# Coupling Saturation-Based Provers by Exchanging Positive/Negative Information

@inproceedings{Fuchs1998CouplingSP, title={Coupling Saturation-Based Provers by Exchanging Positive/Negative Information}, author={Dirk Fuchs}, booktitle={RTA}, year={1998} }

We examine different possibilities of coupling saturationbased theorem provers by exchanging positive/negative information. Positive information is given by facts that should be employed for proving a proof goal, negative information is represented by facts that do not appear to be useful. We introduce a basic model for cooperative theorem proving employing both kinds of information. We present theoretical results regarding the exchange of positive/negative information as well as practicalâ€¦Â

## 8 Citations

Requirement-Based Cooperative Theorem Proving

- Computer ScienceJELIA
- 1998

An approach for demand-driven cooperative theorem proving that is well-suited for saturation-based theorem provers and an abstract framework for requirement-based cooperation is introduced, which aims to allowing more orientation on current needs of provers in comparison with conventional cooperation concepts.

Cooperation of Heterogeneous Provers

- Computer ScienceIJCAI
- 1999

Results are reported on on experiments regarding the cooperation of the provers SPASS, SETHEO and DISCOUNT in domains of the TPTP library and with problems stemming from an application in software component retrieval.

System Description: Cooperation in Model Elimination: CPTHEO

- Computer ScienceCADE
- 1998

This description presents a concept for a cooperative parallel theorem prover which combines goal oriented search with a saturating approach and gives a short assessment of the results of first experiments with CPTHEO, followed by a listing of topics planned for the future improvement of the prover.

Controlled Use of Clausal Lemmas in Connection Tableau Calculi

- Computer Science, MathematicsJ. Symb. Comput.
- 2000

A method to augment a given set of clauses by a lemma set in a preprocessing phase is developed and the ability of this technique to reduce proof lengths and depths and to provide an appropriate reordering of the search space is discussed.

Cooperation between Top-Down and Bottom-Up Theorem Provers

- Computer ScienceJ. Artif. Intell. Res.
- 1999

In order to identify subgoal clauses and lemmas which are actually relevant for the proof task, the ability of the techniques to shorten proofs as well as to reorder the search space in an appropriate manner is discussed.

On the Use of Subgoal Clauses in Bottom-up and Top-down Calculi

- Computer ScienceFundam. Informaticae
- 1999

Top-down lemmas, so-called subgoal clauses, are introduced, and their potential to reduce proof lengths and searches in top-down and bottom-up theorem proving is examined and some heuristics are developed so as to make the use of sub goal clauses efficient in practice.

Integrating Deduction Techniques in a Software Reuse Application

- Computer ScienceJ. Univers. Comput. Sci.
- 1999

This work uses the Ilf-system as a control and integration shell to combine two di erent combination styles, competition and cooperation, and describes the system architecture, a pipeline of lters of increasing deductive strength, in which theorem provers are applied.

Logics in Artificial Intelligence

- PhilosophyLecture Notes in Computer Science
- 1999

This study introduces the knowledge theoretic interpretation of LP as a logic for representing definitional knowledge and argues that the well-founded semantics (wfs) overcomes these problems and hence, provides a superior formalisation of the principle of inductive definition.

## References

SHOWING 1-10 OF 29 REFERENCES

Cooperation in Theorem Proving by Loosely Coupled Heuristics

- Computer Science
- 1999

A cooperation concept for automated theorem provers that is based on a periodical interchange of selected results between several incarnation of a prover, which allows the dis-tributed system to find proofs much faster than single heuristics working alone.

Caching and Lemmaizing in Model Elimination Theorem Provers

- Computer Science, MathematicsCADE
- 1992

This paper reports on work done to modify a model elimination theorem prover using two techniques, caching and lemmaizing, that have reduced by more than an order of magnitude the time required to find proofs of several problems and that have enabled the prover to prove theorems previously unobtainable by top-down model eliminationorem provers.

Distributing Equational Theorem Proving

- Computer ScienceRTA
- 1993

It is shown by non-trivial examples that drastical time speed-ups are possible for a cooperating team of experts compared to the time needed by the best expert in the team.

Inference Rights for Controlling Search in Generating Theorem Provers

- Computer ScienceEPIA
- 1997

The problems that arise from the inflexibility of existing approaches to heuristically control the search of automated deduction systems are pointed out, and the application of inference rights that are well-suited for controlling the search more flexibly are proposed.

SCOTT: A Model-Guided Theorem Prover

- Computer ScienceIJCAI
- 1993

SCOTT (Semantically Constrained Otter) is a resolution-based automatic theorem prover for first order logic. It is based on the high performance prover OTTER by W. McCune and also incorporates aâ€¦

Goal Oriented Equational Theorem Proving Using Team Work

- Computer ScienceKI
- 1994

This paper implements the team work method for pure equational logic using the unfailing Knuth-Bendix completion procedure as basic prover and presents three classes of experts working in a goal oriented fashion.

On Gaining Efficiency in Completion-Based Theorem Proving

- Computer ScienceRTA
- 1996

The new Waldmeister prover is introduced which shows an increase in overall system performance of more than one order of magnitude as compared with standard techniques.

Rewrite-Based Equational Theorem Proving with Selection and Simplification

- Computer ScienceJ. Log. Comput.
- 1994

This paper forms an abstract notion of redundancy and shows that the deletion of redundant clauses during the theorem proving process preserves refutation completeness, and presents various refutationally complete calculi for first-order clauses with equality that allow for arbitrary selection of negative atoms in clauses.

Experiments in Automated Deduction with Condensed Detachment

- MathematicsCADE
- 1992

Two new features of Otter are presented: the refined method for selecting the next formula on which to focus, and a method for controlling memory usage.

CODE: A Powerful Prover for Problems of Condensed Detachment

- Computer ScienceCADE
- 1997

CODE is currently the most powerful proving system for problems of CD and is substantiated by presenting ample experimental evidence in form of a comparison with OTTER as the probably only serious competitor in the area of CD.