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## Herod and Pilate: two Tableau Provers for Basic Hybrid Logic

Citations: | 2 - 1 self |

### Citations

65 | The SAT phase transition
- Gent, Walsh
- 1994
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Citation Context ...the X-axis group all sets with the same number of clauses, independently of their modal depth. Pilate seems to be more sensible to the phase transition in the easy-hard-easy pattern of the benchmarks =-=[8]-=-. 4 Pilate Herod 45 "Pilate" "Herod" 40 35 3 30 time (s) 2 time (s) 25 20 1 15 10 0 5 0 60 80 100 120 140 160 180 200 number of clauses 20 40 60 80 100 120 140 size Figure 1: Pilate and Herod average ... |

22 | The Objective Caml system: release 3.11; documentation and user’s manual,
- Leroy, Doligez, et al.
- 2008
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Citation Context ...ilate (“What crime has he committed?”) implements the calculus P, and Herod is the implementation of the slaughter of the innocents represented by H. The two systems are implemented in Objective Caml =-=[12]-=- and are available at Herod web page [13]. In the rest of this section a description of the implementations is given, with some simplifications and abstractions. Bothsystemstakeasinputafilespecifyinga... |

15 | Htab: a terminating tableaux system for hybrid logic.
- Hoffmann, Areces
- 2009
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Citation Context ...ever, that Pilate constitutes a more or less “ad literam” implementation of P and that more effective ways of treating its Id rule can be conceived. For this reason, Herod has been compared with HTab =-=[11]-=-, whichimplementstheprefixedcalculuspresentedin[3]. HTabimplementsequality by means of equivalence classes of nominals and prefixes, that are created, enlarged and merged while the tableau constructio... |

12 |
Spartacus: A Tableau Prover for Hybrid Logic.
- Gotzmann, Kaminski, et al.
- 2010
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Citation Context ...as also considered another prover, Spartacus [10]. 2 Spartacus processes nominal equalities by merging the content of the corresponding “nodes”, and electing one of them as the representative of both =-=[9]-=-. Both HTab and Spartacus are much more mature provers than Herod, handling a richer logic and implementing many important optimisation strategies. On the contrary, at present, the only simple rule ap... |

10 |
hGen: A Random CNF Formula Generator for Hybrid Languages
- Areces, Heguiabehere
- 2003
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Citation Context ..., though abstract, reformulation of the expansion rules can be found. This presentation describes the implementations and some experimental results, run on sets of formulae randomly generated by hGen =-=[1]-=-. 1The experiments show that the approach to nominal equalities in H, although theoretically less elegant than P’s, has important practical advantages. The systems are also briefly compared to other ... |

5 | An efficient approach to nominal equalities in hybrid logic tableaux
- Cerrito, Mayer
- 2010
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Citation Context ...ithout loop-checking and with no restriction on rule application strategies. The two calculi were independently proposed, respectively, in [3] and [5] (a revised and extended version of the latter is =-=[4]-=-). The main difference between them is the treatment of nominal equalities, that is essentially carried out by means of an elegant and simple rule in the first calculus ([3], here named P), which copi... |

5 |
Terminating tableaux for HL(@) without loopchecking
- Cerrito, Mayer
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Citation Context ...asic hybrid logic HL(@), which havebeenimplementedwiththeaimofcomparingtheinternalisedtableau calculi independently proposed, respectively, by Bolander and Blackburn [3] and Cerrito and Cialdea Mayer =-=[5]-=-. Experimental results are reported, evaluating, from the practical point of view, the different treatment of nominal equalities of the two calculi. 1 A Brief Presentation of the Calculi P and H The t... |

4 | Two tableau provers for basic hybrid logic
- Mayer, Cerrito, et al.
- 2009
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Citation Context ...involved rule, requiring explicit substitution (the Sub rule). AnanalysisandcomparisonofPandH,highlighting theirrespectivesimilarities and differences from a theoretical point of view can be found in =-=[7]-=-, where also an application-oriented, though abstract, reformulation of the expansion rules can be found. This presentation describes the implementations and some experimental results, run on sets of ... |

2 | Tableaux with substitution for hybrid logic with the global and converse modalities - Cerrito, Mayer - 2009 |

1 |
A benchmark method for thepropositionalmodallogicsK,KT,S4
- Balsiger, Heuerding, et al.
(Show Context)
Citation Context ...owing that that all the difference between the systems is due to their treatment of equalities, are obtained when running the two provers on the hand-tailored collection of modal formulae proposed in =-=[2]-=-, where in fact Pilate and Herod show the same behaviour. It must be remarked, however, that Pilate constitutes a more or less “ad literam” implementation of P and that more effective ways of treating... |