## Hyperresolution for guarded formulae (2000)

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### Other Repositories/Bibliography

Venue: | J. Symbolic Computat |

Citations: | 16 - 9 self |

### BibTeX

@ARTICLE{Georgieva00hyperresolutionfor,

author = {Lilia Georgieva and Ullrich Hustadt and Renate A. Schmidt},

title = {Hyperresolution for guarded formulae},

journal = {J. Symbolic Computat},

year = {2000},

volume = {36},

pages = {2003}

}

### OpenURL

### Abstract

Abstract. This paper investigates the use of hyperresolution as a decision procedure and model builder for guarded formulae. In general hyperresolution is not a decision procedure for the entire guarded fragment. However we show that there are natural fragments which can be decided by hyperresolution. In particular, we prove decidability of hyperresolution with or without splitting for the fragment GF1 − and point out several ways of extending this fragment without loosing decidability. As hyperresolution is closely related to various tableaux methods the present work is also relevant for tableaux methods. We compare our approach to hypertableaux, and mention the relationship to other clausal classes which are decidable by hyperresolution. 1

### Citations

225 | Reasoning in description logics - Dononi, Lenzerini, et al. - 1996 |

218 | Modal languages and bounded fragments of predicate logic
- Andreka, Benthem, et al.
- 1998
(Show Context)
Citation Context ...t work is also relevant for tableaux methods. We compare our approach to hypertableaux, and mention the relationship to other clausal classes which are decidable by hyperresolution. 1 Introduction In =-=[1, 2]-=- Andréka, van Benthem and Neméti investigate whether there exist natural fragments of first-order logic extending the modal fragment which corresponds to basic modal logic (via the relational translat... |

202 |
Rewrite~Based Equational Theorem Proving with Selection and Simplification. Journal of Logic and Computation. Revised version of
- BACHMAIR, GANZINGER
- 1993
(Show Context)
Citation Context ...perresolution. As usual we make a minimal assumption that at any stage in the derivation the clause set contains no duplicate clauses. For soundness and refutational completeness of R hyp see [23] or =-=[4, 5]-=-. For the classes of clause sets we consider in the present paper the positive premises will always be ground, in particular, because we use splitting, the positive premises will always be ground unit... |

194 | A structure-preserving clause form translation - Plaisted, Greenbaum - 1986 |

162 | Resolution theorem proving
- Bachmair, Ganzinger
- 2001
(Show Context)
Citation Context ...perresolution. As usual we make a minimal assumption that at any stage in the derivation the clause set contains no duplicate clauses. For soundness and refutational completeness of R hyp see [23] or =-=[4, 5]-=-. For the classes of clause sets we consider in the present paper the positive premises will always be ground, in particular, because we use splitting, the positive premises will always be ground unit... |

127 | Tableau methods for modal and temporal logics
- Goré
- 1999
(Show Context)
Citation Context ...his is an interesting contrast to the literature on decidable modal logics and description logics, where tableaux-based decision procedures are predominant for testing satisfiability (see for example =-=[10, 14]-=-). In [22] Lutz, Sattler and Tobies investigate whether tableaux-based decision procedures exist for subclasses of the guarded fragment. In this paper we continue the line of investigation making use,... |

124 | On the restraining power of guards
- Grädel
- 1999
(Show Context)
Citation Context ...y show that the guarded fragment (GF) shares all these properties with basic modal logic. Decidability was also shown for various extensions of the guarded fragment, like the loosely guarded fragment =-=[12, 15]-=-, guarded fixpoint logic [16], or monadic GF 2 with transitive guards [13]. The various decision procedures exploit the finite model property, use ordered resolution, alternating automata, or embeddin... |

93 | Combining superposition, sorts and splitting
- Weidenbach
- 2001
(Show Context)
Citation Context ...contains a ground clause C1 ∨ C2 then the resolution refutation is performed independently on N ∪ � � � � C1 and N ∪ ¬C1,C2 . The level cut improvement corresponds to branch condensing (used in SPASS =-=[24]-=-) or backjumping (used in tableaux methods [17]). On the side we remark that hyperresolution with splitting avoids the ‘memory management’ problem of hyperresolution highlighted in [8]. Related Clausa... |

72 | Hyper Tableaux
- Baumgartner, Furbach, et al.
(Show Context)
Citation Context ...ion the form of the derived clauses. The obtained results are more general than those previously known. Another aim is to study how the method relates to other inference methods such as hypertableaux =-=[8]-=-, and how the work fits into the bigger picture of hyperresolution as a decision procedure [11, 21]. The structure of the paper is as follows. We give preliminary definitions in Section 2. Section 3 c... |

58 | A superposition decision procedure for the guarded fragment with equality
- Ganzinger, Nivelle
- 1999
(Show Context)
Citation Context ...y show that the guarded fragment (GF) shares all these properties with basic modal logic. Decidability was also shown for various extensions of the guarded fragment, like the loosely guarded fragment =-=[12, 15]-=-, guarded fixpoint logic [16], or monadic GF 2 with transitive guards [13]. The various decision procedures exploit the finite model property, use ordered resolution, alternating automata, or embeddin... |

50 |
Automatic deduction with hyper-resolution
- Robinson
- 1965
(Show Context)
Citation Context ...(iii) hyperresolution. As usual we make a minimal assumption that at any stage in the derivation the clause set contains no duplicate clauses. For soundness and refutational completeness of R hyp see =-=[23]-=- or [4, 5]. For the classes of clause sets we consider in the present paper the positive premises will always be ground, in particular, because we use splitting, the positive premises will always be g... |

47 |
Resolution decision procedures
- Fermüller, Leitsch, et al.
- 2001
(Show Context)
Citation Context ...ly known. Another aim is to study how the method relates to other inference methods such as hypertableaux [8], and how the work fits into the bigger picture of hyperresolution as a decision procedure =-=[11, 21]-=-. The structure of the paper is as follows. We give preliminary definitions in Section 2. Section 3 contains a definition of GF1 − and the schematic form of the corresponding clausal class. Decidabili... |

42 | Resolution-Based Methods for Modal Logics
- Nivelle, Schmidt, et al.
(Show Context)
Citation Context ...e correspondence between tableauxbased decision procedure for modal logics and hyperresolution combined with splitting on an encoding of modal formulae in clausal logic, as previously demonstrated in =-=[9, 20]-=-, and in [18, 19] for description logics. By using a structure preserving transformation of guarded formulae into clausal form we are able to recast the method of Lutz et al. in a first-order setting ... |

38 | Issues of decidability for description logics in the framework of resolution, in
- Hustadt, Schmidt
- 2000
(Show Context)
Citation Context ... between tableauxbased decision procedure for modal logics and hyperresolution combined with splitting on an encoding of modal formulae in clausal logic, as previously demonstrated in [9, 20], and in =-=[18, 19]-=- for description logics. By using a structure preserving transformation of guarded formulae into clausal form we are able to recast the method of Lutz et al. in a first-order setting using in particul... |

35 | The two-variable guarded fragment with transitive relations
- Ganzinger, Meyer, et al.
- 1999
(Show Context)
Citation Context ...odal logic. Decidability was also shown for various extensions of the guarded fragment, like the loosely guarded fragment [12, 15], guarded fixpoint logic [16], or monadic GF 2 with transitive guards =-=[13]-=-. The various decision procedures exploit the finite model property, use ordered resolution, alternating automata, or embeddings into monadic secondorder logic. This is an interesting contrast to the ... |

32 | Back and forth between modal logic and classical logic
- Andréka, Benthem, et al.
- 1995
(Show Context)
Citation Context ...t work is also relevant for tableaux methods. We compare our approach to hypertableaux, and mention the relationship to other clausal classes which are decidable by hyperresolution. 1 Introduction In =-=[1, 2]-=- Andréka, van Benthem and Neméti investigate whether there exist natural fragments of first-order logic extending the modal fragment which corresponds to basic modal logic (via the relational translat... |

32 | FDPLL – A First-Order Davis-Putnam-Logeman-Loveland Procedure
- Baumgartner
- 2000
(Show Context)
Citation Context ...essentially the same. Consequently, the results for R hyp are also true for hypertableaux, and another alternative to R hyp is hypertableaux (and for that matter also the descendants of hypertableaux =-=[6, 7]-=-). For practical considerations this link allows us to transfer several improvements of hypertableaux discussed in [8] to R hyp . These include factorisation and level cut. Factorisation has the effec... |

23 | Using resolution for testing modal satisfiability and building models
- Hustadt, Schmidt
- 2002
(Show Context)
Citation Context ...e correspondence between tableauxbased decision procedure for modal logics and hyperresolution combined with splitting on an encoding of modal formulae in clausal logic, as previously demonstrated in =-=[9, 20]-=-, and in [18, 19] for description logics. By using a structure preserving transformation of guarded formulae into clausal form we are able to recast the method of Lutz et al. in a first-order setting ... |

22 | Decision procedures for guarded logics
- Grädel
- 1999
(Show Context)
Citation Context ...(GF) shares all these properties with basic modal logic. Decidability was also shown for various extensions of the guarded fragment, like the loosely guarded fragment [12, 15], guarded fixpoint logic =-=[16]-=-, or monadic GF 2 with transitive guards [13]. The various decision procedures exploit the finite model property, use ordered resolution, alternating automata, or embeddings into monadic secondorder l... |

17 | On the relation of resolution and tableaux proof systems for description logics
- Hustadt, Schmidt
- 1999
(Show Context)
Citation Context ... between tableauxbased decision procedure for modal logics and hyperresolution combined with splitting on an encoding of modal formulae in clausal logic, as previously demonstrated in [9, 20], and in =-=[18, 19]-=- for description logics. By using a structure preserving transformation of guarded formulae into clausal form we are able to recast the method of Lutz et al. in a first-order setting using in particul... |

17 |
Deciding clause classes by semantic clash resolution
- Leitsch
- 1993
(Show Context)
Citation Context ...ion provers can be used without adaptation (for example, FDPLL, OTTER, PROTEIN, SPASS, and VAMPIRE). Currently we are looking into defining an abstract atom complexity measure µ in analogy to Leitsch =-=[21]-=- which would generalise the specific complexity measures and orderings used in the termination proofs presented in this paper and in [9, 18–20]. We are also attempting to define a larger solvablesclas... |

16 | Soft typing for ordered resolution - Ganzinger, Meyer, et al. - 1997 |

14 | Consolution as a framework for comparing calculi - Baumgartner, Furbach - 1993 |

13 |
A Non-Elementary Speed Up in Proof Length by Structural Clause Form Transformation
- Baaz, Fermüller, et al.
- 1994
(Show Context)
Citation Context ...s outside the boundaries of GF1 − . The transformation of GF1 − formulae into clausal form makes use of structural transformation, also known as definitional form transformation or renaming (cf. e.g. =-=[3, 20]-=-). In particular, we require the introduction of new symbols for non-atomic subformula of the original formula with the exception of implications and conjunctions immediately below quantifiers. The tr... |

12 | A proposal for an nary description logic
- Lutz, Sattler, et al.
- 1999
(Show Context)
Citation Context ...resting contrast to the literature on decidable modal logics and description logics, where tableaux-based decision procedures are predominant for testing satisfiability (see for example [10, 14]). In =-=[22]-=- Lutz, Sattler and Tobies investigate whether tableaux-based decision procedures exist for subclasses of the guarded fragment. In this paper we continue the line of investigation making use, however, ... |

11 | Nivelle and M. de Rijke. Deciding the guarded fragments by resolution - de |

8 | Simplification and backjumping in modal tableau
- Hustadt, Schmidt
- 1998
(Show Context)
Citation Context ...ution refutation is performed independently on N ∪ � � � � C1 and N ∪ ¬C1,C2 . The level cut improvement corresponds to branch condensing (used in SPASS [24]) or backjumping (used in tableaux methods =-=[17]-=-). On the side we remark that hyperresolution with splitting avoids the ‘memory management’ problem of hyperresolution highlighted in [8]. Related Clausal Classes. We have already referred to the rela... |

8 | Superposition with simpli as a decision procedure for the monadic class with equality - Bachmair, Ganzinger, et al. - 1993 |

5 |
Hyper tableau: The next generation
- Baumgartner
- 1998
(Show Context)
Citation Context ...essentially the same. Consequently, the results for R hyp are also true for hypertableaux, and another alternative to R hyp is hypertableaux (and for that matter also the descendants of hypertableaux =-=[6, 7]-=-). For practical considerations this link allows us to transfer several improvements of hypertableaux discussed in [8] to R hyp . These include factorisation and level cut. Factorisation has the effec... |

5 | Using resolution for testing modal satis and building models - Hustadt, Schmidt - 2000 |

5 | On the restraining power of guards, Manuscript - Grädel - 1997 |

3 | FDPLL: A Davis-Putnam-Logeman-Loveland procedure - Baumgartner - 2000 |