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74
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 312 (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.
Complexity and Expressive Power of Logic Programming
, 1997
"... This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results ..."
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Cited by 281 (57 self)
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This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.
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 224 (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.
A Novel Combination of Answer Set Programming with Description Logics for the Semantic Web
 IN PROC. KR2004
, 2004
"... Abstract. We present a novel combination of disjunctive logic programs under the answer set semantics with description logics for the Semantic Web. The combination is based on a wellbalanced interface between disjunctive logic programs and description logics, which guarantees the decidability of th ..."
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Cited by 204 (47 self)
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Abstract. We present a novel combination of disjunctive logic programs under the answer set semantics with description logics for the Semantic Web. The combination is based on a wellbalanced interface between disjunctive logic programs and description logics, which guarantees the decidability of the resulting formalism without assuming syntactic restrictions. We show that the new formalism has very nice semantic properties. In particular, it faithfully extends both disjunctive programs and description logics. Furthermore, we describe algorithms for reasoning in the new formalism, and we give a precise picture of its computational complexity. We also provide a special case with polynomial data complexity. 1
ArgumentBased Extended Logic Programming With Defeasible Priorities
"... . Inspired by legal reasoning, this paper presents a semantics and proof theory of a system for defeasible argumentation. Arguments are expressed in a logicprogramming language with both weak and strong negation. Conflicts between arguments are decided with the help of priorities on the rules. An i ..."
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Cited by 190 (27 self)
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. Inspired by legal reasoning, this paper presents a semantics and proof theory of a system for defeasible argumentation. Arguments are expressed in a logicprogramming language with both weak and strong negation. Conflicts between arguments are decided with the help of priorities on the rules. An important feature of the system is that these priorities are not fixed, but are themselves defeasibly derived as conclusions within the system. Thus debates on the choice between conflicting arguments can also be modelled. The semantics of the system is given with a fixpoint definition, while its proof theory is stated in dialectical style, where a proof takes the form of a dialogue between a proponent and an opponent of an argument: an argument is shown to be justified if the proponent can make the opponent run out of moves in whatever way the opponent attacks. KEYWORDS: Argumentation, Nonmonotonic reasoning, Extended logic programming, Legal reasoning, Defeasible priorities Introduction W...
Efficient Implementation of the Wellfounded and Stable Model Semantics
 Proceedings of the Joint International Conference and Symposium on Logic Programming
, 1996
"... An implementation of the wellfounded and stable model semantics for rangerestricted functionfree normal programs is presented. It includes two modules: an algorithm for implementing the two semantics for ground programs and an algorithm for computing a grounded version of a rangerestricted funct ..."
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Cited by 139 (16 self)
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An implementation of the wellfounded and stable model semantics for rangerestricted functionfree normal programs is presented. It includes two modules: an algorithm for implementing the two semantics for ground programs and an algorithm for computing a grounded version of a rangerestricted functionfree normal program. The latter algorithm does not produce the whole set of ground instances of the program but a subset which is sufficient in the sense that no stable models are lost. The implementation of the stable model semantics for ground programs is based on bottomup backtracking search. It works in linear space and employs a powerful pruning method based on an approximation technique for stable models which is closely related to the wellfounded semantics. The implementation includes an efficient algorithm for computing the wellfounded model of a ground program. The implementation has been tested extensively and compared with a state of the art implementation of the stable mode...
Well Founded Semantics for Logic Programs with Explicit Negation
 EUROPEAN CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 1992
"... The aim of this paper is to provide a semantics for general logic programs (with negation by default) extended with explicit negation, subsuming well founded semantics [22]. The Well Founded semantics for extended logic programs (WFSX) is expressible by a default theory semantics we have devised [11 ..."
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Cited by 122 (54 self)
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The aim of this paper is to provide a semantics for general logic programs (with negation by default) extended with explicit negation, subsuming well founded semantics [22]. The Well Founded semantics for extended logic programs (WFSX) is expressible by a default theory semantics we have devised [11]. This relationship improves the crossfertilization between logic programs and default theories, since we generalize previous results concerning their relationship [3, 4, 7, 1, 2], and there is an increasing use of logic programming with explicit negation for nonmonotonic reasoning [7, 15, 16, 13, 23]. It also clarifies the meaning of logic programs combining both explicit negation and negation by default. In particular, it shows that explicit negation corresponds exactly to classical negation in the default theory, and elucidates the use of rules in logic programs. Like defaults, rules are unidirectional, so their contrapositives are not implicit; the rule connective, /, is not materi...
WellFounded Semantics for Extended Logic Programs with Dynamic Preferences
 Journal of Artificial Intelligence Research
, 1996
"... The paper describes an extension of wellfounded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This is achieved by using a reserved predicate symbol and a naming ..."
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Cited by 91 (10 self)
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The paper describes an extension of wellfounded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This is achieved by using a reserved predicate symbol and a naming technique. Conflicts among rules are resolved whenever possible on the basis of derived preference information. The wellfounded conclusions of prioritized logic programs can be computed in polynomial time. A legal reasoning example illustrates the usefulness of the approach. 1. Introduction: Why Dynamic Preferences are Needed Preferences among defaults play a crucial role in nonmonotonic reasoning. One source of preferences that has been studied intensively is specificity (Poole, 1985; Touretzky, 1986; Touretzky, Thomason, & Horty, 1991). In case of a conflict between defaults we tend to prefer the more specific one since this default provides more reliable information. E.g., if we know t...
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 86 (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
Wellfounded semantics for description logic programs in the Semantic Web
, 2009
"... The realization of the Semantic Web vision, in which computational logic has a prominent role, has stimulated a lot of research on combining rules and ontologies, which are formulated in different formalisms, into a framework that is more useful for describing semantic content. In particular, combin ..."
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Cited by 57 (17 self)
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The realization of the Semantic Web vision, in which computational logic has a prominent role, has stimulated a lot of research on combining rules and ontologies, which are formulated in different formalisms, into a framework that is more useful for describing semantic content. In particular, combining logic programming with the Web Ontology Language (OWL), which is a standard based on description logics, emerged as an important issue for linking the Rules and Ontology Layers of the Semantic Web. Nonmonotonic description logic programs (or dlprograms) were introduced for such a combination, in which a pair (L,P) of a description logic knowledge base L and a set of rules P with negation as failure is given a modelbased semantics that generalizes the answer set semantics of logic programs. In this paper, we reconsider dlprograms and present a wellfounded semantics for them as an analog for the other main semantics of logic programs. It generalizes the canonical definition of the wellfounded semantics based on unfounded sets, and, as we show, lifts many of the wellknown properties from ordinary logic programs to dlprograms. Among these properties: our semantics amounts to a partial model approximating the answer set semantics, which yields for positive and stratified dlprograms a total model coinciding with the answer set semantics; it has polynomial data complexity provided the access to the description logic