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Goal Oriented Equational Theorem Proving Using Team Work
 University of Kaiserslautern
, 1994
"... The team work method is a concept for distributing automated theorem provers and so to activate several experts to work on a given problem. We have implemented this for pure equational logic using the unfailing KnuthBendix completion procedure as basic prover. In this paper we present three classes ..."
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Cited by 25 (12 self)
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The team work method is a concept for distributing automated theorem provers and so to activate several experts to work on a given problem. We have implemented this for pure equational logic using the unfailing KnuthBendix completion procedure as basic prover. In this paper we present three classes of experts working in a goal oriented fashion. In general, goal oriented experts perform their job "unfair" and so are often unable to solve a given problem alone. However, as a team member in the team work method they perform highly efficient, even in comparison with such respected provers as Otter 3.0 or REVEAL, as we demonstrate by examples, some of which can only be proved using team work. The reason for these achievements results from the fact that the team work method forces the experts to compete for a while and then to cooperate by exchanging their best results. This allows one to collect "good" intermediate results and to forget "useless" ones. Completion based proof methods are fr...
Distributing Equational Theorem Proving
, 1993
"... In this paper we show that distributing the theorem proving task to several experts is a promising idea. We describe the team work method which allows the experts to compete for a while and then to cooperate. In the cooperation phase the best results derived in the competition phase are collected an ..."
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Cited by 22 (6 self)
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In this paper we show that distributing the theorem proving task to several experts is a promising idea. We describe the team work method which allows the experts to compete for a while and then to cooperate. In the cooperation phase the best results derived in the competition phase are collected and the less important results are forgotten. We describe some useful experts and explain in detail how they work together. We establish fairness criteria and so prove the distributed system to be both, complete and correct. We have implemented our system and show by nontrivial examples that drastical time speedups are possible for a cooperating team of experts compared to the time needed by the best expert in the team.
AgentOriented Integration of Distributed Mathematical Services
 Journal of Universal Computer Science
, 1999
"... Realworld applications of automated theorem proving require modern software environments that enable modularisation, networked interoperability, robustness, and scalability. These requirements are met by the AgentOriented Programming paradigm of Distributed Artificial Intelligence. We argue that ..."
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Cited by 19 (10 self)
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Realworld applications of automated theorem proving require modern software environments that enable modularisation, networked interoperability, robustness, and scalability. These requirements are met by the AgentOriented Programming paradigm of Distributed Artificial Intelligence. We argue that a reasonable framework for automated theorem proving in the large regards typical mathematical services as autonomous agents that provide internal functionality to the outside and that, in turn, are able to access a variety of existing external services. This article describes...
Planning for distributed theorem proving: The team work approach
 Proc. KI96, Dresden, LNAI 1137
, 1996
"... This paper presents a new way to use planning in automated theorem proving by means of distribution. To overcome the problem that often subtasks for a proof problem can not be detected a priori (which prevents the use of the known planning and distribution techniques) we use a team of experts that w ..."
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Cited by 16 (10 self)
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This paper presents a new way to use planning in automated theorem proving by means of distribution. To overcome the problem that often subtasks for a proof problem can not be detected a priori (which prevents the use of the known planning and distribution techniques) we use a team of experts that work independently with different heuristics on the problem. After a certain amount of time referees judge their results using the impact of the results on the behaviour of the expert and a supervisor combines the selected results to a new starting point. This supervisor also selects the experts that can work on the problem in the next round. This selection is a reactive planning task. We outline which information the supervisor can use to fulfill this task and how this information is processed to result in a plan or to revise a plan. We also show that the use of planning for the assignment of experts to the team allows the system to solve many different examples in an acceptable time with th...
A Taxonomy of Parallel Strategies for Deduction
 Annals of Mathematics and Artificial Intelligence
, 1999
"... This paper presents a taxonomy of parallel theoremproving methods based on the control of search (e.g., masterslaves versus peer processes), the granularity of parallelism (e.g., fine, medium and coarse grain) and the nature of the method (e.g., orderingbased versus subgoalreduction) . We anal ..."
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Cited by 14 (1 self)
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This paper presents a taxonomy of parallel theoremproving methods based on the control of search (e.g., masterslaves versus peer processes), the granularity of parallelism (e.g., fine, medium and coarse grain) and the nature of the method (e.g., orderingbased versus subgoalreduction) . We analyze how the di#erent approaches to parallelization a#ect the control of search: while fine and mediumgrain methods, as well as masterslaves methods, generally do not modify the sequential search plan, parallelsearch methods may combine sequential search plans (multisearch) or extend the search plan with the capability of subdividing the search space (distributed search). Precisely because the search plan is modified, the latter methods may produce radically di#erent searches than their sequential base, as exemplified by the first distributed proof of the Robbins theorem generated by the Modified ClauseDi#usion prover Peersmcd. An overview of the state of the field and directions...
An Implementation of Distributed Mathematical Services
, 1998
"... Realworld applications of theorem proving require open and modern software environments that enable modularization, distribution, interoperability, networking, and coordination. This paper describes the DMS architecture for automated theorem proving that connects a widerange of mathematical servi ..."
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Cited by 1 (0 self)
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Realworld applications of theorem proving require open and modern software environments that enable modularization, distribution, interoperability, networking, and coordination. This paper describes the DMS architecture for automated theorem proving that connects a widerange of mathematical services by a common, mathematical software bus. It also presents an implementation, OzDMS, of the architecture in the Oz programming language. OzDMS provides the functionality to turn existing theorem proving systems and tools into mathematical services that are homogeneously integrated into a networked proof development environment. The environment thus gains the services from these particular modules, but each module in turn gains from using the features of other, pluggedin components. 1 Introduction The work reported in this paper originates in the effort to develop a practical mathematical assistant system that integrates external deductive components. The\Omega megasystem [BCF + 97...
Coordination of Mathematical Agents
, 2001
"... Mathematical Services . . . . . . . . . . . . . . . . . . . 10 2.3.2 Autonomy and Decentralization . . . . . . . . . . . . . . . . . . . 11 2.3.3 Coordination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3 Distributed Articial Intelligence 12 3.1 AgentOriented Programming . . . . . ..."
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Mathematical Services . . . . . . . . . . . . . . . . . . . 10 2.3.2 Autonomy and Decentralization . . . . . . . . . . . . . . . . . . . 11 2.3.3 Coordination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3 Distributed Articial Intelligence 12 3.1 AgentOriented Programming . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 The Knowledge Query and Manipulation Language . . . . . . . . . . . . 13 3.3 Coordination in MultiAgent Systems . . . . . . . . . . . . . . . . . . . 13 4 Agent Technology for Distributed Mathematical Reasoning 15 4.1 MathWeb Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.2 Communication between MathWeb agents . . . . . . . . . . . . . . . . . 18 4.2.1 Technical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2.2 Characterization of Reasoning Capabilities . . . . . . . . . . . . 18 4.2.3 Context in Mathematical Communication . . . . . . . . . . . . . 19 4.3 Coordination of MathWeb Agents . . . . . . . . . . . . . . . . . . . . . 20 5 Summary and Work Plan 22 5.1 Work Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1