## Logic Programs with Stable Model Semantics as a Constraint Programming Paradigm

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@MISC{Niemelä_logicprograms,

author = {Ilkka Niemelä},

title = {Logic Programs with Stable Model Semantics as a Constraint Programming Paradigm},

year = {}

}

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### Citations

1557 | The stable model semantics for logic programming
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...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 ... |

1492 | A logic for default reasoning - Reiter - 1980 |

1035 | Fast planning through planning graph analysis - Blum, Furst - 1997 |

877 | The well-founded semantics for general logic programs
- Gelder, Ross, et al.
- 1991
(Show Context)
Citation Context ...t included in the stable model) [Nie95, NS96a]. The search space is pruned efficiently by exploiting an approximation technique for stable models which is closely related to the wellfounded semantics =-=[VGRS91]-=-. The same approximation technique is employed in a powerful dynamic search heuristics. One of the advantages of our implementation method is that it has linear space requirements. This makes it possi... |

812 | The Semantics of Constraint Logic Programs
- Jaffar, Maher, et al.
- 1998
(Show Context)
Citation Context ...ation techniques by allowing, e.g., arithmetic constraints in the rules and by integrating the necessary constraint solvers into a logic programming system. This constraint logic programming paradigm =-=[JL87]-=- has been extended to include nonmonotonic reasoning capabilities such as abduction [KM97]. However, the constraint logic programming paradigm differs significantly from our approach where the rules h... |

736 | Predicate logic as programming language
- Kowalski
- 1974
(Show Context)
Citation Context ...ble 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 negative body literals are allowed in the program rules. For a ground (variable-free) program P , the stable models are defined as follows. The reduct of a program P with respect to... |

631 | Towards a theory of declarative knowledge - APT, BLAIR, et al. - 1988 |

458 | Semantical considerations on nonmonotonic logics - Moore - 1985 |

399 | Representing actions and change by logic programs - Gelfond, Lifschitz - 1993 |

344 |
Logic programs with classical negation
- Gelfond, Lifschitz
- 1990
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Citation Context ...sed truth maintenance system (TMS) when logic programming rules are seen as justifications in a TMS [Elk90] and to default extensions when rules are treated as default rules in Reiter's default logic =-=[GL90]-=-. The rest of the paper is organized as follows. First we show that traditional Boolean constraints, i.e. propositional satisfiability, can be embedded in a simple way to LPSM and argue that from a kn... |

326 | Linear-Time Algorithms for Testing the Satisfiability of Propositional Horn Formulae - Dowling, Gallier |

270 | Tabled Evaluation with Delaying for General Logic Programs - Chen, Warren |

267 | Smodels—An implementation of the stable model and well-founded semantics for normal LP
- Niemelä, Simons
- 1997
(Show Context)
Citation Context ...een obtained when applying the system. Reasonably large combinatorial problems (e.g., graph colorings and Hamiltonian circuits) have been solved using the system [NS96a, NS96b, NS97]. In SAT problems =-=[NS97]-=- the system shows similar performance as the best Davis-Putnam implementations (e.g., Crawford's tableau [CA96]) even for hard instances such as the random 3-SAT problems in the phase transition regio... |

253 | Stable models and an alternative logic programming paradigm - Marek, Truszczynski - 1999 |

196 |
Autoepistemic logic
- Marek, Truszczynski
- 1991
(Show Context)
Citation Context ...ce, a program can possess multiple stable models but sometimes none at all as is the case for the program p / not p: The problem of deciding whether a ground program has a stable model is NP-complete =-=[MT91]-=-. For a nonground program P , the stable models are those of the ground instantiation of the program with respect to its Herbrand universe. The constraint interpretation of the rules provided by the s... |

142 | Experimental results on the crossover point in random 3-SAT
- Crawford, Auton
- 1996
(Show Context)
Citation Context ...tonian circuits) have been solved using the system [NS96a, NS96b, NS97]. In SAT problems [NS97] the system shows similar performance as the best Davis-Putnam implementations (e.g., Crawford's tableau =-=[CA96]-=-) even for hard instances such as the random 3-SAT problems in the phase transition region [CA96]. The system has been applied to the planning domain [DNK97] where it provides comparable and occasiona... |

139 | E cient implementation of the well-founded and stable model semantics
- Niemela, Simons
- 1996
(Show Context)
Citation Context ...tribute to the search space. This is different from, e.g., propositional satisfiability where each new atom can potentially increase the search space. This property is exploited in our implementation =-=[NS96a]-=-. (iii) Stable models can be approximated using wellfounded models [VGRS91]. We have generalized this approximation scheme so that stable models can be dynamically approximated in each point of the se... |

137 | Constraint logic programming - Jaar, Lassez - 1987 |

124 | Complexity results for planning - Bylander - 1991 |

118 | The KR system dlv: Progress report comparisons and benchmarks - Eiter, Leone, et al. - 1998 |

115 | Encoding planning problems in nonmonotonic logic programs
- Dimopoulos, Nebel, et al.
- 1997
(Show Context)
Citation Context ...m implementations (e.g., Crawford's tableau [CA96]) even for hard instances such as the random 3-SAT problems in the phase transition region [CA96]. The system has been applied to the planning domain =-=[DNK97]-=- where it provides comparable and occasionally significantly better performance than the best general purpose planners such as Graphplan. In order to provide a flavor of the performance of the system ... |

69 | Default reasoning system deres - Cholewinski, Marek, et al. - 1996 |

51 | Using logic programs with stable model semantics to solve deadlock and reachability problems for 1-safe petri nets - Heljanko - 1999 |

47 | Computation of stable models and its integration with logical query processing - Chen, Warren - 1996 |

47 |
A rational reconstruction of nonmonotonic truth maintenance systems
- Elkan
- 1990
(Show Context)
Citation Context ...ct, stable models have been shown to correspond exactly to the models computed by a justification-based truth maintenance system (TMS) when logic programming rules are seen as justifications in a TMS =-=[Elk90]-=- and to default extensions when rules are treated as default rules in Reiter's default logic [GL90]. The rest of the paper is organized as follows. First we show that traditional Boolean constraints, ... |

44 | Mixed integer programming methods for computing non-monotonic deductive databases - Bell, Nerode, et al. - 1994 |

42 | NP-SPEC: An executable specification language for solving all problems in NP - Cadoli, Palopoli, et al. - 1999 |

37 | Linear-time algorithms for testing the satis of propositional Horn formulae - Dowling, Gallier - 1984 |

37 | The Stanford GraphBase - Knuth - 1993 |

36 | Experimenting with nonmonotonic reasoning - Cholewinski, Marek, et al. - 1995 |

31 | WFS + branch and bound = stable models - Subrahmanian, Nau, et al. - 1995 |

31 | An abstract machine for computing the well-founded semantics - Sagonas, Swift, et al. - 1996 |

29 | Towards efficient default reasoning, in - Niemelä - 1995 |

29 | Towards constraint satisfaction through logic programs and the stable model semantics, Research report A47 - Simons - 1997 |

28 | Experimental results on the crossover point - Crawford, Auton - 1996 |

25 | Fully local and efficient evaluation of alternating fixed points - LIU, RAMAKRISHNAN, et al. - 1998 |

22 | Implementation of Local Grounding for Logic Programs with Stable Model Semantics - Syrjanen - 1998 |

17 | ACLP: Flexible solutions to complex problems, in
- Kakas, Mourlas
- 1997
(Show Context)
Citation Context ... the necessary constraint solvers into a logic programming system. This constraint logic programming paradigm [JL87] has been extended to include nonmonotonic reasoning capabilities such as abduction =-=[KM97]-=-. However, the constraint logic programming paradigm differs significantly from our approach where the rules have a declarative semantics and can be understood themselves as constraints. Hence in our ... |

15 | Circumscribing DATALOG: Expressive power and complexity - Cadoli, Palopoli - 1998 |

7 | Iterative belief revision in extended logic programming, Theor
- You, Cartwright, et al.
- 1996
(Show Context)
Citation Context ...and (iii) finally we include the rules satisfied / c 1 ; : : : ; c n f / not f; not satisfied where f is a new atom and c 1 ; : : : ; c n are all the atoms introduced for the clauses in S. You et al. =-=[YCL96]-=- present a reduction from propositional satisfiability to logic programs which is based on similar ideas as the mapping above but they use as the target language extended logic programs (with classica... |

7 | Fully local and ecient evaluation of alternating points - Liu, Ramakrishnan, et al. - 1998 |

6 | Towards ecient default reasoning - Niemela - 1995 |

4 | NP-SPEC: An executable speci language for solving all problems in NP - Cadoli, Palopoli, et al. - 1999 |

4 | Linear-time Algorithms for Testing the Satisfiablity of Propositional Horn Formulae - Dowling, Gallier - 1984 |

4 | and Miroslaw Truszczy nski. Autoepistemic logic - Marek - 1991 |

1 | Towards programming in default logic, in - Cholewiński - 1996 |

1 | alk er. T o w ards a theory of declarativ e kno wledge - Apt, W - 1988 |

1 | urst. F ast planning through planning graph analysis. A rtificial Intel ligenc e - Blum, F - 1997 |

1 | Cadoli and Luigi P alop oli. Circumscribing D A T ALOG: Expressiv e p o w er and complexit y . The or etic al Computer Scienc e - Marco - 1998 |

1 | o c e e dings of the First International Workshop on Pr actic al Asp e cts of De clar ative L anguages - Chen, arren - 1999 |