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## Splitting a Logic Program (1994)

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Venue: | Principles of Knowledge Representation |

Citations: | 293 - 15 self |

### Citations

2070 | Foundations of Logic Programming - Lloyd - 1987 |

1811 | The Stable Model Semantics for Logic Programming
- Gelfond, Lifschitz
- 1988
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Citation Context ...re positive, then we can dene f(L) as the smallest such that L 2 U . Proposition 3 leads to a new proof of a familiar property of stratied nondisjunctive programs without classical negation ( [ =-=Gelfond and Lifschitz, 1988-=- ] , Corollary 1): Proposition 4. Every stratied, nondisjunctive program without classical negation has a unique answer set. Proof. Let P be a stratied, nondisjunctive program without classical nega... |

1631 | A logic for default reasoning - Reiter - 1980 |

1063 | Negation as Failure - CLARK - 1978 |

1032 | Classical Negation in Logic Programs and Disjunctive Databases
- Gelfond, Lifschitz
- 1991
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Citation Context ... [1992] to the denition of a \stratied pair," and Dix [1992] to the denitions of \relevance" and \modularity." In this paper, we discuss splitting in the context of the \answer set semantics" of [ =-=Gelfond and Lifschitz, 1991-=- ] . The main theorem shows how computing the answer sets for a program can be simplied when the program is split into parts. The programs covered by the theorem may use both negation as failure and ... |

991 | The Well-Founded Semantics for General Logic Programs - Gelder, Ross, et al. - 1991 |

801 | The semantics of predicate logic as a programming language - Emden, Kowalski - 1976 |

734 | A lattice-theoretical fixpoint theorem and its applications - Tarski - 1955 |

681 | Towards a theory of declarative knowledge - Apt, Blair, et al. - 1988 |

611 | The role of abduction in logic programming - Kakas, Kowalski, et al. - 1998 |

526 | Applications of circumscription to formalizing common sense knowledge - McCarthy - 1986 |

492 | Semantical considerations on non-monotonic logic - Moore - 1985 |

483 | First-Order Logic and Automated Theorem Proving, 2nd Edition - Fitting - 1996 |

412 | Representing action and change by logic programs - Gelfond, Lifschitz - 1993 |

381 | Programs with Common Sense - McCarthy - 1968 |

366 |
Logic Programs with Classical Negation
- GELFOND, LIFSCHITZ
- 1990
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Citation Context ... programs instead of programs without classical negation, and about head-consistent nondisjunctive programs instead of normal programs. 5 Nondisjunctive programs are also known as extended programs [ =-=Gelfond and Lifschitz, 1990-=- ] . The objects we here call logic programs are also known as extended disjunctive programs [ Gelfond and Lifschitz, 1991 ] . 4 3 Signings Denition. Let P be a constraint-free program, with S a subs... |

322 | On closed world data bases - Reiter - 1978 |

278 | On the declarative semantics of deductive databases and logic programs - Przymusinski - 1988 |

273 |
Nonmonotonic Logic and Temporal Projection
- HANKS, MCDERMOTT
- 1987
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Citation Context ...related to signings can be of use in showing the translation correct. Full details are available in the longer version of the paper. We will consider yet another variant of the Yale Shooting domain [ =-=Hanks and McDermott, 1987-=- ] , which can be called the \two-guns" domain. There is a pilgrim and a turkey. The pilgrim has two guns. Initially, the turkey is alive, but if the pilgrimres a loaded gun, the turkey dies. Further... |

270 | R.N.: Logic programming and negation: A survey - Apt, Bol - 1994 |

247 | Towards a logical reconstruction of relational database theory - Reiter - 1984 |

240 | Logic programming and knowledge representation - Baral, Gelfond - 1994 |

194 | Foundations of Disjunctive Logic Programming - Lobo, Minker, et al. - 1992 |

181 | Acyclic programs - Apt, Bezem - 1990 |

168 | Stable Semantics for Disjunctive Programs - Przymusinski - 1991 |

166 | Consistency of Clark’s completion and existence of stable models
- Fages
- 1994
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Citation Context ...elate the idea of splitting to the syntactic property of programs called \order-consistency"; that property is important in view of the fact that it implies the existence of at least one answer set [ =-=Fages, 1994-=- ] . Order-consistent programs can be characterized in terms of splitting also. After a brief review of the syntax and semantics of (disjunctive) programs (Section 2), we state the special case of the... |

139 | Negation as failure using tight derivations for general logic programs - Gelder - 1988 |

129 | Well founded semantics for logic programs with explicit negation
- Schweimeier, Pereira, et al.
- 1992
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Citation Context ...correspond, essentially, to a proposal by Przymusinski [1990], extending the well-founded semantics to nondisjunctiveprograms with classical negation. Further work in this direction can be found in [ =-=Pereira and Alferes, 1992-=- ] . 6 This theorem shows, for instance, that if a nondisjunctive program P with signing S is consistent, then P has a \standard" answer set expressible in terms of WF ? (P ), WF > (P ) and S. We also... |

120 | On stratified autoepistemic theories - Gelfond - 1987 |

104 | Answer sets in general nonmonotonic reasoning (preliminary report - Lifschitz, Woo - 1992 |

99 | Extended stable semantics for normal and disjunctive programs. Pages 459–477 of - Przymusinski - 1990 |

90 | Signed data dependencies in logic programs - Kunen - 1989 |

85 | Efficient top-down computation of queries under the well-founded semantics - CHEN, SWIFT, et al. - 1995 |

79 | clause queries and generalizations - Horn - 1985 |

74 | Negation in logic programming - Shepherdson - 1987 |

62 | Representing Incomplete Knowledge in Abductive Logic Programming - Denecker, Schreye - 1995 |

59 | Formalizing Common Sense: Papers by - McCarthy - 1990 |

59 | Disjunctive deductive databases - Fernandez, Minker - 1992 |

55 | A Survey of Deductive Database Systems - Ramakrishnan, Ullman - 1994 |

46 |
A lattice-theoretical theorem and its applications
- Tarski
- 1955
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Citation Context ...a nondisjunctive program P are thesxpoints of P . It is easy to verify that P is anti-monotone. Consequently, 2 P is monotone. Because 2 P is monotone, we know by the Knaster{Tarski theorem [ =-=Tarski, 1955-=- ] that 2 P has a least and a greatestsxpoint. Denition. Let P be a nondisjunctive program. By WF ? (P ) we denote the leastsxpoint of 2 P , and by WF > (P ) the greatest. If P is a normal progra... |

45 | Representing actions in logic programming and its applications in database updates - Dung - 1993 |

43 | Minimalism subsumes default logic and circumscription - Bidoit, Froidevaux - 1987 |

41 | Alferes. Non–monotonic reasoning with logic programming - Pereira, cio, et al. - 1993 |

31 | Classifying semantics of disjunctive logic programs (extended abstract - Dix - 1992 |

30 | On positive occurrences of negation as failure - Inoue, Sakama - 1994 |

29 | Continuity, consistency and completeness properties for logic programs. Pages 571–584 of - Cavedon - 1989 |

29 | Reasoning with Negative Information I - Strong Negation - Pearce, Wagner - 1990 |

29 | Restricted Monotonicity
- lifschitz
- 1993
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Citation Context ...ograms in the same language, both with signing S. If h S (P ) h S (Q) and h S (Q) h S (P ), then Cn(P ) \ S Cn(Q) \ S. 11 The notion of restricted monotonicity is given a general denition in [ =-=Lifschitz, 1993-=- ] . 12 As subsequent discussion will illustrate, this third condition makes the denition of the ordering for rules more general than that used in [ Turner, 1993 ] , even when we consider only nond... |

28 | Completed logic programs and their consistency - Sato - 1990 |

26 | On the Relations between Stable and Well-Founded Semantics of Logic Programs - DUNG - 1992 |

16 | consistent and computable completions for unrestricted logic programs - Tight - 1993 |

15 | Towards a Programming Methodology Founded on Partial Deduction - Komorowski - 1990 |

10 |
Halina Przymusi 'nska, and Miroslaw Truszczy'nski. Disjunctive defaults
- Gelfond, Lifschitz
- 1991
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Citation Context ...a family of programs for reasoning about action. 1 Introduction In this paper we explore the notion of a \signing" of a logic program, in the framework of the answer set (or stable model) semantics [ =-=Gelfond and Lifschitz, 1991-=- ] . In particular, we generalize and extend the notion of a signing, and show that even for programs with classical negation and disjunction the existence of a signing is a simple syntactic criterion... |

10 | A monotonicity theorem for extended logic programs
- Turner
- 1993
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Citation Context ...rogram, so when Gelfond and Lifschitz [1993] recast the denition to apply directly to the rules of innite propositional normal programs, the notion of a signing was made strictly more general. In [ =-=Turner, 1993-=- ] the denition was extended to the class of nondisjunctive programs with classical negation. In this paper it is generalized slightly and further extended to apply to programs with disjunction as we... |

7 | A complete calculus for pure Prolog - Mints - 1986 |

6 | Loop checking and the well-founded semantics - Lifschitz, McCain, et al. - 1995 |

6 | Constructive Negation and Grounding - SLDNF - 1995 |

6 | Language independence and language tolerance in logic programs
- McCain, Turner
- 1993
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Citation Context ...sefulness of splitting is illustrated in this paper by several applications. The Splitting Set Theorem is also employed in the paper \Language Independence and Language Tolerance in Logic Programs" [ =-=McCain and Turner, 1993-=- ] , which appears in this volume. It is used there to prove one of the central results|Theorem 6.1, which shows that, under some conditions, one can ignore the fact that the language of a logic progr... |

3 | Several formal systems of the Logic Programming - Mints - 1990 |

2 |
De in Epistemic Speci
- Gelfond, Przymusinska
- 1991
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Citation Context ...disjunctive heads. The usefulness of the concept of splitting for the investigation of answer sets is illustrated by several applications. First, we generalize a conservative extension theorem from [ =-=Gelfond and Przymusinska, 1991-=- ] and the theorem on the closed world assumption from [ Gelfond and Lifschitz, 1991 ] , and show that these generalizations can be easily proved as consequences of the splitting theorem. Second, (loc... |

2 | Actions and Speci - Holldobler, Thielscher - 1993 |

1 |
Halina Przymusinska and Teodor Przymusinski. Weakly perfect model semantics for logic programs
- Przymusinska, Przymusinski
- 1988
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Citation Context ...of P . In fact, this step-by-step reduction to a series of positive programs is sometimes applicable even when P is not stratied. This observation leads to the notion of a weakly stratied program [ =-=Przymusinska and Przymusinski, 1988-=- ] . The notion of a stratication has been also extended in two other directions. First, it may be possible to split a program into an innite|or even transnite|sequence of parts, instead of asnite ... |

1 | Taisuke Sato. Completed logic programs and their consistency - Kaufmann, Mateo, et al. - 1988 |

1 |
Towards eective evaluation of general logic programs
- Chen, Warren
- 1993
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Citation Context ...t due to Dung [1992], who has shown that the answer set and well-founded semantics coincide for \bottom-stratied & top-strict" programs. Notice that this result shows that interpreters such as SLG [ =-=Chen and Warren, 1993-=- ] , which compute the well-founded semantics, can also be used to compute the consequences of such programs under the answer set semantics. 1 4. There is a monotonicity theorem for signed normal prog... |