## Model Elimination without Contrapositives (1994)

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Citations: | 16 - 6 self |

### BibTeX

@MISC{Baumgartner94modelelimination,

author = {Peter Baumgartner and Ulrich Furbach},

title = {Model Elimination without Contrapositives},

year = {1994}

}

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### Abstract

We present modifications of model elimination which do not necessitate the use of contrapositives. These restart model elimination calculi are proven sound and complete. The corresponding proof procedures are evaluated by a number of runtime experiments and they are compared to other well known provers. Finally we relate our results to other calculi, namely the connection method, modified problem reduction format and Near-Horn Prolog.

### Citations

409 |
First-Order Logic and Automated Theorem Proving
- Fitting
- 2012
(Show Context)
Citation Context ...restart model elimination. Soundness of the calculus follows immediately by showing that every restart model elimination proof can be mapped to a proof in the free variable semantic tableau calculus (=-=[Fit90]-=-), while completeness will be proven directly. Theorem 6. (Soundness) Restart model elimination is sound. Theorem 7. (Completeness) Let f be a selection function and S be a clause set in goal-normal f... |

151 |
Logic for Computer Science. Foundation of Automatic Theorem Proving
- Gallier
- 1986
(Show Context)
Citation Context ...They are goal-oriented, and neither of these needs contrapositives. We will discuss both of them. The simplified problem reduction format (SPRF) is a variant of the Gentzen sequent calculus (see e.g. =-=[Gal87]-=-). A sequent is pair, written as \Gamma ! L where \Gamma is a list of literals, and L is a literal. From the model elimination point of view a sequent \Gamma ! L corresponds to the path \Gamma ffi h:L... |

148 |
Automated Theorem Proving
- Bibel
- 1987
(Show Context)
Citation Context ...start model elimination finds a proof more quickly, which suggest to us that it is an interesting alternative to traditional model elimination. 5 Related Work Connection Method. The connection method =-=[Bib87]-=- is an analytic calculus closely related to model elimination. Clause sets are called matrices there, and a path through a matrix is obtained by taking exactly one literal from every clause in the mat... |

82 |
N-prolog: an extension of prolog with hypothetical implications. i
- Gabbay, Reyle
- 1984
(Show Context)
Citation Context ...to :prove(X ) by introducing a new variable. Such observations had been the motivation for the development of calculi which need no contrapositives, e.g. Loveland's NearHorn-Prolog. Gabbay's N-Prolog =-=[Gab85]-=- when restricted to clause logic is general enough to be instantiated to both NearHorn-Prolog and problem reduction formats ([Pla88], see also Section 5 below; [RL92] contains a comparison of these). ... |

49 | Caching and lemmaizing in model elimination theorem provers
- Astrachan, Stickel
- 1992
(Show Context)
Citation Context ...ives for a given n-literal clause. Model elimination [Lov68] is a calculus, which is the base of numerous proof procedures for first order deduction. There are high speed theorem provers, like METEOR =-=[AS92]-=- or SETHEO [LSBB92]. The implementation of model elimination provers can take advantage of techniques developed for Prolog. For instance, Stickel's Prolog technology theorem proving system (PTTP, [Sti... |

40 | PROTEIN: A PROver with a theory extension INterface
- Baumgartner, Furbach
- 1994
(Show Context)
Citation Context ... already noticed that the restart variant can be implemented very easily using the PTTP-technique. Indeed, we implemented the restart model elimination calculus in the theorem proving system PROTEIN (=-=[BF94]-=-). Both the implementation language and the target language for the compiled code is ECL i PS e , an enhanced Prolog-dialect. We ran several examples known from the literature, and some new ones. We c... |

37 |
A Linear Format for Resolution with Merging and a New Technique for Establishing Completeness
- Anderson, Bledsoe
- 1970
(Show Context)
Citation Context ...al occurrences of) the clause C . Let k(S ) denote the number of occurrences of positive literals in S minus the number of definite clauses 2 in S (k(S ) is related to the excess literal parameter in =-=[AB70]-=-). Now we prove the claim by induction on k(S ). 2 A definite clause is a clause containing exactly one positive literal. Induction start (k(S) = 0): M must be a set of Horn clauses. By Theorem 2 ther... |

17 | A model elimination calculus with built-in theories
- Baumgartner
- 1992
(Show Context)
Citation Context ...s does not assume a special selection function which determines which path is to be extended or reduced next. Correctness and completeness of this calculus follows immediately from a result proved in =-=[Bau92]-=-. 3 Restart Model Elimination Calculi Let us now modify the calculus given above, such that no contrapositives are needed. In order to get a complete calculus, we have to assume that there exists only... |

14 | Consolution as a framework for comparing calculi
- Baumgartner, Furbach
- 1993
(Show Context)
Citation Context ...t one of the NearHorn-Prologs, namely InH-Prolog ([LR89]), can be seen as one of our modified model elimination procedures. As a final point, we discovered that the connection method ([Bib87, Ede92], =-=[BF93]-=- contains a comparative study) is complete without contrapositives and without any change to the calculus. This surprising result is due to a relaxed complementary-literal condition which subsumes the... |

12 |
Consolution and its relation with resolution
- Eder
- 1991
(Show Context)
Citation Context ...ffers from the original one presented by [Lov68]; it is described in [LSBB92] as the base for the prover SETHEO. In [BF93] this calculus is discussed in detail by presenting it in a consolution style =-=[Ede91]-=- and comparing it to various other calculi. This model elimination manipulates trees by extension- and reduction-steps. In order to recall the calculus and to state a running example consider the clau... |

4 |
Relative Complexities of First Order Languages
- Eder
- 1992
(Show Context)
Citation Context ...n contrapositives are either given more explicitly (as in the SETHEO prover [LSBB92]) or more implicitly (as in the connection method by allowing to set up a connection with every literal in a clause =-=[Ede92]). The dis-=-tinction is merely a matter of presentation and will be given up for this paper. Now, by a system "without contrapositives" we mean more precisely a system which does not need all n contrapo... |