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27
Consistency of Clark's Completion and Existence of Stable Models
, 1994
"... 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 wellsupported Herbrand models of the program, and a new fixed point semantics that formalizes the bottomup truth mainten ..."
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Cited by 142 (2 self)
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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 wellsupported Herbrand models of the program, and a new fixed point semantics that formalizes the bottomup truth maintenance procedure of [4] is based on that characterization. Here we focus our attention on the abstract notion of wellsupportedness in order to derive sufficient conditions for the existence of stable models. We show that if a logic program \Pi is positiveorderconsistent (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 positiveorderconsistent programs. Then we show that a negative cycle free ...
SSemantics Approach: Theory and Applications
, 1994
"... 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 semanticsbased program analysis. The approach leads to the intr ..."
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Cited by 115 (26 self)
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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 semanticsbased 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 (topdown) and a fixpoint (bottomup) construction. It can also be characterized from the modeltheoretic 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 semanticsbased program transformation and analysis.
Disjunctive Semantics based upon Partial and BottomUp Evaluation
 Proceedings of the 12th Int. Conf. on Logic Programming
, 1995
"... 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 bottomup queryeva ..."
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Cited by 45 (12 self)
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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 bottomup 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 DWFS. Our semantics coincides for normal programs with the wellfounded semantics WFS. For positive disjunctive programs DWFS coincides with the generalized closed world semantics GCWA. As a byproduct, we get new characterizations of WFS and GCWA. DWFS is strongly related to Przymusinski's STATIC semantics: we conjecture that they coincide w.r.t. to the derivati...
TransformationBased BottomUp Computation of the WellFounded Model
, 1997
"... . We present a bottomup algorithm for the computation of the wellfounded model of nondisjunctive 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 functionfre ..."
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Cited by 38 (4 self)
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. We present a bottomup algorithm for the computation of the wellfounded model of nondisjunctive 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 functionfree programs our "program remainder " is always polynomial in the size, i.e. the number of tuples, of the extensional database (EDB). As in the SLGresolution 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 goaldirectedness, which needs additional concepts, our approach can be seen as a simplified bottomup version of SLGresolution applicable to rangerestricted 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 resolutionbased, fixpointbased, and transformationbased ev...
On The Correctness Of Unfold/fold Transformation Of Normal And Extended Logic Programs
 JOURNAL OF LOGIC PROGRAMMING
, 1995
"... ..."
Super Logic Programs
, 1996
"... 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 ..."
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Cited by 21 (2 self)
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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 nonmonotonic formalism which clearly links it to other wellestablished nonmonotonic formalisms. In this paper we propose a specific class of extended logic programs which will be (modestly) called super logic programs or just superprograms. We will argue that the class of superprograms satisfies all of the above conditions, and, in addition, is su#ciently flexible to allow various applicationdependent extensions and modifications. We also provide a brief description of a Prolog implementation of a queryanswering interpreter for the class of superprograms which is available via FTP and WWW. Keywords: NonMonotonic 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. 529541. + Partially supported by the National Science Fou...
Characterizations of the Stable Semantics by Partial Evaluation
 Logic Programming and NonMonotonic Reasoning, Proceedings of the Third International Conference, LNCS 928
, 1995
"... . 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 3valued models, ..."
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Cited by 18 (7 self)
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. 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 3valued models, notably WFS and its disjunctive counterparts, there are no other semantics consisting of 2valued models. We argue that the reason for this is the Partial Evaluationproperty (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 2valued 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...
Beyond TamakiSato Style Unfold/Fold Transformations for Normal Logic Programs
 IN ASIAN, LNCS 1742
, 1999
"... Unfold/fold transformation systems for logic programs have been extensively investigated. Existing unfold/fold transformation systems for normal logic programs allow only TamakiSato style folding using clauses from a previous program in the transformation sequence: i.e., they fold using a singl ..."
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Cited by 11 (3 self)
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Unfold/fold transformation systems for logic programs have been extensively investigated. Existing unfold/fold transformation systems for normal logic programs allow only TamakiSato style folding using clauses from a previous program in the transformation sequence: i.e., they fold using a single, nonrecursive 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 wellfounded model and stable model semantics.
ArgumentationBased Abduction in Disjunctive Logic Programming
 Journal of Logic programming
, 2000
"... In this paper we propose an argumentationbased semantic framework, called DAS, for disjunctive logic programming. The basic idea is to translate a disjunctive logic program into an argumentationtheoretic framework. One unique feature of our proposed framework is to consider the disjunctions of ..."
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Cited by 11 (4 self)
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In this paper we propose an argumentationbased semantic framework, called DAS, for disjunctive logic programming. The basic idea is to translate a disjunctive logic program into an argumentationtheoretic framework. One unique feature of our proposed framework is to consider the disjunctions of negative literals as possible assumptions so as to represent incomplete information. In our framework, three semantics PDH, CDH and WFDH are defined by three kinds of acceptable hypotheses to represent credulous, moderate and skeptical reasoning in AI, respectively. Further more, our semantic framework can be extended to a wider class than that of disjunctive programs (called bidisjunctive logic programs). In addition to being a first serious attempt of establishing an argumentationtheoretic framework for disjunctive logic programming, DAS integrates and naturally extends many key semantics, such as the minimal models, EGCWA, the wellfounded model, and the disjunctive stable models. In particular, novel and interesting argumentationtheoretic characterizations of the EGCWA and the disjunctive stable semantics are shown. Thus the framework presented in this paper does not only provide a new way of performing argumentation (abduction) in disjunctive deductive databases, but also is a simple, intuitive and unifying semantic framework for disjunctive logic programming.