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The WellFounded Semantics for General Logic Programs
 Journal of the ACM
, 1991
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The Alternating Fixpoint of Logic Programs with Negation
, 1995
"... The alternating fixpoint of a logic program with negation is defined constructively. The underlying idea is monotonically to build up a set of negative conclusions until the least fixpoint is reached, using a transformation related to the one that defines stable models. From a fixed set of negative ..."
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Cited by 248 (2 self)
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The alternating fixpoint of a logic program with negation is defined constructively. The underlying idea is monotonically to build up a set of negative conclusions until the least fixpoint is reached, using a transformation related to the one that defines stable models. From a fixed set of negative conclusions, the positive conclusions follow (without deriving any further negative ones), by traditional Horn clause semantics. The union of positive and negative conclusions is called the alternating xpoint partial model. The name "alternating" was chosen because the transformation runs in two passes; the first pass transforms an underestimate of the set of negative conclusions into an (intermediate) overestimate; the second pass transforms the overestimate into a new underestimate; the composition of the two passes is monotonic. The principal contributions of this work are (1) that the alternating fixpoint partial model is identical to the wellfounded partial model, and (2) that alternating xpoint logic is at least as expressive as xpoint logic on all structures. Also, on finite structures, fixpoint logic is as expressive as alternating fixpoint logic.
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 fu ..."
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Cited by 51 (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
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Improving the Alternating Fixpoint: The Transformation Approach
, 1997
"... . We present a bottomup algorithm for the computation of the wellfounded model of nondisjunctive logic programs which is based on the set of elementary program transformations studied by Brass and Dix [4, 5]. The transformation approach has been introduced in more detail in [7]. In this paper we ..."
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Cited by 9 (0 self)
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. We present a bottomup algorithm for the computation of the wellfounded model of nondisjunctive logic programs which is based on the set of elementary program transformations studied by Brass and Dix [4, 5]. The transformation approach has been introduced in more detail in [7]. In this paper we present a deeper analysis of its complexity and describe an optimized SCCoriented evaluation. We show that by our method no more work is done than by the alternating fixpoint procedure [23, 24] and that there are examples where our algorithm is significantly superior. 1 Introduction It is likely that the next generation of deductive database systems will support the full class of normal programs and that the wellfounded semantics will be chosen by nearly all system designers, because it has a unique model. Whereas the SLGresolution of Chen and Warren [10, 11, 12] is an elaborate topdown method for the computation of the wellfounded model of a normal program that already led to a full...
Computation of the Semantics of Autoepistemic Belief Theories
, 1999
"... Recently, one of the authors introduced a simple and yet powerful nonmonotonic knowledge representation framework, called the Autoepistemic Logic of Beliefs, AEB. Theories in AEB are called autoepistemic belief theories. Every belief theory T has been shown to have the least static expansion T whi ..."
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Cited by 6 (4 self)
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Recently, one of the authors introduced a simple and yet powerful nonmonotonic knowledge representation framework, called the Autoepistemic Logic of Beliefs, AEB. Theories in AEB are called autoepistemic belief theories. Every belief theory T has been shown to have the least static expansion T which is computed by iterating a natural monotonic belief closure operator \Psi T starting from T . This way, the least static expansion T of any belief theory provides its natural nonmonotonic semantics which is called the static semantics. It is easy to see that if a belief theory T is finite then the construction of its least static expansion T stops after countably many iterations. However, a somewhat surprising result obtained in this paper shows that the least static expansion of any finite belief theory T is in fact obtained by means of a single iteration of the belief closure operator \Psi T (although this requires T to be of a special form, we also show that T can be always put in th...
WinMove is CoordinationFree (Sometimes)
"... In a recent paper by Hellerstein [15], a tight relationship was conjectured between the number of strata of a Datalog ¬ program and the number of “coordination stages ” required for its distributed computation. Indeed, Ameloot et al. [9] showed that a query can be computed by a coordinationfree rela ..."
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Cited by 5 (4 self)
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In a recent paper by Hellerstein [15], a tight relationship was conjectured between the number of strata of a Datalog ¬ program and the number of “coordination stages ” required for its distributed computation. Indeed, Ameloot et al. [9] showed that a query can be computed by a coordinationfree relational transducer network iff it is monotone, thus answering in the affirmative a variant of Hellerstein’s CALM conjecture, based on a particular definition of coordinationfree computation. In this paper, we present three additional models for declarative networking. In these variants, relational transducers have limited access to the way data is distributed. This variation allows transducer networks to compute more queries in a coordinationfree manner: e.g., a transducer can check whether a ground atom A over the input schema is in the “scope ” of the local node, and then send either A or ¬A to other nodes. We show the surprising result that the query given by the wellfounded semantics of the unstratifiable winmove program is coordinationfree in some of the models we consider. We also show that the original transducer network model [9] and our variants form a strict hierarchy of classes of coordinationfree queries. Finally, we identify different syntactic, called semimonotone programs, which can be used as declarative network programming languages, whose distributed computation is guaranteed to be eventually consistent and coordinationfree. fragments of Datalog ¬¬
Characterizations and Implementation of Static Semantics of Disjunctive Programs
, 1996
"... Recently, considerable interest and research effort 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 ..."
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Cited by 2 (1 self)
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Recently, considerable interest and research effort 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: ffl the proposed syntax of such programs resembles the syntax of logic programs but it applies to a significantly broader class of programs; ffl the proposed semantics of such programs constitutes an intuitively natural extension of the semantics of normal logic programs; ffl there exists a reasonably simple procedural mechanism allowing, at least in principle, to compute the semantics; ffl 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 whic...
The Differential Fixpoint of General Logic Programs
 Proc. of the Workshop DDLP'96 on Deductive Databases and Logic Programming. 4th Workshop in conjunction with JICSLP'96
, 1996
"... We present a version of the alternating fixpoint procedure that is fully incremental. Using ideas of partial evaluation techniques we can compute the wellfounded model of logic programs with negation bottomup without any recomputations. Further extensions of the semantics, e.g. to stable models or ..."
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We present a version of the alternating fixpoint procedure that is fully incremental. Using ideas of partial evaluation techniques we can compute the wellfounded model of logic programs with negation bottomup without any recomputations. Further extensions of the semantics, e.g. to stable models or disjunctive programs are possible this way. We show how to implement the algorithm efficiently using indexbased data structures and describe an extension to handle magic set transformed programs. This setoriented bottomup algorithm is compatible with the wellknown optimizations of deductive databases, e.g. seminaive fixpoint iteration, and of relational databases, e.g. index techniques that enable the processing of large amounts of data. Thus, a bottomup alternative to the already known efficient topdown methods for the wellfounded semantics seems to be feasible. 1 Introduction A very influential and wellaccepted semantics for logic programs with negation is the wellfounded semanti...