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49
The Stable Model Semantics For Logic Programming
, 1988
"... We propose a new declarative semantics for logic programs with negation. Its formulation is quite simple; at the same time, it is more general than the iterated fixed point semantics for stratied programs, and is applicable to some useful programs that are not stratified. ..."
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Cited by 1492 (62 self)
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We propose a new declarative semantics for logic programs with negation. Its formulation is quite simple; at the same time, it is more general than the iterated fixed point semantics for stratied programs, and is applicable to some useful programs that are not stratified.
Circumscription
, 1996
"... The idea of circumscription can be explained on a simple example. We would like to represent information about the locations of blocks in a blocks world, using the "default": ..."
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Cited by 322 (13 self)
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The idea of circumscription can be explained on a simple example. We would like to represent information about the locations of blocks in a blocks world, using the "default":
Extending and Implementing the Stable Model Semantics
, 2002
"... A novel logic program like language, weight constraint rules, is developed for answer set programming purposes. It generalizes normal logic programs by allowing weight constraints in place of literals to represent, e.g., cardinality and resource constraints and by providing optimization capabilities ..."
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Cited by 310 (5 self)
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A novel logic program like language, weight constraint rules, is developed for answer set programming purposes. It generalizes normal logic programs by allowing weight constraints in place of literals to represent, e.g., cardinality and resource constraints and by providing optimization capabilities. A declarative semantics is developed which extends the stable model semantics of normal programs. The computational complexity of the language is shown to be similar to that of normal programs under the stable model semantics. A simple embedding of general weight constraint rules to a small subclass of the language called basic constraint rules is devised. An implementation of the language, the smodels system, is developed based on this embedding. It uses a two level architecture consisting of a frontend and a kernel language implementation. The frontend allows restricted use of variables and functions and compiles general weight constraint rules to basic constraint rules. A major part of the work is the development of an ecient search procedure for computing stable models for this kernel language. The procedure is compared with and empirically tested against satis ability checkers and an implementation of the stable model semantics. It offers a competitive implementation of the stable model semantics for normal programs and attractive performance for problems where the new types of rules provide a compact representation.
Logic Programming and Negation: A Survey
 JOURNAL OF LOGIC PROGRAMMING
, 1994
"... We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the prooftheoretic and modeltheoretic issues and the relationships between them. ..."
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Cited by 242 (8 self)
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We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the prooftheoretic and modeltheoretic issues and the relationships between them.
Logic Programming and Knowledge Representation
 Journal of Logic Programming
, 1994
"... In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and sh ..."
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Cited by 223 (21 self)
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In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and show how each of the added features extends the representational power of the language.
HiLog: A foundation for higherorder logic programming
 JOURNAL OF LOGIC PROGRAMMING
, 1993
"... We describe a novel logic, called HiLog, and show that it provides a more suitable basis for logic programming than does traditional predicate logic. HiLog has a higherorder syntax and allows arbitrary terms to appear in places where predicates, functions and atomic formulas occur in predicate calc ..."
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Cited by 213 (40 self)
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We describe a novel logic, called HiLog, and show that it provides a more suitable basis for logic programming than does traditional predicate logic. HiLog has a higherorder syntax and allows arbitrary terms to appear in places where predicates, functions and atomic formulas occur in predicate calculus. But its semantics is firstorder and admits a sound and complete proof procedure. Applications of HiLog are discussed, including DCG grammars, higherorder and modular logic programming, and deductive databases.
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 209 (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.
A Logic for Reasoning with Inconsistency
, 1992
"... Most known computational approaches to reasoning have problems when facing inconsistency, so they assume that a given logical system is consistent. Unfortunately, the latter is difficult to verify and very often is not true. It may happen that addition of data to a large system makes it inconsistent ..."
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Cited by 95 (8 self)
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Most known computational approaches to reasoning have problems when facing inconsistency, so they assume that a given logical system is consistent. Unfortunately, the latter is difficult to verify and very often is not true. It may happen that addition of data to a large system makes it inconsistent, and hence destroys the vast amount of meaningful information. We present a logic, called APC (annotated predicate calculus; cf. annotated logic programs of [3], that treats any set of clauses, either consistent or not, in a uniform way. In this logic, consequences of a contradiction are not nearly as damaging as in the standard predicate calculus, and meaningful information can still be extracted from an inconsistent set of formulae. APC has a resolutionbased sound and complete proof procedure. We also introduce a novel notion of "epistemic entailment" and show its importance for investigating inconsistency in predicate calculus as well as its application to nonmonotonic reasoning. Most importantly, our claim that a logical theory is an adequate model of human perception of inconsistency, is actually backed by rigorous arguments.
The expressive powers of logic programming semantics
 Abstract in Proc. PODS 90
, 1995
"... We study the expressive powers of two semantics for deductive databases and logic programming: the wellfounded semantics and the stable semantics. We compare them especially to two older semantics, the twovalued and threevalued program completion semantics. We identify the expressive power of the ..."
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Cited by 84 (5 self)
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We study the expressive powers of two semantics for deductive databases and logic programming: the wellfounded semantics and the stable semantics. We compare them especially to two older semantics, the twovalued and threevalued program completion semantics. We identify the expressive power of the stable semantics, and in fairly general circumstances that of the wellfounded semantics. In particular, over infinite Herbrand universes, the four semantics all have the same expressive power. We discuss a feature of certain logic programming semantics, which we call the Principle of Stratification, a feature allowing a program to be built easily in modules. The threevalued program completion and wellfounded semantics satisfy this principle. Over infinite Herbrand models, we consider a notion of translatability between the threevalued program completion and wellfounded semantics which is in a sense uniform in the strata. In this sense of uniform translatability we show the wellfounded semantics to be more expressive than the threevalued program completion. The proof is a corollary of our result that over nonHerbrand infinite models, the wellfounded semantics is more expressive than the threevalued program completion semantics. 1