Results 1  10
of
59
The DLV System for Knowledge Representation and Reasoning
 ACM Transactions on Computational Logic
, 2002
"... Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely believ ..."
Abstract

Cited by 455 (102 self)
 Add to MetaCart
Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely believed assumptions, DLP is strictly more expressive than normal (disjunctionfree) logic programming, whose expressiveness is limited to properties decidable in NP. Importantly, apart from enlarging the class of applications which can be encoded in the language, disjunction often allows for representing problems of lower complexity in a simpler and more natural fashion. This paper presents the DLV system, which is widely considered the stateoftheart implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, functionfree disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to ∆P 3complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of
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 va ..."
Abstract

Cited by 294 (16 self)
 Add to MetaCart
In many cases, a logic program can be divided into two parts, so that one of them, the \bottom &quot; part, does not refer to the predicates de ned in the \top &quot; part. The \bottom &quot; 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 &quot; 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
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 ..."
Abstract

Cited by 242 (20 self)
 Add to MetaCart
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.
On the Computational Cost of Disjunctive Logic Programming: Propositional Case
, 1995
"... This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of wellknown semantics, as well as the complexity of deciding whethe ..."
Abstract

Cited by 141 (26 self)
 Add to MetaCart
This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of wellknown semantics, as well as the complexity of deciding whether a propositional formula is satised by all models according to a given semantics. We concentrate on nite propositional disjunctive programs with as wells as without integrity constraints, i.e., clauses with empty heads; the problems are located in appropriate slots of the polynomial hierarchy. In particular, we show that the consistency check is P 2 complete for the disjunctive stable model semantics (in the total as well as partial version), the iterated closed world assumption, and the perfect model semantics, and we show that the inference problem for these semantics is P 2 complete; analogous results are derived for the an
A Survey of Research on Deductive Database Systems
 JOURNAL OF LOGIC PROGRAMMING
, 1993
"... The area of deductive databases has matured in recent years, and it now seems appropriate to re ect upon what has been achieved and what the future holds. In this paper, we provide an overview of the area and briefly describe a number of projects that have led to implemented systems. ..."
Abstract

Cited by 119 (7 self)
 Add to MetaCart
(Show Context)
The area of deductive databases has matured in recent years, and it now seems appropriate to re ect upon what has been achieved and what the future holds. In this paper, we provide an overview of the area and briefly describe a number of projects that have led to implemented systems.
Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics, and Computation
 Information and Computation
, 1997
"... Disjunctive logic programs have become a powerful tool in knowledge representation and commonsense reasoning. This paper focuses on stable model semantics, currently the most widely acknowledged semantics for disjunctive logic programs. After presenting a new notion of unfounded sets for disjunct ..."
Abstract

Cited by 89 (20 self)
 Add to MetaCart
(Show Context)
Disjunctive logic programs have become a powerful tool in knowledge representation and commonsense reasoning. This paper focuses on stable model semantics, currently the most widely acknowledged semantics for disjunctive logic programs. After presenting a new notion of unfounded sets for disjunctive logic programs, we provide two declarative characterizations of stable models in terms of unfounded sets. One shows that the set of stable models coincides with the family of unfoundedfree models (i.e., a model is stable iff it contains no unfounded atoms). The other proves that stable models can be defined equivalently by a property of their false literals, as a model is stable iff the set of its false literals coincides with its greatest unfounded set. We then generalize the wellfounded WP operator to disjunctive logic programs, give a fixpoint semantics for disjunctive stable models and present an algorithm for computing the stable models of functionfree programs. The algor...
Negation As Failure In The Head
, 1998
"... The class of logic programs with negation as failure in the head is a subset of the logic of MBNF introduced by Lifschitz and is an extension of the class of extended disjunctive programs. An interesting feature of such programs is that the minimality of answer sets does not hold. This paper conside ..."
Abstract

Cited by 67 (2 self)
 Add to MetaCart
The class of logic programs with negation as failure in the head is a subset of the logic of MBNF introduced by Lifschitz and is an extension of the class of extended disjunctive programs. An interesting feature of such programs is that the minimality of answer sets does not hold. This paper considers the class of {\em general extended disjunctive programs\/} (GEDPs) as logic programs with negation as failure in the head. First, we discuss that the class of GEDPs is useful for representing knowledge in various domains in which the principle of minimality is too strong. In particular, the class of abductive programs is properly included in the class of GEDPs. Other applications include the representation of inclusive disjunctions and circumscription with fixed predicates. Secondly, the semantic nature of GEDPs is analyzed by the syntax of programs. In acyclic programs, negation as failure in the head can be shifted to the body without changing the answer sets of the program. On the other hand, supported sets of any program are always preserved by the same transformation. Thirdly, the computational complexity of the class of GEDPs is shown to remain in the same complexity class as normal disjunctive programs. Through the simulation of negation as failure in the head, computation of answer sets and supported sets is realized using any proof procedure for extended or positive disjunctive programs. Finally, a simple translation of GEDPs into autoepistemic logic is presented.
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 ..."
Abstract

Cited by 65 (8 self)
 Add to MetaCart
(Show Context)
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...
Logic and Databases: a 20 Year Retrospective
, 1996
"... . At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire ..."
Abstract

Cited by 58 (1 self)
 Add to MetaCart
. At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire and Nicolas in Toulouse, France, which culminated in a workshop held in Toulouse, France in 1977. It is appropriate, then to provide an assessment as to what has been achieved in the twenty years since the field started as a distinct discipline. In this retrospective I shall review developments that have taken place in the field, assess the contributions that have been made, consider the status of implementations of deductive databases and discuss the future of work in this area. 1 Introduction As described in [234], the use of logic and deduction in databases started in the late 1960s. Prominent among the developments was the work by Levien and Maron [202, 203, 199, 200, 201] and Kuhns [1...
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 ..."
Abstract

Cited by 58 (12 self)
 Add to MetaCart
(Show Context)
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