## Finite Model Building: Improvements and Comparisons (2003)

Venue: | In: Model Computation – Principles, Algorithms, Applications, CADE-19 Workshop W4 |

Citations: | 5 - 0 self |

### BibTeX

@INPROCEEDINGS{Tammet03finitemodel,

author = {Tanel Tammet},

title = {Finite Model Building: Improvements and Comparisons},

booktitle = {In: Model Computation – Principles, Algorithms, Applications, CADE-19 Workshop W4},

year = {2003}

}

### OpenURL

### Abstract

The paper ivestigates nite model building for rst order logic. We consider two main categories of methods: Mace-type and Falcontype methods. The paper has two goals: rst, presenting several improvements and strategies for the basic Mace-type and Falcon-type algorithms, second, comparing the eciency of dierent methods. The improvements to the Mace-type algorithms are focused on decreasing the size of the propositional subtasks. A new cell selection heuristics is introduced for the Falcon-type algorithms. The methods are implemented in the Gandalf theorem prover. We present both the eect of the introduced improvements and the comparison of method categories for several problem classes, based on their syntactical characteristics. Finally, several suggestions for further investigations are given.

### Citations

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Citation Context ... methods forsnite model building. Again, the main methods forsnite model building fall into one of the two categories: { Mace-style model building. This method, introduced by W. McCune in [McCune98], =-=[McCune01]-=- and implemented in his model builder Mace creates large propositional subproblems and relies heavily on the eciency of propositional provers. { Falcon-style model building. This method, introduced by... |

46 | Resolution Methods for the Decision Problem - Fermüller, Leitsch, et al. - 1993 |

39 |
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(Show Context)
Citation Context ...havesnite models, but in practice the class of formulas where the method is successful is much smaller than the class wheresnite model building methods are successful. See [Tammet91], [Fermuller93], [=-=Handbook01]-=-. In the following we will consider only methods forsnite model building. Again, the main methods forsnite model building fall into one of the two categories: { Mace-style model building. This method,... |

37 | Splitting without Backtracking
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(Show Context)
Citation Context ...practice gives an enourmous speedup to the propositional proof search and the model construction algorithm as a whole. The splitting algorithm is a well-known method in automated theorem proving, see =-=[Riazanov01]-=-. The version of the method we use here is sometimes called 'pseudo-splitting': it takes a clause C and replaces it with a set of clauses SC, where each clause contains fewer variables that C. The sim... |

28 |
Using resolution for deciding solvable classes and building finite models
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Citation Context ...es of formulas which do not havesnite models, but in practice the class of formulas where the method is successful is much smaller than the class wheresnite model building methods are successful. See =-=[Tammet91-=-], [Fermuller93], [Handbook01]. In the following we will consider only methods forsnite model building. Again, the main methods forsnite model building fall into one of the two categories: { Mace-styl... |

23 | Automatic Proofs and Counterexamples for Some Ortholattice
- McCune
- 1998
(Show Context)
Citation Context ... cannot be provable. Asnite counter model can be viewed as pointing to concrete bugs in the system or the specication. However, not all non-provable formulas havesnite counter-models. See [Zhang96], [=-=McCune98-=-], [McCune02]. { Ordered resolution. A proof search algorithm with specic completenesspreserving ordering restrictions is used for attempting to prove F . In case all possible search paths are exhaust... |

19 |
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Citation Context ...know that F cannot be provable. Asnite counter model can be viewed as pointing to concrete bugs in the system or the specication. However, not all non-provable formulas havesnite counter-models. See [=-=Zhang96-=-], [McCune98], [McCune02]. { Ordered resolution. A proof search algorithm with specic completenesspreserving ordering restrictions is used for attempting to prove F . In case all possible search paths... |

3 |
Towards ecient subsumption, in
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(Show Context)
Citation Context ...ace algorithm enhanced with nonground splitting and the beforementioned classes of heuristics for Falcon style algorithms are implemented in our theorem prover and modelsnder Gandalf, see [Tammet97], =-=[Tammet98-=-], [Tammet02]. The current version of Gandalf uses Zcha by L. Zhang (see [Zhang01]) as a propositional prover for solving propositional clause sets generated by the MACE algorithm. For each model size... |

3 |
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(Show Context)
Citation Context ...roduced typically bind literals together. IV Instead of being restricted to ground splitting, we will use the version of splitting called 'non-ground splitting'. Non-ground splitting was presented in =-=[Schulz01]-=- for the purposes of saturating clause sets not containing function symbols. The idea of non-ground splitting is to allow using new literals S 1 (x 1 ; :::; x s ) and S 2 (x 1 ; :::; x s ) instead of ... |

3 |
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Citation Context ...heuristics for Falcon style algorithms are implemented in our theorem prover and modelsnder Gandalf, see [Tammet97], [Tammet98], [Tammet02]. The current version of Gandalf uses Zcha by L. Zhang (see [=-=Zhang01-=-]) as a propositional prover for solving propositional clause sets generated by the MACE algorithm. For each model size n Gandalf creates the saturated propositional inputsle for Zcha and calls the la... |

2 |
Journal of Automated Reasoning vol 18 No 2
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(Show Context)
Citation Context ...iments The Mace algorithm enhanced with nonground splitting and the beforementioned classes of heuristics for Falcon style algorithms are implemented in our theorem prover and modelsnder Gandalf, see =-=[Tammet97-=-], [Tammet98], [Tammet02]. The current version of Gandalf uses Zcha by L. Zhang (see [Zhang01]) as a propositional prover for solving propositional clause sets generated by the MACE algorithm. For eac... |

1 |
SEM: A System for Enumerating Models. IJCAI-95
- Zhang, Zhang
(Show Context)
Citation Context ... Mace creates large propositional subproblems and relies heavily on the eciency of propositional provers. { Falcon-style model building. This method, introduced by J.Zhang and H.Zhang, see [Zhang96], =-=[Zhang95-=-], [McCune02], avoids large propositional subproblems, building the model incrementally during search. Mace-style and Falcon-style model building behave very dierently on different classes of problems... |

1 |
Experiments with non-ground splitting and model building
- Claessen
(Show Context)
Citation Context ...l building, we see these two methods as largely complementary. Hence we are sceptical about the perspectives to integrate these two into a "common" method. It has been pointed out by Koen Cl=-=aessen in [Claesse-=-n] that dierent suboptimal algorithms for non-ground splitting give widely dierent results. It is clearly important to continue research for improving algorithms for non-ground splitting: these algori... |