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Abduction in Logic Programming
"... Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over th ..."
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Cited by 537 (73 self)
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Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over the last ten years and to take a critical view of these developments from several perspectives: logical, epistemological, computational and suitability to application. The paper attempts to expose some of the challenges and prospects for the further development of the field.
Representing Action and Change by Logic Programs
 Journal of Logic Programming
, 1993
"... We represent properties of actions in a logic programming language that uses both classical negation and negation as failure. The method is applicable to temporal projection problems with incomplete information, as well as to reasoning about the past. It is proved to be sound relative to a semantics ..."
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Cited by 381 (27 self)
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We represent properties of actions in a logic programming language that uses both classical negation and negation as failure. The method is applicable to temporal projection problems with incomplete information, as well as to reasoning about the past. It is proved to be sound relative to a semantics of action based on states and transition functions. 1 Introduction This paper extends the work of Eshghi and Kowalski [6], Evans [7] and Apt and Bezem [1] on representing properties of actions in logic programming languages with negation as failure. Our goal is to overcome some of the limitations of the earlier work. The existing formalizations of action in logic programming are adequate for only the simplest kind of temporal reasoning"temporal projection." In a temporal projection problem, we are given a description of the initial state of the world, and use properties of actions to determine what the world will look like after a series of actions is performed. Moreover, the existing ...
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
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 279 (56 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.
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 260 (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
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.
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