## A Method for Building Models Automatically. Experiments with an extension of OTTER (1994)

Venue: | In Proceedings of CADE-12 |

Citations: | 28 - 14 self |

### BibTeX

@INPROCEEDINGS{Bourely94amethod,

author = {Christophe Bourely and Ricardo Caferra and Nicolas Peltier},

title = {A Method for Building Models Automatically. Experiments with an extension of OTTER},

booktitle = {In Proceedings of CADE-12},

year = {1994},

pages = {72--86},

publisher = {Springer}

}

### OpenURL

### Abstract

. A previous work on Herbrand model construction is extended in two ways. The first extension increases the capabilities of the method, by extending one of its key rules. The second, more important one, defines a new method for simultaneous search of refutations and models for set of equational clauses. The essential properties of the new method are given. The main theoretical result of the paper is the characterization of conditions assuring that models can be built. Both methods (for equational and non equational clauses) have been implemented as an extension of OTTER. Several running examples are given, in particular a new automatic solution of the ternary algebra problem first solved by Winker. The examples emphasize the unified approach to model building allowed by the ideas underlying our method and the usefulness of using constrained clauses. Several problems open by the present work are the main lines of future work. 1 Introduction It is trivial to say that the use of models o...

### Citations

112 | SATCHMO: A theorem prover implemented in Prolog
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- 1988
(Show Context)
Citation Context ...his and other striking results Wos wrote recently [WOS93] page 17: "I also note that our programs are still not effective for model generation". Some more recent approaches must be mentioned=-=. SATCHMO [MB88]-=- is a specialized theorem prover that applies to a restricted class of (non equational) clauses. It is based on the use of a bottom up strategy, splitting of positive ground clauses and backtracking. ... |

104 | Equational problems and disunification
- Comon, Lescanne
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(Show Context)
Citation Context ...rence rule its disinference counterpart and introduce some essentially new rules, which are not inference rules in the usual sense. Constraints are represented by equational problems, in the sense of =-=[CL89]. Equational problem-=-s are formulas containing only equalities and inequalities, connected by "" and "", quantified in a particular way (9 8 ). A solution of an equational problem is a ground substitut... |

53 |
Automatic generation of some results in finite algebra
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- 1993
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Citation Context ...es. Slaney's method combines clever enumeration and backtracking techniques for building finite models. It has been used to prove some open results for certain classes of quasigroups (see for example =-=[FSB93]-=-). A more detailed analysis of all these methods is done elsewhere [BCP94]. One common feature of almost all the approaches mentioned above is that they are able to build only small finite models and ... |

48 | N.: A method for simultanous search for refutations and models by equational constraint solving
- Caferra, Zabel
- 1992
(Show Context)
Citation Context ...S2 := S2 \Gamma fC 00 g (where C 00 is the ancestor of C 0 ) else STOP end EGPL terminates and S [ [[L(t) : X pure ]] is satisfiable iff S is satisfiable (the proof comes down trivially to the one in =-=[CZ92]-=- pages 625-626). Remark: The same procedure applies when dealing with set of equational clauses (but in this case EGPL will not always terminate). Here is the appropriate place for describing succintl... |

38 |
Automatic theorem proving with renamable and semantic resolution
- Slagle
- 1967
(Show Context)
Citation Context ... first one is the use of diagrams (models) as a powerful heuristic to prune the proof search in plane geometry in GTM (Geometric Theoremproving Machine) [GHL83]. The second one is semantic resolution =-=[SLA67]-=- in which models play an essential role in the application of the resolution rule. Semantic resolution corresponds roughly, as Slagle pointed out, to the system used in GTM. It is worth citing a state... |

35 | Superposition with Simplification as a Decision Procedure for the Monadic Class with Equality - Bachmair, Ganzinger, et al. - 1993 |

20 | Extending resolution for model construction - Caferra, Zabel - 1991 |

20 |
Model Building by Resolution
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(Show Context)
Citation Context ...almost all the approaches mentioned above is that they are able to build only small finite models and several of the used techniques are applicable only for this kind of models. The only exception is =-=[FL92]-=- which can build rather large finite models. The present paper is an extension of previous work by the authors [CZ91, CZ92]. The method presented in [CZ91, CZ92] builds models automatically for sets o... |

20 | Generation and verification of finite models and counterexamples using an automated theorem prover answering two open questions - Winker - 1982 |

13 |
Empirical explorations of the geometry theorem proving machine
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- 1963
(Show Context)
Citation Context ...Two pioneer works deserves to be mentioned. The first one is the use of diagrams (models) as a powerful heuristic to prune the proof search in plane geometry in GTM (Geometric Theoremproving Machine) =-=[GHL83]-=-. The second one is semantic resolution [SLA67] in which models play an essential role in the application of the resolution rule. Semantic resolution corresponds roughly, as Slagle pointed out, to the... |

12 |
Automated Reasoning
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Citation Context ...as been partially supported by ESPRIT-BRA No 6471 "Medlar 2" and PRC-IA (MRE-CNRS, FRANCE) boolean algebra (see for example [WIN82, WOS93]). Despite this and other striking results Wos wrote=-= recently [WOS93] page 17: -=-"I also note that our programs are still not effective for model generation". Some more recent approaches must be mentioned. SATCHMO [MB88] is a specialized theorem prover that applies to a ... |

6 |
Decidability of a portion of the predicate calculus
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Citation Context ...nd 3 verified ** Found = YES. f: g1(x) -? x. f: g2(x) -? x. f: x -? f(x) if (all y z.x != g1(y) & x != g2(z)). g1: x -? g1(x). g2: x -? g2(x). Comments: This particularly simple example is taken from =-=[SHE77]-=- page 32. In most cases of decidability, as Shelah points out, the existence of a model implies the existence of a finite model, but this is not the case for this formula. The following steps go into ... |

3 |
Resolution Methods for the Decision Problem
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Citation Context ... 5 [] -S(f(x),x,a) : TRUE. 6 [] -S(f(x),x,b) : TRUE. 3 [] R(f(a),g(a),a) : TRUE. 11 [egpl,10] S(f(x),x,x) : (a != x) & (b != x). 13 [egpl,12] R(f(x),g(x),x) : (a != x). Comments: This example is from =-=[FLTZ93]-=- page 169. It belongs to the AM class and is used by Tammet to illustrate its approach. AM class is the class for which Tammet's method is able to build models. AM is a finitely controllable class and... |

1 |
Model building in automated deduction. Forthcoming
- BOURELY, CAFERRA, et al.
- 1994
(Show Context)
Citation Context ...s for building finite models. It has been used to prove some open results for certain classes of quasigroups (see for example [FSB93]). A more detailed analysis of all these methods is done elsewhere =-=[BCP94]-=-. One common feature of almost all the approaches mentioned above is that they are able to build only small finite models and several of the used techniques are applicable only for this kind of models... |

1 | Automated Theorem Proving after 25 years, volume 29 of Contemporary Mathematics - BLEDSOE, LOVELAND - 1984 |