## FDPLL – A First-Order Davis-Putnam-Logeman-Loveland Procedure (2000)

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Venue: | CADE-17 – The 17th International Conference on Automated Deduction, volume 1831 of Lecture Notes in Artificial Intelligence |

Citations: | 32 - 8 self |

### BibTeX

@INPROCEEDINGS{Baumgartner00fdpll–,

author = {Peter Baumgartner},

title = {FDPLL – A First-Order Davis-Putnam-Logeman-Loveland Procedure},

booktitle = {CADE-17 – The 17th International Conference on Automated Deduction, volume 1831 of Lecture Notes in Artificial Intelligence},

year = {2000},

pages = {200--219},

publisher = {Springer}

}

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### Abstract

Abstract. FDPLL is a directly lifted version of the well-known Davis-Putnam-Logeman-Loveland (DPLL) procedure. While DPLL is based on a splitting rule for case analysis wrt. ground and complementary literals, FDPLL uses a lifted splitting rule, i.e. the case analysis is made wrt. non-ground and complementary literals now. The motivation for this lifting is to bring together successful first-order techniques like unification and subsumption to the propositionally successful DPLL procedure. At the heart of the method is a new technique to represent first-order interpretations, where a literal specifies truth values for all its ground instances, unless there is a more specific literal specifying opposite truth values. Based on this idea, the FDPLL calculus is developed and proven as strongly complete. 1

### Citations

1074 | A computing procedure for quantification theory - Davis, Putnam - 1962 |

739 | A Machine Program for Theorem Proving - Davis, Logemann, et al. - 1962 |

276 |
Symbolic Logic and Mechanical Theorem Proving
- Chang
- 1973
(Show Context)
Citation Context ...proves the existence of a concrete, fair strategy. Finally, some conclusions are drawn, including related work. 2 Preliminaries The usual notions ofsrst-order logic are applied in a way consistent to =-=[CL73]-=-. A literal is an atom or a negated atom. The letters K and L are reserved to denote literals. The complement of a literal L is L = A, if L = :A for some atom A, or else L = :L; by jLj the atom of L i... |

136 | AUTON: Experimental results on the crossover point in random 3-SAT
- CRAWFORD, LARRY
- 1996
(Show Context)
Citation Context ...ty, space eciency (\one branch at a time"), few inference rules (one is sucient), ecient and adaptable implementations (the most ecient systematical propositional methods are based on DPLL, e.g. =-=NTAB [CA96]-=- and SATO [Zha97]), existence of non-clausal versions [BBOS98], and, the possibility to immediately extract a model in case that no refutation exists. A goal of this work is to keep these features for... |

112 | SATCHMO: A theorem prover implemented in Prolog
- Manthey, Bry
- 1988
(Show Context)
Citation Context ...in Section 1). FDPLL was in uenced and is intended as a successor of the hyper tableau calculus [Bau98] (which in turn is a successor of the calculus in [BFN96], a calculus in the tradition of Satchmo=-=[MB88]). Am-=-ong other things, FDPLL improves on this calculus by not needing to store instances of clauses as the derivation proceeds { only the \current interpretation" needs to be kept. Beyond this, FDPLL ... |

100 | The TPTP problem library
- Sutcliffe, Suttner, et al.
- 1994
(Show Context)
Citation Context ... no built-in equality treatment yet). In the respective subdivisions SAT and NNE of the CASC-16 system competition 1999, FDPLL scored rank 4 of 6 and rank 4 of 10, respectively. From the TPTP library =-=[SSY94-=-], FDPLL can also solve some dicult unsatisable problems quite quickly (e.g. ANA002-4, the intermediate value theorem, in 3 seconds). The overall success rate is about 40% (Otter: 52%) for a time limi... |

72 | Hyper Tableaux
- Baumgartner, Furbach, et al.
(Show Context)
Citation Context ... in a similar way (cf. \description of FDPLL " in Section 1). FDPLL was in uenced and is intended as a successor of the hyper tableau calculus [Bau98] (which in turn is a successor of the calculu=-=s in [BFN96]-=-, a calculus in the tradition of Satchmo[MB88]). Among other things, FDPLL improves on this calculus by not needing to store instances of clauses as the derivation proceeds { only the \current interpr... |

64 | Hyperresolution and automated model building - Fermuller, Leitsch - 1996 |

57 | A computing procedure for quanti theory - Davis, Putnam - 1960 |

46 |
Properties of substitutions and unifications
- Eder
- 1985
(Show Context)
Citation Context ...d in the standard way in the simultaneous case as well. Further, a simultaneous most general unifier (simply called MGU as well) can be computed by iterative application of unify to Q1, . . .,Qn. See =-=[Ede85]-=- for a thorough treatment. Thus, we may suppose as given a simultaneous unification algorithm s-unify and write σ = s-unify({Q1, . . . , Qn}) in analogy to σ = unify(Q) above. For literals K and L def... |

45 |
Eliminating duplication with the hyperlinking strategy
- Plaisted
- 1992
(Show Context)
Citation Context ...qually to the disconnection method [Bil96]. Also, no model computation result was given for this calculus. Also related are Plaisted's hyper-linking calculi: the semantic hyper-linking calculus (SHL) =-=[LP92-=-] proceeds by searching in a guided way for (not necessarily ground) instances of input clauses, which are tested for unsatisability by a propositional DPLL procedure. Much of what was said about hype... |

31 | Hyper Tableaux | The Next Generation
- Baumgartner
- 1998
(Show Context)
Citation Context ... related to FDPLL in the sense that variables are treated in a similar way (cf. \description of FDPLL " in Section 1). FDPLL was in uenced and is intended as a successor of the hyper tableau calc=-=ulus [Bau98]-=- (which in turn is a successor of the calculus in [BFN96], a calculus in the tradition of Satchmo[MB88]). Among other things, FDPLL improves on this calculus by not needing to store instances of claus... |

23 | Ordered semantic hyper-linking
- Plaisted, Zhu
- 1997
(Show Context)
Citation Context ... DPLL in SHL by FDPLL, or picking up the idea of guided instance generation in SHL to improve FDPLL. However, this is future work. Quite dierent is the ordered semantic hyper linking (OSHL) calculus [=-=PZ97]. OSH-=-L has many interesting features, for instance \semantical guidance". In the intersection with FDPLL, it can be described as a calculus that applies unitresulting resolution as long as possible, a... |

20 | Model Building by Resolution - Fermuller, Leitsch - 1992 |

18 | Decision Procedures using Model Building Techniques
- Caferra, Peltier
- 1996
(Show Context)
Citation Context ...ost advancedsrst-order tableau system tailored for model computation is Ramcet [Pel99], which is a successor of Peltier's and his coworkers resolution calculus and previous tableaux calculi (see e.g. =-=[CP95]). As-=- a drawback, Ramcet needs additional inference rules for model computation. In particular, the \model explosion" rule seems problematic, as it branches out wrt. the whole signature of the formula... |

17 | Eliminating the irrelevant from mechanical proofs - Davis |

14 |
and François Bry. SATCHMO: a theorem prover implemented in Prolog
- Manthey
- 1988
(Show Context)
Citation Context ...n Section 1). FDPLL was influenced and is intended as a successor of the hyper tableau calculus [Bau98] (which in turn is a successor of the calculus in [BFN96], a calculus in the tradition of Satchmo=-=[MB88]-=-). Among other things, FDPLL improves on this calculus by not needing to store instances of clauses as the derivation proceeds – only the “current interpretation” needs to be kept. Beyond this, FDPLL ... |

13 |
The disconnection method
- Billon
(Show Context)
Citation Context ...single inference rule. The latter is more general and \builds in" standard improvements like factorization automatically. What was said about hyper tableau applies equally to the disconnection me=-=thod [Bil96]-=-. Also, no model computation result was given for this calculus. Also related are Plaisted's hyper-linking calculi: the semantic hyper-linking calculus (SHL) [LP92] proceeds by searching in a guided w... |

12 |
Ilkka Niemelä. Hyper Tableaux
- Baumgartner, Furbach
(Show Context)
Citation Context ... in a similar way (cf. “description of FDPLL” in Section 1). FDPLL was influenced and is intended as a successor of the hyper tableau calculus [Bau98] (which in turn is a successor of the calculus in =-=[BFN96]-=-, a calculus in the tradition of Satchmo[MB88]). Among other things, FDPLL improves on this calculus by not needing to store instances of clauses as the derivation proceeds – only the “current interpr... |

11 | 1999], A confluent connection calculus
- Baumgartner, Eisinger, et al.
(Show Context)
Citation Context ... strong completeness theorem holds). While these properties go without a saying for propositional DPLL, they are an issue for certain first-order methods, e.g. tableau and connection calculi (but see =-=[BEF99]-=- for a proof confluent strongly complete connection calculus). Beyond this, FDPLL is known to be a decision procedure for the Bernays-Schönfinkel class, i.e. clause logic without function symbols but ... |

7 |
Pruning the search space and extracting more models in tableaux
- Peltier
- 1999
(Show Context)
Citation Context ... enumeration with calls to the resolution procedure again in order to determine the \next" ground literal. The probably most advancedsrst-order tableau system tailored for model computation is Ra=-=mcet [Pel99]-=-, which is a successor of Peltier's and his coworkers resolution calculus and previous tableaux calculi (see e.g. [CP95]). As a drawback, Ramcet needs additional inference rules for model computation.... |

6 |
A con connection calculus
- Baumgartner, Eisinger, et al.
- 1999
(Show Context)
Citation Context ... a strong completeness theorem holds). While these properties go without a saying for propositional DPLL, they are an issue for certainsrst-order methods, e.g. tableau and connection calculi (but see =-=[BEF9-=-9] for a proof con uent strongly complete connection calculus). Beyond this, FDPLL is known to be a decision procedure for the Bernays-Schonnkel class, i.e. clause logic without function symbols but c... |

4 |
Working with Arms: Complexity Results on Atomic Representations of Herbrand Models
- Gottlob, Pichler
- 1998
(Show Context)
Citation Context ...ality treatment and improved termination behavior to name a few. On the theoretical level, the relationship between the model representation capabilities in FDPLL and the atomic model representationss=-=[GP98-=-] used in the resolution and tableau world should be claried. Acknowledgments. I am grateful to the members of our group for discussions about FDPLL. David Plaisted, Mark Stickel and Ryuzo Hasegawa re... |

3 | Integration und Uniformierung von Methoden des tableaubasierten Theorembeweisens - Beckert - 1998 |

3 |
Properties of substitutions and uni
- Eder
- 1985
(Show Context)
Citation Context ... the standard way in the simultaneous case as well. Further, a simultaneous most general unier (simply called MGU as well) can be computed by iterative application of unify to Q 1 ; : : : ; Qn . See [=-=Ede-=-85] for a thorough treatment. Thus, we may suppose as given a simultaneous unication algorithm s-unify and write = s-unify(fQ 1 ; : : : ; Qng) in analogy to = unify(Q) above. For literals K and L de... |

2 |
SATO: An Efficient Propositional Theorem Prover
- Zhang
- 1997
(Show Context)
Citation Context ...ranch at a time”), few inference rules (one is sufficient), efficient and adaptable implementations (the most efficient systematical propositional methods are based on DPLL, e.g. NTAB [CA96] and SATO =-=[Zha97]-=-), existence of non-clausal versions [BBOS98], and, the possibility to immediately extract a model in case that no refutation exists. A goal of this work is to keep these features for the lifted versi... |

1 |
Volume I, Chapter 5: Compressions and Extensions
- Bibel, Bruning, et al.
- 1998
(Show Context)
Citation Context ...les (one is sucient), ecient and adaptable implementations (the most ecient systematical propositional methods are based on DPLL, e.g. NTAB [CA96] and SATO [Zha97]), existence of non-clausal versions =-=[BBOS98]-=-, and, the possibility to immediately extract a model in case that no refutation exists. A goal of this work is to keep these features for the lifted version FDPLL. FDPLL is in particular space ecient... |

1 |
SATO: An Ecient Propositional Theorem Prover
- Zhang
(Show Context)
Citation Context ...y (\one branch at a time"), few inference rules (one is sucient), ecient and adaptable implementations (the most ecient systematical propositional methods are based on DPLL, e.g. NTAB [CA96] and =-=SATO [Zha97]-=-), existence of non-clausal versions [BBOS98], and, the possibility to immediately extract a model in case that no refutation exists. A goal of this work is to keep these features for the lifted versi... |