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34
Classical Negation in Logic Programs and Disjunctive Databases
 New Generation Computing
, 1991
"... An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic progra ..."
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Cited by 853 (75 self)
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An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic programs by including classical negation, in addition to negationasfailure. The semantics of such extended programs is based on the method of stable models. The concept of a disjunctive database can be extended in a similar way. We show that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available. Computationally, classical negation can be eliminated from extended programs by a simple preprocessor. Extended programs are identical to a special case of default theories in the sense of Reiter. 1 Introduction An important limitation of traditional logic programming as a knowledge representation tool, in comp...
Splitting a Logic Program
 Principles of Knowledge Representation
, 1994
"... In many cases, a logic program can be divided into two parts, so that one of them, the \bottom " part, does not refer to the predicates de ned in the \top " part. The \bottom " rules can be used then for the evaluation of the predicates that they de ne, and the computed values can be ..."
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Cited by 267 (15 self)
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In many cases, a logic program can be divided into two parts, so that one of them, the \bottom " part, does not refer to the predicates de ned in the \top " part. The \bottom " rules can be used then for the evaluation of the predicates that they de ne, and the computed values can be used to simplify the \top " de nitions. We discuss this idea of splitting a program in the context of the answer set semantics. The main theorem shows how computing the answer sets for a program can be simpli ed when the program is split into parts. The programs covered by the theorem may use both negation as failure and classical negation, and their rules may have disjunctive heads. The usefulness of the concept of splitting for the investigation of answer sets is illustrated by several applications. First, we show that a conservative extension theorem by Gelfond and Przymusinska and a theorem on the closed world assumption by Gelfond and Lifschitz are easy consequences of the splitting theorem. Second, (locally) strati ed programs are shown to have a simple characterization in terms of splitting. The existence and uniqueness of an answer set for such a program can be easily derived from this characterization. Third, we relate the idea of splitting to the notion of orderconsistency. 1
Propositional Semantics for Disjunctive Logic Programs
 Annals of Mathematics and Artificial Intelligence
, 1994
"... In this paper we study the properties of the class of headcyclefree extended disjunctive logic programs (HEDLPs), which includes, as a special case, all nondisjunctive extended logic programs. We show that any propositional HEDLP can be mapped in polynomial time into a propositional theory such th ..."
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Cited by 149 (2 self)
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In this paper we study the properties of the class of headcyclefree extended disjunctive logic programs (HEDLPs), which includes, as a special case, all nondisjunctive extended logic programs. We show that any propositional HEDLP can be mapped in polynomial time into a propositional theory such that each model of the latter corresponds to an answer set, as defined by stable model semantics, of the former. Using this mapping, we show that many queries over HEDLPs can be determined by solving propositional satisfiability problems. Our mapping has several important implications: It establishes the NPcompleteness of this class of disjunctive logic programs; it allows existing algorithms and tractable subsets for the satisfiability problem to be used in logic programming; it facilitates evaluation of the expressive power of disjunctive logic programs; and it leads to the discovery of useful similarities between stable model semantics and Clark's predicate completion. 1 Introduction ...
Answer Set Programming and Plan Generation
 ARTIFICIAL INTELLIGENCE
, 2002
"... The idea of answer set programming is to represent a given computational problem by a logic program whose answer sets correspond to solutions, and then use an answer set solver, such as smodels or dlv, to find an answer set for this program. Applications of this method to planning are related to the ..."
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Cited by 137 (5 self)
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The idea of answer set programming is to represent a given computational problem by a logic program whose answer sets correspond to solutions, and then use an answer set solver, such as smodels or dlv, to find an answer set for this program. Applications of this method to planning are related to the line of research on the frame problem that started with the invention of formal nonmonotonic reasoning in 1980.
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...
Answer Sets in General Nonmonotonic Reasoning (Preliminary Report)
, 1992
"... Languages of declarative logic programming differ from other modal nonmonotonic formalisms by lack of syntactic uniformity. For instance, negation as failure can be used in the body of a rule, but not in the head; in disjunctive programs, disjunction is used in the head of a rule, but not in the bod ..."
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Cited by 103 (9 self)
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Languages of declarative logic programming differ from other modal nonmonotonic formalisms by lack of syntactic uniformity. For instance, negation as failure can be used in the body of a rule, but not in the head; in disjunctive programs, disjunction is used in the head of a rule, but not in the body; in extended programs, negation as failure can be used on top of classical negation, but not the other way around. We argue that this lack of uniformity should not be viewed as a distinguishing feature of logic programming in general. As a starting point, we take a translation from the language of disjunctive programs with negation as failure and classical negation into MBNFthe logic of minimal belief and negation as failure. A class of theories based on this logic is defined, theories with protected literals, which is syntactically uniform and contains the translations of all programs. We show that theories with protected literals have a semantics similar to the answer set semantics us...
On the Declarative and Procedural Semantics of Logic Programs
 Journal of Automated Reasoning
, 1995
"... One of the most important and difficult problems in logic programming is the problem of finding a suitable declarative or intended semantics for logic programs. The importance of this problem stems from the declarative character of logic programming, whereas its difficulty can be largely attributed ..."
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Cited by 65 (8 self)
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One of the most important and difficult problems in logic programming is the problem of finding a suitable declarative or intended semantics for logic programs. The importance of this problem stems from the declarative character of logic programming, whereas its difficulty can be largely attributed to the nonmonotonic character of the negation operator used in logic programs. The problem can therefore be viewed as the problem of finding a suitable formalization of the type of nonmonotonic reasoning used in logic programming. In this paper we introduce a semantics of logic programs based on the class PERF(P) of all, not necessarily Herbrand, perfect models of a program P and we show that the proposed semantics is not only natural but it also combines many of the desirable features of previous approaches, at the same time eliminating some of their drawbacks. For a positive program P, the class PERF(P) of perfect models coincides with the class MIN(P) of all minimal models of P. The per...
Semantic Issues in Deductive Databases and Logic Programs
 Formal Techniques in Artificial Intelligence
, 1990
"... this paper. In particular, the paper reports on a very significant progress made recently in this area. It also presents some results which have not yet appeared in print. The paper is organized as follows. In the next two sections we define deductive databases and logic programs. Subsequently, in ..."
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Cited by 54 (12 self)
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this paper. In particular, the paper reports on a very significant progress made recently in this area. It also presents some results which have not yet appeared in print. The paper is organized as follows. In the next two sections we define deductive databases and logic programs. Subsequently, in Sections 4 and 5, we discuss model theory and fixed points, which play a crucial role in the definition of semantics. Section 6 is the main section of the paper and is entirely devoted to a systematic exposition and comparison of various proposed semantics. In Section 7 we discuss the relationship between declarative semantics of deductive databases and logic programs and nonmonotonic reasoning. Section 8 contains concluding remarks. 2 Deductive Databases
Default Logic as a Query Language
, 1997
"...  Research in nonmonotonic reasoning has focused largely on the idea of representing knowledge about the world via rules that are generally true but can be defeated. Even if relational databases are nowadays the main tool for storing very large sets of data, the approach of using nonmonotonic AI f ..."
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Cited by 43 (11 self)
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 Research in nonmonotonic reasoning has focused largely on the idea of representing knowledge about the world via rules that are generally true but can be defeated. Even if relational databases are nowadays the main tool for storing very large sets of data, the approach of using nonmonotonic AI formalisms as relational database query languages has been investigated to a much smaller extent. In this work we propose a novel application of Reiter's default logic by introducing a default query language (DQL) for nite relational databases, which is based on default rules. The main result of this paper is that DQL is as expressive as SO 98 , the existentialuniversal fragment of secondorder logic. This result is not only of theoretical importance: We exhibit queries {which are useful in practice{ that can be expressed with DQL and can not with other query languages based on nonmonotonic logics such as DATALOG with negation under the stable model semantics. In particular, we show that DQ...