Top-down and bottom-up theorem proving approaches have each specific ad-vantages and disadvantages. Bottom-up provers profit from strong redundancycontrol and suffer from the lack of goal-orientation, whereas top-down provers aregoal-oriented but have weak calculi when their proof lengths are considered. Inorder to integrate both approaches our method is to achieve cooperation betweena top-down and a bottom-up prover: The top-down prover generates subgoalclauses, then they are processed by a bottom-up prover. We discuss theoreticaspects of this methodology and we introduce techniques for a relevancy-basedfiltering of generated subgoal clauses. Experiments with a model eliminationand a superposition-based prover reveal the high potential of our cooperation approach.The author was supported by the Deutsche Forschungsgemeinschaft (DFG).
We present a cooperation concept for automated theorem provers that isbased on a periodical interchange of selected results between several incarnationsof a prover. These incarnations differ from each other in the search heuristic theyemploy for guiding the search of the prover. Depending on the strengths' andweaknesses of these heuristics different knowledge and different communicationstructures are used for selecting the results to interchange.Our concept is easy to implement and can easily be integrated into alreadyexisting theorem provers. Moreover, the resulting cooperation allows the dis-tributed system to find proofs much faster than single heuristics working alone.We substantiate these claims by two case studies: experiments with the DiCoDesystem that is based on the condensed detachment rule and experiments with theSPASS system, a prover for first order logic with equality based on the super-position calculus. Both case studies show the improvements by our cooperationconcept.
We examine different possibilities of coupling saturation-based theorem pro-vers by exchanging positive/negative information. We discuss which positive ornegative information is well-suited for cooperative theorem proving and show inan abstract way how this information can be used. Based on this study, we in-troduce a basic model for cooperative theorem proving. We present theoreticalresults regarding the exchange of positive/negative information as well as practi-cal methods and heuristics that allow for a gain of efficiency in comparison withsequential provers. Finally, we report on experimental studies conducted in theareas condensed detachment, unfailing completion, and superposition.The author was supported by the Deutsche Forschungsgemeinschaft (DFG).
We investigate the usage of so-called inference rights. We point out the prob-lems arising from the inflexibility of existing approaches to heuristically controlthe search of automated deduction systems, and we propose the application ofinference rights that are well-suited for controlling the search more flexibly. More-over, inference rights allow for a mechanism of "partial forgetting" of facts thatis not realizable in the most controlling aproaches. We study theoretical founda-tions of inference rights as well as the integration of inference rights into alreadyexisting inference systems. Furthermore, we present possibilities to control suchmodified inference systems in order to gain efficiency. Finally, we report onexperimental results obtained in the area of condensed detachment.The author was supported by the Deutsche Forschungsgemeinschaft (DFG).
We present a methodology for coupling several saturation-based theoremprovers (running on different computers). The methodology is well-suited for re-alizing cooperation between different incarnations of one basic prover. Moreover,also different heterogeneous provers - that differ from each other in the calculusand in the heuristic they employ - can be coupled. Cooperation between the dif-ferent provers is achieved by periodically interchanging clauses which are selectedby so-called referees. We present theoretic results regarding the completeness ofthe system of cooperating provers as well as describe concrete heuristics for de-signing referees. Furthermore, we report on two experimental studies performedwith homogeneous and heterogeneous provers in the areas superposition and un-failing completion. The results reveal that the occurring synergetic effects leadto a significant improvement of performance.
We examine an approach for demand-driven cooperative theorem proving.We briefly point out the problems arising from the use of common success-driven cooperation methods, and we propose the application of our approachof requirement-based cooperative theorem proving. This approach allows for abetter orientation on current needs of provers in comparison with conventional co-operation concepts. We introduce an abstract framework for requirement-basedcooperation and describe two instantiations of it: Requirement-based exchangeof facts and sub-problem division and transfer via requests. Finally, we reporton experimental studies conducted in the areas superposition and unfailing com-pletion.The author was supported by the Deutsche Forschungsgemeinschaft (DFG).