## A First-Order Logic Davis-Putnam-Logemann-Loveland Procedure

Citations: | 38 - 6 self |

### BibTeX

@MISC{Baumgartner_afirst-order,

author = {Peter Baumgartner},

title = {A First-Order Logic Davis-Putnam-Logemann-Loveland Procedure},

year = {}

}

### OpenURL

### Abstract

The Davis-Putnam-Logemann-Loveland procedure (DPLL) was introduced in the early

### Citations

2408 | Model Checking - Clarke, Grumberg, et al. - 1999 |

1855 |
Foundations of Logic Programming
- Lloyd
- 1987
(Show Context)
Citation Context ... branches for extension. This choice is completely don't-care nondeterministic, and it corresponds to the selection function used in SLD-Resolution for determing the next subgoal to be expanded (see (=-=Lloyd 1987)). A good-=- branch selection function is the one that selects the "`leftmost" open branch. Since closed branches can be deleted from memory, the resulting tree is degenerated into a linear list then. T... |

1075 |
A computing procedure for quantification theory
- Davis, Putnam
- 1960
(Show Context)
Citation Context ...1968), the Analytic Tableau calculus (Smullyan 1968), and the important Davis-Putnam procedure and its later but equally famous variant now called the DavisPutnam -Logemann-Loveland procedure (DPLL) (=-=Davis and Putnam 1960; Davis, L-=-ogemann, and Loveland 1962; Davis 1963; Chinlund, Davis, Hinman, and McIlroy 1964). Of course, numerous other methods came up, and the "old" methods have been subject to further analysis, ex... |

945 |
A machine-oriented logic based on the resolution principle
- Robinson
- 1965
(Show Context)
Citation Context ...tificial Intelligence. The beginnings date back about 40 years now, and many calculi popular today have their roots in the 1960s. Among the best-known ones from that time are the Resolution calculus (=-=Robinson 1965-=-a), the Model Elimination (ME) calculus (Loveland 1968), the Analytic Tableau calculus (Smullyan 1968), and the important Davis-Putnam procedure and its later but equally famous variant now called the... |

873 | A theory of diagnosis from first principles
- Reiter
- 1987
(Show Context)
Citation Context ...ourses (Baumgartner and Kuhn 2000), in deductive databases models come up as materialized views or help to solve database updates (Bry 1990; Aravindan and Baumgartner 2000), in model based diagnosis (=-=Reiter 1987-=-) a model points at possibly faulty components of a system, and so on. In sum, model computation is among the most versatile services an automated deduction system can offer. Consequently, quite some ... |

815 |
Circumscription: A Form of Nonmonotonic Reasoning
- McCarthy
- 1980
(Show Context)
Citation Context ...essary from a theoretical point of view, this unique name assumption should be built-in to FDPLL. In some domains, minimal models are needed. A respective general reasoning scheme is circumscription (=-=McCarthy 1985-=-), which allows to insist on minimality of certain interesting predicates. For instance, in diagnosis applications, one may insist on explanations of faulty behavior in terms of a minimum number of fa... |

740 | A machine program for theorem proving - Davis, Logemann, et al. - 1962 |

521 | Pushing the envelope: planning, propositional logic and stochastic search
- Kautz, Selman
(Show Context)
Citation Context ... Schmidt 2000) competes very well with dedicated systems. But also model computation within classical first-order logic by itself has many important application areas. For instance, Kautz and Selman (=-=Kautz and Selman 1996-=-) propose a first-order logic formulation of planning problems that can be translated to a propositional logic model computation problem, in natural language discourse representation (Blackburn, Bos, ... |

276 |
Symbolic Logic and Mechanical Theorem Proving
- Chang
- 1973
(Show Context)
Citation Context ... as the "Davis-Putnam" procedure, because the differences were considered as purely pragmatic and not fundamental (Davis 2001). 2 This should be taken with a grain of salt: already in the ea=-=rly book (Chang and Lee 1973) there is-=- a comparable method with directly lifted data structures. The difficulties with this approach are discussed in Section 6.1. 3 Applications of DPLL. The "old", purely propositional part of D... |

255 | A correspondence theory for terminological logics: Preliminary report
- Schild
- 1991
(Show Context)
Citation Context ...y an ever increasing role for such important application areas like the "semantic web". Technically, description logics can be understood as syntactical variant of certain propositional moda=-=l logics (Schild 1991-=-). Sophisticated implementations like the FaCT and DLP systems (Horrocks and Patel-Schneider 1998) are based on propositional modal logics Tableau calculi. Now, although propositional Tableau calculi ... |

169 | GXL: Toward a Standard Exchange Format - HOLT, WINTER, et al. |

154 | Resolution theorem proving
- BACHMAIR, GANZINGER
(Show Context)
Citation Context ... fairness and concrete resource bounds. For Resolution calculi, e.g., one of the earliest strategies is "level saturation", where, essentially, inferenceres to be carried out are put in a qu=-=eue (see (Bachmair and Ganzinger 2001-=-) for an overview of resolution based theorem proving). Within the Tableau world, there are resource bounds that are based, e.g., on the depth of Tableaux (Letz and Stenz 2000) or on the number of var... |

137 | E cient implementation of the well-founded and stable model semantics
- Niemela, Simons
- 1996
(Show Context)
Citation Context ...is the best way to go. The set of clauses fed into the propositional prover may become too large, and many redundancies are not discovered. Even clever strategies as used e.g. in the S-models system (=-=Niemela and Simons 1996-=-) occasionally reach their limits. Some systems, like SATCHMO and its successors perform the reduction to propositional logic during proof search time, but the problems remain. For instance, suppose t... |

136 | AUTON: Experimental results on the crossover point in random 3-SAT
- CRAWFORD, LARRY
- 1996
(Show Context)
Citation Context ...LL. The "old", purely propositional part of DPLL is still among the most efficient methods for propositional logic 3 . A lot of effort has been spent on its analysis and on implementations (=-=see e.g. (Crawford and Auton 1996-=-; Zhang 1997), and, in particular, (Moskewicz, Madigan, Zhao, Zhang, and Malik 2001)), and the central ideas behind it have been grasped and developed further for application areas like description lo... |

112 | SATCHMO: A theorem prover implemented in Prolog
- Manthey, Bry
- 1988
(Show Context)
Citation Context ...s (of course, like for DPLL more generally, there are improvements that aim at a clever way of generating the ground instances (Gallo and Rago 1994)). In a similar way proceeds the SATCHMO procedure (=-=Manthey and Bry 1988), which o-=-pened the stage for a whole family of successor developments (Loveland, Reed, and Wilson 1995; Baumgartner, Furbach, and Niemela 1996, e.g.). The same holds for the "classical" Tableau calcu... |

95 | Building decision procedures for modal logics from propositional decision procedures - the case study of modal K(m
- Giunchiglia, Sebastiani
- 1996
(Show Context)
Citation Context ...positional DPLL procedure, it turns out that the explicit use of DPLL techniques considerably enhances the performance of respective systems (Horrocks and Patel-Schneider 1999). Another system, KSAT (=-=Giunchiglia and Sebastiani 2000-=-) directly generalizes the propositional DPLL procedure towards propositional modal logic 4 . The probably most important trend in software verification over the last ten years is (symbolic) model che... |

94 |
On matrices with connections
- Bibel
- 1981
(Show Context)
Citation Context ...cs, and there is considerable research activity on non-classical and on first6 order logic variants 6 . Contemporary Tableau calculi (Beckert 2000; Giese 2001, e.g.)), the related Connection calculi (=-=Bibel 1981-=-; Baumgartner, Eisinger, and Furbach 1999), and the special case of Model Elimination (Loveland 1968; Letz 1998) (which is among the best methods for theorem proving), they all do not even terminate o... |

87 |
First Order Logic
- Smullyan
- 1968
(Show Context)
Citation Context ...ve their roots in the 1960s. Among the best-known ones from that time are the Resolution calculus (Robinson 1965a), the Model Elimination (ME) calculus (Loveland 1968), the Analytic Tableau calculus (=-=Smullyan 1968-=-), and the important Davis-Putnam procedure and its later but equally famous variant now called the DavisPutnam -Logemann-Loveland procedure (DPLL) (Davis and Putnam 1960; Davis, Logemann, and Lovelan... |

78 | leantap: Lean tableau-based deduction
- Beckert, Posegga
- 1995
(Show Context)
Citation Context ...n based theorem proving). Within the Tableau world, there are resource bounds that are based, e.g., on the depth of Tableaux (Letz and Stenz 2000) or on the number of variants of formulas admissible (=-=Beckert and Posegga 1995-=-). In some cases, things may become quite subtle (see e.g. (Baumgartner, Eisinger, and Furbach 1999; Beckert 2000)). For FDPLL, a resource bound based on a maximal term depth is practical: 26 Definiti... |

72 | Hyper Tableaux - Baumgartner, Furbach, et al. |

69 |
First Order Logic and Automated Theorem Proving
- Fitting
- 1996
(Show Context)
Citation Context ... BS is not easy to find. Following are some considerations about established methods from the viewpoint of the BS class. A class of calculi that has "model building" at its heart are Tableau=-= calculi (Fitting 1990-=-; Beckert and Hahnle 1998). As indicated above, propositional Tableau calculi are successfully applied for e.g. description logics, and there is considerable research activity on non-classical and on ... |

64 |
Intensional updates: Abduction via deduction
- Bry
- 1990
(Show Context)
Citation Context ... different models can be kept to represent different readings of discourses (Baumgartner and Kuhn 2000), in deductive databases models come up as materialized views or help to solve database updates (=-=Bry 1990-=-; Aravindan and Baumgartner 2000), in model based diagnosis (Reiter 1987) a model points at possibly faulty components of a system, and so on. In sum, model computation is among the most versatile ser... |

64 |
Hyperresolution and automated model building
- Fermuller, Leitsch
- 1996
(Show Context)
Citation Context ...case no solution seems to be known 8 . But even in special cases, when Hyper-Resolution terminates and detects satisfiability, nontrivial post-processing is required to actually compute a model (see (=-=Fermuller and Leitsch 1996-=-)). Now, this I consider one of the strengths of FDPLL: FDPLL is a decision procedure for the BS class. Beyond this, in the satisfiable case FDPLL does not only terminate but also reports a model. Mor... |

55 | Optimising description logic subsumption
- Horrocks, Patel-Schneider
- 1999
(Show Context)
Citation Context ...alculi may already be seen as special instances of the propositional DPLL procedure, it turns out that the explicit use of DPLL techniques considerably enhances the performance of respective systems (=-=Horrocks and Patel-Schneider 1999-=-). Another system, KSAT (Giunchiglia and Sebastiani 2000) directly generalizes the propositional DPLL procedure towards propositional modal logic 4 . The probably most important trend in software veri... |

54 |
Mechanical Theorem Proving by Model Elimination
- Loveland
- 1968
(Show Context)
Citation Context ...40 years now, and many calculi popular today have their roots in the 1960s. Among the best-known ones from that time are the Resolution calculus (Robinson 1965a), the Model Elimination (ME) calculus (=-=Loveland 1968-=-), the Analytic Tableau calculus (Smullyan 1968), and the important Davis-Putnam procedure and its later but equally famous variant now called the DavisPutnam -Logemann-Loveland procedure (DPLL) (Davi... |

52 | On evaluating decision procedures for modal logic
- Hustadt, Schmidt
- 1997
(Show Context)
Citation Context ...rity, it is even easily "forgotten" that DPLL was conceived as a first-order logic proof procedure. 4 There seems to be no uniformly "best" approach, and there is dispute how to me=-=asure systems, cf. (Hustadt and Schmidt 1997). 5 A loo-=-k into recent proceedings of CAV, the Conference on Automated Verification, is recommended. 4 application within "planning" is sketched in the conclusions (Section 7). Currently, all these q... |

49 | Representation and Reasoning with Attributive Descriptions
- Nebel, Smolka
- 1989
(Show Context)
Citation Context ...o decidable fragments of first-order logic. Such translation schemes have been proposed for quite some logics and reasoning schemes for knowledge representation purposes, like for description logics (=-=Nebel and Smolka 1989-=-), for abduction (see (Konolige 1990; Inoue, Ohta, and Hasegawa 1993)), for reasoning under default negation (Prolog-like) principles (Inoue, Koshimura, and Hasegawa 1992), and for certain classes of ... |

49 | Modelling a concurrent ray-tracing algorithm using object-oriented Petri-Nets - Hutten, Philippi |

48 | Specification of Symbols and Implementation of Their Constraints in JKogge - Uhe, Rosendahl |

47 | Embedding negation as failure into a model generation theorem prover - Inoue, Koshimura, et al. |

47 | Furbach. Automated Deduction Techniques for the Management of Personalized Documents - Baumgartner, Ulrich |

47 | Applying GUPRO to GEOS – A Case Study - Lange, Sneed, et al. |

46 |
Properties of substitutions and unifications
- Eder
- 1985
(Show Context)
Citation Context ... most general unifier can be defined analogously as above. A simultaneous most general unifier (simply called MGU as well) can be computed by iterative application of unify to Q 1 ; : : : ; Qn . See (=-=Eder 19-=-85) for a thorough treatment. Thus, we may suppose as given a simultaneous unification algorithm s-unify and write = s-unify(fQ 1 ; : : : ; Qn g) in analogy to = unify(Q) above. 13 A sentence is a f... |

40 | Frieder Stolzenburg. Multiagent Systems Specification by UML Statecharts Aiming at Intelligent Manufacturing - Arai |

36 | MSPASS: Modal reasoning by translation and first-order resolution
- Hustadt, Schmidt
- 2000
(Show Context)
Citation Context ... a first-order logic prover is shown to be very competitive with dedicated systems for description logic reasoning. A competition among modal theorem provers showed that the MSPASS Resolution prover (=-=Hustadt and Schmidt 2000-=-) competes very well with dedicated systems. But also model computation within classical first-order logic by itself has many important application areas. For instance, Kautz and Selman (Kautz and Sel... |

36 |
Translation methods for non-classical logics – an overview
- Ohlbach
- 1993
(Show Context)
Citation Context ...990; Inoue, Ohta, and Hasegawa 1993)), for reasoning under default negation (Prolog-like) principles (Inoue, Koshimura, and Hasegawa 1992), and for certain classes of propositional modal logics (see (=-=Ohlbach 1993-=-)). This way may indeed be feasible also from a performance point of view. For instance, in (Paramasivam and Plaisted 1998) a first-order logic prover is shown to be very competitive with dedicated sy... |

32 | FDPLL—A first-order Davis–Putnam–Logemann–Loveland procedure
- Baumgartner
- 2000
(Show Context)
Citation Context ... kept to represent different readings of discourses (Baumgartner and Kuhn 2000), in deductive databases models come up as materialized views or help to solve database updates (Bry 1990; Aravindan and =-=Baumgartner 2000-=-), in model based diagnosis (Reiter 1987) a model points at possibly faulty components of a system, and so on. In sum, model computation is among the most versatile services an automated deduction sys... |

31 |
Semantically Guided First-Order Theorem Proving Using Hyper Linking
- Chu
- 1994
(Show Context)
Citation Context ...cked up and improved many years later, for instance, in the "partial instantiation prover" in (Chandru, Hooker, Shrivastava, and Rago 1998), or, earlier, in the Semantic Hyper Linking calcul=-=us (SHL) (Chu and Plaisted 1994-=-). SHL contains additional ingredients to guide the search that may drastically improve its performance. This calculus is the basis for the further improved Ordered Semantic Hyper Linking calculus (OS... |

31 |
SATCHMO: A Theorem Prover Implemented
- Manthey, Bry
- 1988
(Show Context)
Citation Context ...ys (of course, like for DPLL more generally, there are improvements that aim at a clever way of generating the ground instances (Gallo and Rago 1994)).In a similar way proceeds the SATCHMO procedure (=-=Manthey and Bry 1988-=-), which opened the stage for a whole family of successor developments (Loveland, Reed, and Wilson 1995;Baumgartner, Furbach, and Niemel"a 1996, e.g.). The same holds for the "classical" Tableau calcu... |

30 | Incremental closure of free variable tableaux
- Giese
- 2001
(Show Context)
Citation Context ...i are successfully applied for e.g. description logics, and there is considerable research activity on non-classical and on first6 order logic variants 6 . Contemporary Tableau calculi (Beckert 2000; =-=Giese 2001-=-, e.g.)), the related Connection calculi (Bibel 1981; Baumgartner, Eisinger, and Furbach 1999), and the special case of Model Elimination (Loveland 1968; Letz 1998) (which is among the best methods fo... |

30 | Resolution strategies as decision procedures
- Joyner
- 1976
(Show Context)
Citation Context ...re are approaches building on the Tableau calculus, like (Peltier 1999). The very interesting calculus in (Bry and Torge 1998) can even compute a finite model whenever one exists. But, starting with (=-=Joyner 1976-=-), by far the most work has been carried out in the context of the Resolution calculus (see (Tammet 1991; Leitsch 1993) as anchors). This discussion is continued in the following section, which concen... |

29 | The prehistory and early history of automated deduction
- Davis
- 1983
(Show Context)
Citation Context ...-- lifted data structures and the use of unification -- are not as dependent on one another as one might expect. This can be explained by a brief look to the history of DPLL and to related work (see (=-=Davis 1983-=-) for detailed account of the history of automated deduction, which also covers DPLL). This look also helps to explain the contributions of the present paper. In brief, unification has been integrated... |

28 |
Using resolution for deciding solvable classes and building finite models
- Tammet
- 1991
(Show Context)
Citation Context ...n (Bry and Torge 1998) can even compute a finite model whenever one exists. But, starting with (Joyner 1976), by far the most work has been carried out in the context of the Resolution calculus (see (=-=Tammet 1991-=-; Leitsch 1993) as anchors). This discussion is continued in the following section, which concentrates on a certain decidable subset of first-order logic. The Bernays-Sch onfinkel class. One of the mo... |

25 | SATCHMORE: SATCHMO with RElevancy - Loveland, Reed, et al. - 1995 |

23 | Ordered semantic hyper-linking
- Plaisted, Zhu
- 1997
(Show Context)
Citation Context ...ngredients to guide the search that may drastically improve its performance. This calculus is the basis for the further improved Ordered Semantic Hyper Linking calculus (OSHL) (Lee and Plaisted 1993; =-=Plaisted and Zhu 2000-=-). Both SHL and OSHL use the propositional DPLL part as a core component. The SHL-calculus is probably the first calculus in the family of modern instance-based calculi. Other such calculi are describ... |

22 | The search efficiency of theorem proving strategies: An analytical comparison
- Plaisted
- 1994
(Show Context)
Citation Context ...and improved many years later, for instance, in the "partial instantiation prover" in (Chandru, Hooker, Shrivastava, and Rago 1998), or, earlier, in the Semantic Hyper Linking calculus (SHL)=-= (Chu and Plaisted 1994-=-). SHL contains additional ingredients to guide the search that may drastically improve its performance. This calculus is the basis for the further improved Ordered Semantic Hyper Linking calculus (OS... |

21 |
Model elimination and connection tableau procedures
- Letz, Stenz
(Show Context)
Citation Context ...in a queue (see (Bachmair and Ganzinger 2001) for an overview of resolution based theorem proving). Within the Tableau world, there are resource bounds that are based, e.g., on the depth of Tableaux (=-=Letz and Stenz 2000-=-) or on the number of variants of formulas admissible (Beckert and Posegga 1995). In some cases, things may become quite subtle (see e.g. (Baumgartner, Eisinger, and Furbach 1999; Beckert 2000)). For ... |

20 | A deduction method complete for refutation and finite satisfiability
- Bry, Torge
- 1998
(Show Context)
Citation Context ...ng as possible, in order to guarantee the termination of the considered deduction system. There are approaches building on the Tableau calculus, like (Peltier 1999). The very interesting calculus in (=-=Bry and Torge 1998-=-) can even compute a finite model whenever one exists. But, starting with (Joyner 1976), by far the most work has been carried out in the context of the Resolution calculus (see (Tammet 1991; Leitsch ... |

20 |
Automated deduction with hyper-resolution
- Robinson
- 1965
(Show Context)
Citation Context ...tificial Intelligence. The beginnings date back about 40 years now, and many calculi popular today have their roots in the 1960s. Among the best-known ones from that time are the Resolution calculus (=-=Robinson 1965-=-a), the Model Elimination (ME) calculus (Loveland 1968), the Analytic Tableau calculus (Smullyan 1968), and the important Davis-Putnam procedure and its later but equally famous variant now called the... |

17 |
Eliminating the irrelevant from mechanical proofs
- Davis
(Show Context)
Citation Context ...he important Davis-Putnam procedure and its later but equally famous variant now called the DavisPutnam -Logemann-Loveland procedure (DPLL) (Davis and Putnam 1960; Davis, Logemann, and Loveland 1962; =-=Davis 1963; Chinlund-=-, Davis, Hinman, and McIlroy 1964). Of course, numerous other methods came up, and the "old" methods have been subject to further analysis, extension and improvement. Nethertheless, at the h... |