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33
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 ..."
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Cited by 320 (78 self)
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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
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.
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 ..."
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Cited by 113 (26 self)
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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 Deductive System for NonMonotonic Reasoning
, 1997
"... Disjunctive Deductive Databases (DDDBs)  functionfree disjunctive logic programs with negation in rule bodies allowed  have been recently recognized as a powerful tool for knowledge representation and commonsense reasoning. Much research has been spent on issues like semantics and complexity ..."
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Cited by 102 (21 self)
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Disjunctive Deductive Databases (DDDBs)  functionfree disjunctive logic programs with negation in rule bodies allowed  have been recently recognized as a powerful tool for knowledge representation and commonsense reasoning. Much research has been spent on issues like semantics and complexity of DDDBs, but the important area of implementing DDDBs has been less addressed so far. However, a thorough investigation thereof is a basic requirement for building systems which render previous foundational work on DDDBs useful for practice. This paper presents the architecture of a DDDB system currently developed at TU Vienna in the FWF project P11580MAT "A Query System for Disjunctive Deductive Databases".
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 ..."
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Cited by 74 (17 self)
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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...
Logic programs with annotated disjunctions
 In Proc. Int’l Conf. on Logic Programming
, 2004
"... Abstract. Current literature offers a number of different approaches to what could generally be called "probabilistic logic programming". These are usually based on Horn clauses. Here, we introduce a new formalism, Logic Programs with Annotated Disjunctions, based on disjunctive logic prog ..."
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Cited by 58 (5 self)
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Abstract. Current literature offers a number of different approaches to what could generally be called "probabilistic logic programming". These are usually based on Horn clauses. Here, we introduce a new formalism, Logic Programs with Annotated Disjunctions, based on disjunctive logic programs. In this formalism, each of the disjuncts in the head of a clause is annotated with a probability. Viewing such a set of probabilistic disjunctive clauses as a probabilistic disjunction of normal logic programs allows us to derive a possible world semantics, more precisely, a probability distribution on the set of all Herbrand interpretations. We demonstrate the strength of this formalism by some examples and compare it to related work.
Disjunctive Deductive Databases
, 1994
"... Background material is presented on deductive and normal deductive databases. A historical review is presented of work in disjunctive deductive databases, starting from 1982. The semantics of alternative classes of disjunctive databases is reviewed with their model and fixpoint characterizations. Al ..."
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Cited by 57 (7 self)
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Background material is presented on deductive and normal deductive databases. A historical review is presented of work in disjunctive deductive databases, starting from 1982. The semantics of alternative classes of disjunctive databases is reviewed with their model and fixpoint characterizations. Algorithms are developed to compute answers to queries in the alternative theories using the concept of a model tree. Open problems in this area are discussed.
Abduction from Logic Programs: Semantics and Complexity
 Theoretical Computer Science
, 1998
"... Abduction from observations and a theory, find using hypotheses an explanation for the observations  gained increasing interest during the last years. This form of reasoning has wide applicability in different areas of computer science; in particular, it has been recognized as an important pr ..."
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Cited by 36 (7 self)
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Abduction from observations and a theory, find using hypotheses an explanation for the observations  gained increasing interest during the last years. This form of reasoning has wide applicability in different areas of computer science; in particular, it has been recognized as an important principle of commonsense reasoning. In this paper, we define a general abduction model for logic programming, where the inference operator (i.e., the semantics to be applied on programs), can be specified by the user. Advanced forms of logic programming have been proposed as valuable tools for knowledge representation and reasoning. We show that logic programming semantics can be more meaningful for abductive reasoning than classical inference by providing examples from the area of knowledge representation and reasoning. The main part of the paper is devoted to an extensive study of the computational complexity of the principal problems in abductive reasoning, which are: Given an inst...
Logic Programming and Reasoning with Incomplete Information
 Annals of Mathematics and Artificial Intelligence
, 1994
"... The purpose of this paper is to expand the syntax and semantics of logic programs and disjunctive databases to allow for the correct representation of incomplete information in the presence of multiple extensions. The language of logic programs with classical negation, epistemic disjunction, and neg ..."
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Cited by 36 (4 self)
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The purpose of this paper is to expand the syntax and semantics of logic programs and disjunctive databases to allow for the correct representation of incomplete information in the presence of multiple extensions. The language of logic programs with classical negation, epistemic disjunction, and negation by failure is further expanded by new modal operators K and M (where for the set of rules T and formula F , KF stands for "F is known to be true by a reasoner with a set of premises T " and MF means " F may be believed to be true" by the same reasoner). Sets of rules in the extended language will be called epistemic specifications. We will define the semantics of epistemic specifications (which expands the semantics of disjunctive databases from [GL91]) and demonstrate their applicability to formalization of various forms of commonsense reasoning. In particular, we suggest a new formalization of the closed world assumption which seems to better correspond to the assumption's intuitive...
Knowledge Representation with Logic Programs
 DEPT. OF CS OF THE UNIVERSITY OF KOBLENZLANDAU
, 1996
"... In this tutorialoverview, which resulted from a lecture course given by the authors at ..."
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Cited by 31 (6 self)
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In this tutorialoverview, which resulted from a lecture course given by the authors at