on 3-valued models, notably WFS and its disjunctive counterparts, there are no other semantics consisting of 2-valued models. We argue that the reason for this is the Partial Evaluation-property (also called Unfolding or Partial Deduction) wellknown from Logic Programming. In fact, we prove characterizations of these semantics and show that if a semantics SEM satisfies Partial Evaluation and Elimination of Tautologies then (1) SEM is based on 2-valued minimal models for positive programs, and (2) if SEM satisfies in addition Elimination of Contradictions, it is based on stable models. We also show that if we require Isomorphy and Relevance then STABLE is completely determined on the class of all stratified...

We inv estigate the declarative semantics of logic programs with negation. First, we propose the extended well-founded model semantics. Then we establish three important criteria of declarative semantics for logic programs. Finally we justify our extension through the comparison of different semantics. 1.

We study the xpoint completion, proposed by Dung and Kanchanasut in [DK89]. The fixpoint completion is a program transformation - it performs a kind of unfolding of recursion through positive atoms in the clauses of a program f that was shown to preserve the semantics of a program in a certain sense. We generalize the results from [DK89] in some ways and show how the handling of negation is transformed by the fixpoint completion. We thereby obtain a more clarified view of both the fixpoint completion itself and the relationship between well-founded and Fitting semantics.

Unfold/fold transformation systems for logic programs have been extensively investigated. Existing unfold/fold transformation systems for normal logic programs allow only Tamaki-Sato style folding using clauses from a previous program in the transformation sequence: i.e., they fold using a single, non-recursive clause. In this paper we present a transformation system that permits folding in the presence of recursion, disjunction, as well as negation. We show that the transformations are correct with respect to various semantics of negation including the well-founded model and stable model semantics.