## The Differential Fixpoint of General Logic Programs (1996)

Venue: | Proc. of the Workshop DDLP'96 on Deductive Databases and Logic Programming. 4th Workshop in conjunction with JICSLP'96 |

Citations: | 2 - 2 self |

### BibTeX

@INPROCEEDINGS{Zukowski96thedifferential,

author = {Ulrich Zukowski and Burkhard Freitag},

title = {The Differential Fixpoint of General Logic Programs},

booktitle = {Proc. of the Workshop DDLP'96 on Deductive Databases and Logic Programming. 4th Workshop in conjunction with JICSLP'96},

year = {1996},

pages = {45--56}

}

### OpenURL

### Abstract

We present a version of the alternating fixpoint procedure that is fully incremental. Using ideas of partial evaluation techniques we can compute the well-founded model of logic programs with negation bottom-up without any recomputations. Further extensions of the semantics, e.g. to stable models or disjunctive programs are possible this way. We show how to implement the algorithm efficiently using index-based data structures and describe an extension to handle magic set transformed programs. This set-oriented bottomup algorithm is compatible with the well-known optimizations of deductive databases, e.g. semi-naive fixpoint iteration, and of relational databases, e.g. index techniques that enable the processing of large amounts of data. Thus, a bottom-up alternative to the already known efficient top-down methods for the well-founded semantics seems to be feasible. 1 Introduction A very influential and well-accepted semantics for logic programs with negation is the wellfounded semanti...

### Citations

858 | The Well-Founded Semantics for General Logic Programs
- Gelder, Ross, et al.
- 1991
(Show Context)
Citation Context ...nded semantics seems to be feasible. 1 Introduction A very influential and well-accepted semantics for logic programs with negation is the wellfounded semantics (WFS) introduced by Van Gelder et. al. =-=[VGRS91]-=-. Van Gelder also proposed the alternating fixpoint procedure [VG93] as a natural evaluation method for the well-founded semantics. Kemp et. al. [KSS95] defined the doubled program approach as an impl... |

249 | On the Power of Magic
- Beeri, Ramakrishnan
- 1987
(Show Context)
Citation Context ...s contained in I. We rely on the definition of the well-founded partial model of P denoted by W P as given in [VGRS91]. We further assume familiarity with the concepts of the magic set transformation =-=[BR91]-=-. 3 Alternating Fixpoint In this section we recall the definition of the alternating fixpoint procedure [VG93] and its modified version used in the doubled program approach [KSS95]. To this end, we ne... |

212 | The alternating fixpoint of logic programs with negation
- Gelder
- 1989
(Show Context)
Citation Context ... and well-accepted semantics for logic programs with negation is the wellfounded semantics (WFS) introduced by Van Gelder et. al. [VGRS91]. Van Gelder also proposed the alternating fixpoint procedure =-=[VG93]-=- as a natural evaluation method for the well-founded semantics. Kemp et. al. [KSS95] defined the doubled program approach as an implementation method of the alternating fixpoint that incorporates dedu... |

101 | Modular Stratification and Magic Sets for Datalog Programs With Negation - Ross - 1990 |

81 | Efficient top-down computation of queries under the well-founded semantics - Chen, Swift, et al. - 1995 |

61 | Query Evaluation under the Well Founded Semantics - Chen, Warren - 1993 |

45 | Disjunctive Semantics based upon Partial and Bottom-Up Evaluation
- Brass, Dix
- 1995
(Show Context)
Citation Context ...1/:\DeltaC 1 ; : : : ; Am /:\DeltaC m 2 I and C = fB 1 ; : : : ; B n g [ S m i=1 C i g 2 The conditional fixpoint operator derives the same possible answers as the alternating fixpoint procedure (see =-=[BD95a]-=- for a deeper comparison). But when information about the truth of the conditions becomes available, the set does not need to be recomputed, but it can be transformed directly at the syntactical level... |

36 |
Logic programming as constructivism: A formalization and its application to databases
- Bry
- 1989
(Show Context)
Citation Context ...an be derived incrementally, some information about possible answers needs to be recomputed in every iteration step. Thus, even some very simple programs are evaluated with suboptimal efficiency. Bry =-=[Bry89]-=- and Dung and Kanchanasut [DK89] introduced independently the notion of conditional facts and the conditional fixpoint procedure. Brass and Dix [BD95a, BD95b] extended this work to a more general part... |

31 | Controlling the search in bottom-up evaluation
- Ramakrishnan, Srivastava, et al.
- 1992
(Show Context)
Citation Context ...her bottom-up approaches for the well-founded semantics are based on the alternating fixpoint as well, e.g. the well-founded ordered search algorithm [SS93], that extends the ordered search algorithm =-=[RSS92]-=- which is limited to the class of modularly stratified programs [Ros94]. Although the magic set transformation does not in general preserve the semantics of logic programs with negation, the alternati... |

26 | Bottom-Up Evaluation and Query Optimization of Well-Founded models. Theoretical computer science
- Kemp, Srivastava, et al.
- 1995
(Show Context)
Citation Context ...mantics (WFS) introduced by Van Gelder et. al. [VGRS91]. Van Gelder also proposed the alternating fixpoint procedure [VG93] as a natural evaluation method for the well-founded semantics. Kemp et. al. =-=[KSS95]-=- defined the doubled program approach as an implementation method of the alternating fixpoint that incorporates deductive database optimizations such as semi-naive bottom-up iteration. Most other bott... |

25 | A General Approach to Bottom-Up Computation of Disjunctive Semantics - Brass, Dix - 1995 |

14 |
Well-founded ordered search
- Stuckey, Sudarshan
- 1993
(Show Context)
Citation Context ...ns such as semi-naive bottom-up iteration. Most other bottom-up approaches for the well-founded semantics are based on the alternating fixpoint as well, e.g. the well-founded ordered search algorithm =-=[SS93]-=-, that extends the ordered search algorithm [RSS92] which is limited to the class of modularly stratified programs [Ros94]. Although the magic set transformation does not in general preserve the seman... |

10 |
A natural semantics of logic programs with negation. Pages 70–80 of
- Dung, Kanchansut
- 1989
(Show Context)
Citation Context ... information about possible answers needs to be recomputed in every iteration step. Thus, even some very simple programs are evaluated with suboptimal efficiency. Bry [Bry89] and Dung and Kanchanasut =-=[DK89]-=- introduced independently the notion of conditional facts and the conditional fixpoint procedure. Brass and Dix [BD95a, BD95b] extended this work to a more general partial evaluation framework. They s... |

1 | Computing the well-founded model by partial evaluation - Brass, Zukowski - 1996 |