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V.: The stable model semantics for logic programming (1988)

by M Gelfond, Lifschitz
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Classical negation in logic programs and disjunctive databases

by Michael Gelfond, Vladimir Lifschitz - 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 ..."
Abstract - Cited by 1044 (73 self) - Add to MetaCart
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 negation-as-failure. 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

The Well-Founded Semantics for General Logic Programs

by Kenneth A. Ross - Journal of the ACM , 1991
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Abstract - Cited by 997 (15 self) - Add to MetaCart
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...thus faulty. Thus failure to have a perfect model was thought to indicate a flaw in the program rather than in the definition of perfect models. Recent experience has cast doubt on this attitude (see =-=[11] for discu-=-ssion), and spurred the search for further improvements in the definition of the "canonical model." Gelfond and Lifschitz propose an elegant definition of a stable model that is closely rela...

Logical foundations of object-oriented and frame-based languages

by Michael Kifer, Georg Lausen, James Wu - JOURNAL OF THE ACM , 1995
"... We propose a novel formalism, called Frame Logic (abbr., F-logic), that accounts in a clean and declarative fashion for most of the structural aspects of object-oriented and frame-based languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods, ..."
Abstract - Cited by 876 (65 self) - Add to MetaCart
We propose a novel formalism, called Frame Logic (abbr., F-logic), that accounts in a clean and declarative fashion for most of the structural aspects of object-oriented and frame-based languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods, encapsulation, and others. In a sense, F-logic stands in the same relationship to the objectoriented paradigm as classical predicate calculus stands to relational programming. F-logic has a model-theoretic semantics and a sound and complete resolution-based proof theory. A small number of fundamental concepts that come from object-oriented programming have direct representation in F-logic; other, secondary aspects of this paradigm are easily modeled as well. The paper also discusses semantic issues pertaining to programming with a deductive object-oriented language based on a subset of F-logic.
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...per. Last, but not least, thanks goes to the anonymous referees for their constructive critique. A Appendix: A Perfect-Model Semantics for F-logic To adapt the various semantics for negation (such as =-=[89, 46, 105, 104, 90, 5, 62]-=-) to F-logic, the general principle is to use method names in contexts where predicates are used in the classical setting. For the perfect-model semantics [89], this means that stratification has to b...

Abduction in Logic Programming

by Marc Denecker, Antonis Kakas
"... 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 ..."
Abstract - Cited by 624 (77 self) - Add to MetaCart
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.
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...2]. 4.2 Approaches under Stable and Well-Founded Semantics In Logic Programming other semantics have been proposed as refinements of the completion semantics. These include the stable model semantics =-=[38]-=- and the well-founded model semantics [116]. The following ALP frameworks use these semantics for their underlying LP framework. SLDNFA and ID-logic. SLDNFA [17,20] is an abductive extension of SLDNFr...

The DLV System for Knowledge Representation and Reasoning

by Nicola Leone, Gerald Pfeifer, Wolfgang Faber, Thomas Eiter, Georg Gottlob, Simona Perri, Francesco Scarcello - 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 456 (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 (disjunction-free) 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 state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, function-free 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 3-complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of

Representing Action and Change by Logic Programs

by Michael Gelfond, Vladimir Lifschitz - 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 ..."
Abstract - Cited by 414 (25 self) - Add to MetaCart
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 ...
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...ng that the translation is incomplete. A possible way of achieving completeness is discussed in the last section. Second, the proof of the main theorem depends on a relationship between stable models =-=[11]-=- and signings [18], that may be interesting as a part of the general theory of logic programming. The language A is introduced in Section 2, and Section 3 is a brief review of extended logic programs....

Extending and Implementing the Stable Model Semantics

by Patrik Simons, Ilkka Niemelä, Timo Soininen , 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 ..."
Abstract - Cited by 396 (9 self) - Add to MetaCart
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 front-end and a kernel language implementation. The front-end 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.
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... any other atoms are false. The program asb bsc; not d dsnot b csa has, perhaps surprisingly, only one stable model: the set fdg. The stable model semantics for a logic program P is dened as follows [=-=22]-=-. The reduct P A of P with respect to the set of atoms A is obtained by 1. deleting each rule in P that has a not-atom not x in its body such that x 2 A, and by 2. deleting all not-atoms in the remain...

Logic Programs with Stable Model Semantics as a Constraint Programming Paradigm

by Ilkka Niemelä
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Abstract - Cited by 389 (16 self) - Add to MetaCart
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...ectly for expressing constraints without extending the language to allow constraint expressions in the rules. A very natural definition for the solution sets is provided by the stable model semantics =-=[GL88]-=- which is one of the leading declarative semantics of logic programs. The stable model semantics generalizes in a simple way the minimal model semantics of definite programs [vEK76] to the case where ...

Complexity and Expressive Power of Logic Programming

by Evgeny Dantsin, Thomas Eiter, Georg Gottlob, Andrei Voronkov , 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 ..."
Abstract - Cited by 366 (57 self) - Add to MetaCart
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.
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...in an . 5 from the body, then fl2,[! & = fl2,!C9& if .5 is positive, and fl2,!m& fl2,[!#9& if .*5 is negative. The reduct of a normal logic program A by a Herbrand interpretation N =-=[64]-=-, denoted A ffi , is obtained from l9b]Y[_\ !CAD& as follows: first remove every clause , with a negative literal . in the body such that . N , and then remove all negative literals from the ...

Supporting Multiple Access Control Policies in Database Systems

by Elisa Bertino, Sushil Jajodia, Pierangela Samarati - ACM Transactions on Database Systems , 1996
"... Although there are several choices of policies for protection of information, access control models have been developed for a fixed set pre-defined access control policies that are then built into the corresponding access control mechanisms. This becomes a problem, however, if the access control req ..."
Abstract - Cited by 306 (45 self) - Add to MetaCart
Although there are several choices of policies for protection of information, access control models have been developed for a fixed set pre-defined access control policies that are then built into the corresponding access control mechanisms. This becomes a problem, however, if the access control requirements of an application are different from the policies built into a mechanism. In most cases, the only solution is to enforce the requirements as part of the application code, but this makes verification, modification, and adequate enforcement of these policies impossible. In this paper, we propose a flexible authorization mechanism that can support different security policies. The mechanism enforces a general authorization model onto which multiple access control policies can be mapped. The model permits negative and positive authorizations, authorizations that must be strongly obeyed and authorizations that allow for exceptions, and enforces ownership together with delegation of admin...
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