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ΩANTS  An open approach at combining Interactive and Automated Theorem Proving
 IN PROC. OF CALCULEMUS2000. AK PETERS
, 2000
"... We present the ΩAnts theorem prover that is built on top of an agentbased command suggestion mechanism. The theorem prover inherits beneficial properties from the underlying suggestion mechanism such as runtime extendibility and resource adaptability. Moreover, it supports the distributed integ ..."
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Cited by 35 (23 self)
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We present the ΩAnts theorem prover that is built on top of an agentbased command suggestion mechanism. The theorem prover inherits beneficial properties from the underlying suggestion mechanism such as runtime extendibility and resource adaptability. Moreover, it supports the distributed integration of external reasoning systems. We also introduce some notions that need to be considered to check completeness and soundness of such a system with respect to an underlying calculus.
Experiments with an Agentoriented Reasoning System
 In In Proc. of KI 2001, volume 2174 of LNAI
, 2001
"... Abstract. This paper discusses experiments with an agent oriented approach to automated and interactive reasoning. The approach combines ideas from two subfields of AI (theorem proving/proof planning and multiagent systems) and makes use of state of the art distribution techniques to decentralise a ..."
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Cited by 12 (8 self)
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Abstract. This paper discusses experiments with an agent oriented approach to automated and interactive reasoning. The approach combines ideas from two subfields of AI (theorem proving/proof planning and multiagent systems) and makes use of state of the art distribution techniques to decentralise and spread its reasoning agents over the internet. It particularly supports cooperative proofs between reasoning systems which are strong in different application areas, e.g., higherorder and firstorder theorem provers and computer algebra systems. 1
Distributed Assertion Retrieval
, 2001
"... ning with respect to given assumptions at the assertion level. We can depict the assertion tactic as a general inference rule in the following way P rems Goal Assertion(Ass) where P rems is a list of premises, Goal is the conclusion and Ass is the assertion that is applied. Determining possible ..."
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Cited by 3 (1 self)
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ning with respect to given assumptions at the assertion level. We can depict the assertion tactic as a general inference rule in the following way P rems Goal Assertion(Ass) where P rems is a list of premises, Goal is the conclusion and Ass is the assertion that is applied. Determining possible assertion applications for subsequent subgoals in a proof attempt can easily become a very dicult task and a direct, sequential interleaving of assertion applicability tests with the main theorem proving loop is a rather ineligible option. 1 Firstly, there might be too many assertions in the database to be checked sequentially in each proof step. This motivates a concurrent mechanism; optimally one with anytime behavior, that allows to continue the proving process regardless of termination of applicability checks for assertions but also to resume those checks if necessary. Secondly, each applicabilit
ΩMEGA: Computer supported mathematics
 IN: PROCEEDINGS OF THE 27TH GERMAN CONFERENCE ON ARTIFICIAL INTELLIGENCE (KI 2004)
, 2004
"... The year 2004 marks the fiftieth birthday of the first computer generated proof of a mathematical theorem: “the sum of two even numbers is again an even number” (with Martin Davis’ implementation of Presburger Arithmetic in 1954). While Martin Davis and later the research community of automated dedu ..."
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Cited by 3 (3 self)
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The year 2004 marks the fiftieth birthday of the first computer generated proof of a mathematical theorem: “the sum of two even numbers is again an even number” (with Martin Davis’ implementation of Presburger Arithmetic in 1954). While Martin Davis and later the research community of automated deduction used machine oriented calculi to find the proof for a theorem by automatic means, the Automath project of N.G. de Bruijn – more modest in its aims with respect to automation – showed in the late 1960s and early 70s that a complete mathematical textbook could be coded and proofchecked by a computer. Classical theorem proving procedures of today are based on ingenious search techniques to find a proof for a given theorem in very large search spaces – often in the range of several billion clauses. But in spite of many successful attempts to prove even open mathematical problems automatically, their use in everyday mathematical practice is still limited. The shift
Towards Concurrent Resource Managed Deduction
 UNIVERSITY OF BIRMINGHAM, SCHOOL OF COMPUTER SCIENCE. URL
, 1999
"... In this paper, we describe an architecture for resource guided concurrent mechanised deduction which is motivated by some findings in cognitive science. Its benefits are illustrated by comparing it with traditional proof search techniques. In particular, we introduce the notion of focused search ..."
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Cited by 3 (2 self)
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In this paper, we describe an architecture for resource guided concurrent mechanised deduction which is motivated by some findings in cognitive science. Its benefits are illustrated by comparing it with traditional proof search techniques. In particular, we introduce the notion of focused search and show that a reasoning system can be built as the cooperative collection of concurrently acting specialised problem solvers. These reasoners typically perform well in a particular problem domain. The system architecture that we describe assesses the subgoals of a theorem and distributes them to the specialised solvers that look the most promising. Furthermore it allocates resources (above all computation time and memory) to the specialised reasoners. This technique is referred to as resource management. Each reasoner terminates its search for a solution of a given subgoal when the solution is found or when it runs out of its assigned resources. We argue that the effect of resource ma...
Towards FineGrained Proof Planning with Critical Agents
, 1999
"... ,u:L 1 ) (s:L 2 ,u:L 1 ,pl:(1)) : : : goal is HO goal is HO goal is HO message: goal is HO Classif. Agent Figure 1: The two layered suggestion mechanism. We have developed a mechanism that suggests commands, applicable in the current proof state together with a suitable argument instanti ..."
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Cited by 2 (1 self)
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,u:L 1 ) (s:L 2 ,u:L 1 ,pl:(1)) : : : goal is HO goal is HO goal is HO message: goal is HO Classif. Agent Figure 1: The two layered suggestion mechanism. We have developed a mechanism that suggests commands, applicable in the current proof state together with a suitable argument instantiations [1]. It is based on two layers of societies of autonomous, concurrent agents which steadily work in the background of a system and dynamically update their computational behavior to the state of the proof and/or specific user queries to the suggestion mechanism (cf. Fig. 1). By exchanging relevant results via blackboards the agents cooperatively accumulate useful command suggestions which can be heuristically sorted and presented to the user. The architecture has been prototypically implemented in the\Omega mega mathematical assistant system [4] for interactive tactical theorem provi
Agent based mathematical reasoning
 IN PROCEEDINGS OF THE CALCULEMUS WORKSHOP: SYSTEMS FOR INTEGRATED COMPUTATION AND DEDUCTION
, 1999
"... In this contribution we propose an agent architecture for theorem proving which we intend to investigate in depth in the future. The work reported in this paper is in an early state, and by no means finished. We present and discuss our proposal in order to get feedback from the Calculemus community. ..."
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Cited by 1 (1 self)
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In this contribution we propose an agent architecture for theorem proving which we intend to investigate in depth in the future. The work reported in this paper is in an early state, and by no means finished. We present and discuss our proposal in order to get feedback from the Calculemus community.
Semantically Guided ΩMEGA Proof Planner
, 2001
"... Proof planning is an application of AIplanning in mathematical domains. The planning operators, called methods, encode proving steps. One of the strength of proof planning comes from the usage of mathematical knowledge that heuristically restricts the search space. Semantically guided proof plannin ..."
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Proof planning is an application of AIplanning in mathematical domains. The planning operators, called methods, encode proving steps. One of the strength of proof planning comes from the usage of mathematical knowledge that heuristically restricts the search space. Semantically guided proof planning takes a different perspective and uses semantic information as search control heuristics. In this report we describe the realisation of semantically guided proof planning in the framework of the Ωmega system. We realised a module that answers queries from Multi, a multistrategy proof planner of Ωmega, whether a concrete method application is suitable with respect to the semantic information as well as how promising the method application is. Provided with this information Multi rejects unsuitable method applications and prefers the most promising ones.