## Refinements of Theory Model Elimination and a Variant without Contrapositives (1994)

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Venue: | University of Koblenz, Institute for Computer Science |

Citations: | 8 - 6 self |

### BibTeX

@INPROCEEDINGS{Baumgartner94refinementsof,

author = {Peter Baumgartner},

title = {Refinements of Theory Model Elimination and a Variant without Contrapositives},

booktitle = {University of Koblenz, Institute for Computer Science},

year = {1994},

pages = {90--94},

publisher = {Wiley}

}

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### Abstract

Theory Reasoning means to build-in certain knowledge about a problem domain into a deduction system or calculus, which is in our case model elimination. Several versions of theory model elimination (TME) calculi are presented and proven complete: on the one hand we have highly restricted versions of total and partial TME. These restrictions allow (1) to keep fewer path literals in extension steps than in related calculi, and (2) discard proof attempts with multiple occurrences of literals along a path (i.e. regularity holds). On the other hand, we obtain by small modifications to TME versions which do not need contrapositives (a la Near-Horn Prolog). We show that regularity can be adapted for these versions. The independence of the goal computation rule holds for all variants. Comparative runtime results for our PTTP-implementations are supplied. 1 Introduction The model elimination calculus (ME calculus) has been developed already in the early days of automated theorem proving [Lovel...

### Citations

456 | Termination of Rewriting - Dershowitz - 1987 |

280 | R.: Symbolic Logic and Mechanical Theorem Proving - Chang, Lee - 1987 |

150 | Automated Theorem Proving - Bibel - 1982 |

131 | Krypton: A functional ap- proach to knowledge representation - Brachman, Fikes, et al. - 1983 |

128 | SETHO: A high-performance theorem prover - Letz, Schumann, et al. - 1992 |

123 | Automated deduction by theory resolution - Stickel - 1985 |

108 | Unification theory - Siekmann - 1989 |

102 | A prolog technology theorem prover: implementation by an extended prolog compiler - Stickel - 1988 |

101 | The TPTP problem library
- Sutclie, Suttner
- 1998
(Show Context)
Citation Context ...986 Newsletter of the Association of Automated Reasoning 7 . The selected theory here consists of a transitive and symmetric relation 7 Entries such as MSC/MSC006-1 refer to the respective TPTP-names =-=[24]-=-. All examples were drawn from that problem library without modification --- only the theory part had to be selected by hand. Automated Reasoning 93 P. Baumgartner Restart- RestartExample ME ME TME TM... |

64 | Foundations of Logic Programming. Symbolic computation — Artificial Intelligence - Lloyd - 1987 |

62 | C.: Controlled integration of the cut rule into connection tableau calculi - Letz, Mayr, et al. - 1994 |

58 | A Prolog Technology Theorem Prover: A New Exposition and Implementation - Stickel - 1992 |

55 | Mechanical theorem proving by model elimination - Loveland - 1968 |

50 | Caching and Lemmaizing in Model Elimination Theorem Provers - Astrachan, Stickel - 1992 |

40 | A prolog technology theorem prover - Stickel - 1984 |

40 | PROTEIN: A PROver with a theory extension INterface
- Baumgartner, Furbach
- 1994
(Show Context)
Citation Context ...kwise regular refutations. 4 Practical Experiments We have implemented the calculi variants described in the preceeding sections. The system, called PROTEIN (PROver with a Theory Extension INterface, =-=[8]), is impl-=-emented using the PTTP implementation technique ("Prolog Technology Theorem Prover", [22]) in ECLiPSe Prolog. The implementation of partial theory reasoning is currently tailored for the met... |

38 | A linear format for resolution with merging and a new technique for establishing completeness - Anderson, Bledsoe - 1970 |

36 | Translation methods for non-classical logics – an overview - Ohlbach - 1993 |

32 | E-resolution: extension of resolution to include the equality relation - Morris - 1969 |

31 | Non-Horn clause logic programming without contrapositives - Plaisted - 1988 |

28 | Theorem proving using rigid E-unification: Equational matings - Gallier, Raatz, et al. - 1987 |

28 | Near-Horn Prolog and beyond - Loveland - 1991 |

26 |
An Essential Hybrid Reasoning System
- Brachman, Gilbert, et al.
- 1985
(Show Context)
Citation Context ...easoner that takes advantage of the theories' properties. Theory reasoning is a very general scheme and has many applications, among them reasoning with taxonomical knowledge as in the Krypton system =-=[10]-=-, building in theory-unification procedures and equality reasoning as by Paramodulation or E-resolution. Another source for this work is the upcoming of various (nontheory) calculi which do not need a... |

22 | 1994], `Model Elimination without Contrapositives and its Application to PTTP - Baumgartner, Furbach |

22 | Challenge problems in elementary calculus - Bledsoe - 1990 |

21 | Paramodulation and theorem proving in first order thoeries with equality - Robinson, Wos - 1969 |

19 | Near-Horn Prolog - Loveland - 1987 |

17 | A model elimination calculus with built-in theories - Baumgartner - 1992 |

17 | An ordered theory resolution calculus - Baumgartner - 1992 |

16 | Model Elimination without Contrapositives
- Baumgartner, Furbach
- 1994
(Show Context)
Citation Context ...oidance of contrapositives. a theorem-proving system and needs only one single contrapositive per clause. A detailed comparison of these calculi and of another one, N-Prolog, can be found in [21]. In =-=[7]-=- we have made a small change to model elimination which also avoids contrapositives and allows for a PTTP-implementation. The common idea behind all these calculi is to carry out case analysis wrt. th... |

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

13 | A Comparison of Three Prolog Extensions - Reed, Loveland - 1992 |

12 | Consolution and its relation with resolution - Eder - 1991 |

12 | A sequent-style model elimination strategy and a positive refinement - Plaisted - 1990 |

9 | equality theories and paramodulation - Horn - 1989 |

8 | Theory Resolution: Building in Nonequational Theories," SRI Artificial Intelligence Center Technical Note 286, SRI International, Menlo Park - Stickel - 1983 |

6 | Completeness of the pool calculus with an open built in theory - Petermann - 1993 |

5 | A Unified Approach to Theory Reasoning. Forschungsbericht 15/92 - Baumgartner, Furbach, et al. - 1992 |

5 | Theory Links: Applications to Automated Theorem Proving - Murray, Rosenthal - 1987 |

5 | How to build in an open theory into connection calculi - Petermann - 1991 |

4 | Relative Complexities of First Order Languages - Eder - 1992 |

4 |
SETHEO: A High-Performace Theorem Prover
- Letz, Schumann, et al.
- 1992
(Show Context)
Citation Context ...utationally complete calculus for first order clause logic [15]. It is the base of numerous proof procedures for first order deduction. There are high speed theorem provers, like METEOR [1] or SETHEO =-=[13]-=- and there is a whole class of provers, namely Prolog technology theorem proving (PTTP) as introduced in [22], which rely on model elimination. In this paper we extend in several new ways model elimin... |

3 | Linear Completion: Combining the Linear and the Unit-Resulting Restrictions - Baumgartner - 1993 |

2 | org Siekmann. Reasoning with Assertions and Examples - Kerber, Melis, et al. - 1993 |

2 | First-Order Proof Calculi and Proof Procedures for Automated Deduction - Letz - 1993 |

1 | urgen Ohlbach. Link Inheritance in Abstract Clause Graphs - Hans - 1987 |

1 |
ModelElimination Calculuswith Built-in Theories
- Baumgartner, ‘A
- 1992
(Show Context)
Citation Context ...del elimination towards theory reasoning. Theory reasoningwas introduced by M. Stickel within the general, non-linear resolution calculus [23]; for model elimination it is defined and investigated in =-=[2]-=-. Theory reasoning means to relieve a calculus from explicit reasoning in some domain (e.g. equality, partial orders, taxonomic reasoning) by taking apart the domain knowledgeand treating it by specia... |

1 |
An Ordered Theory Resolution Calculus’, in Logic Programming and Automated Reasoning
- Baumgartner
- 1992
(Show Context)
Citation Context ... 11th European Conference on Artificial Intelligence Edited by A. Cohn Published in 1994 by John Wiley & Sons, Ltd. experimental results. Related Work. Theory reasoning was ported to many calculi. In =-=[3]-=- we showed that total theory resolution is compatible with ordering restrictions. Theory reasoning was defined for matrix methods in [17], for the connection graph calculus in [18] and for the connect... |

1 |
Automated Theorem
- Bibel
- 1987
(Show Context)
Citation Context ...t total theory resolution is compatible with ordering restrictions. Theory reasoning was defined for matrix methods in [17], for the connection graph calculus in [18] and for the connection method in =-=[9, 19]-=-. However there are significant differences between these calculi and model elimination: model elimination is a linear calculus, which means that an initially chosen goal clause is stepwisely processe... |

1 |
Symbolic Logic andMechanical Theorem Proving
- Chang, Lee
- 1973
(Show Context)
Citation Context ...e complicated (cf. [14]). Completeness is stated for the ground case only. Although not quite trivial, lifting to the first order case can be carried out by generalizing standard techniques (see e.g. =-=[11, 14]-=-). Theorem 2.5 (Ground Completeness of Regular Total TME) Let T be a theory, c be a computation rule and let M be a T -unsatisfiable ground clause set. Let C 2 M be such that C is contained in some mi... |