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System Description: MathWeb, an AgentBased Communication Layer for Distributed Automated Theorem Proving
, 1999
"... Realworld applications of theorem proving require open and modern software environments that enable modularization,... ..."
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Cited by 36 (15 self)
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Realworld applications of theorem proving require open and modern software environments that enable modularization,...
PDS  A ThreeDimensional Data Structure for Proof Plans
 PROC. OF ACIDCA'2000
, 2000
"... We present a new data structure that enables to store threedimensional proof objects in a proof development environment. The aim is to handle calculus level proofs as well as abstract proof plans together with information of their correspondences in a single structure. This enables not only differe ..."
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Cited by 28 (8 self)
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We present a new data structure that enables to store threedimensional proof objects in a proof development environment. The aim is to handle calculus level proofs as well as abstract proof plans together with information of their correspondences in a single structure. This enables not only different means of the proof development environment (e.g., rule and tacticbased theorem proving, or proof planning) to act directly on the same proof object but it also allows for easy presentation of proofs on different levels of abstraction. However, the threedimensional structure requires adjustment of the regular techniques for addition and deletion of proof lines and backtracking of the proof planner.
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...
LΩUI: Lovely ΩMEGA User Interface
, 2001
"... The capabilities of a automated theorem prover's interface are essential for the effective use of (interactive) proof systems. LΩUI is the ..."
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Cited by 10 (7 self)
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The capabilities of a automated theorem prover's interface are essential for the effective use of (interactive) proof systems. LΩUI is the
System Description: TRAMP  Transformation of MachineFound Proofs into Natural Deduction Proofs at the Assertion Level
 Proceedings of the 17th International Conference on Automated Deduction, number 1831 in Lecture Notes in Artificial Intelligence
, 2000
"... . The Tramp system transforms the output of several automated theorem provers for rst order logic with equality into natural deduction proofs at the assertion level. Through this interface, other systems such as proof presentation systems or interactive deduction systems can access proofs origin ..."
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Cited by 9 (0 self)
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. The Tramp system transforms the output of several automated theorem provers for rst order logic with equality into natural deduction proofs at the assertion level. Through this interface, other systems such as proof presentation systems or interactive deduction systems can access proofs originally produced by any system interfaced by Tramp only by adapting the assertion level proofs to their own needs. 1 Introduction Today's theorem proving systems (automatic and interactive ones) have reached a considerable strength. However, it has become clear that no single system is capable of handling all sorts of deduction tasks. Therefore, it is a wellestablished approach to delegate subgoals to other (specialist) systems such as automated theorem provers (ATPs). Unfortunately, most ATPs use their own particular formalism. These machineoriented formalisms make the proofs dicult to read. Hence, in order to make use of the results of the ATPs other systems need to adapt the output of ...
A Structured Set of HigherOrder Problems
 Theorem Proving in Higher Order Logics: TPHOLs 2005, LNCS 3603
, 2005
"... Abstract. We present a set of problems that may support the development of calculi and theorem provers for classical higherorder logic. We propose to employ these test problems as quick and easy criteria preceding the formal soundness and completeness analysis of proof systems under development. Ou ..."
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Cited by 8 (5 self)
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Abstract. We present a set of problems that may support the development of calculi and theorem provers for classical higherorder logic. We propose to employ these test problems as quick and easy criteria preceding the formal soundness and completeness analysis of proof systems under development. Our set of problems is structured according to different technical issues and along different notions of semantics (including Henkin semantics) for higherorder logic. Many examples are either theorems or nontheorems depending on the choice of semantics. The examples can thus indicate the deductive strength of a proof system. 1 Motivation: Test Problems for HigherOrder Reasoning Systems Test problems are important for the practical implementation of theorem provers as well as for the preceding theoretical development of calculi, strategies and heuristics. If the test theorems can be proven (resp. the nontheorems cannot) then they ideally provide a strong indication for completeness (resp. soundness). Examples for early publications providing firstorder test problems are [21,29,23]. For more than decade now the TPTP library [28] has been developed as a systematically structured electronic repository of
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...
ΩMEGA  a mathematical assistant system
 ESSAYS DEDICATED TO JOHAN VAN BENTHEM ON THE OCCASION OF HIS 50TH BIRTHDAY
, 1999
"... Classical automated theorem provers can prove nontrivial mathematical theorems in highly specific settings. However they are generally unable to cope with even moderately difficult theorems in mainstream mathematics. While there are many reasons for the failure of the classical searchbased paradig ..."
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Cited by 1 (0 self)
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Classical automated theorem provers can prove nontrivial mathematical theorems in highly specific settings. However they are generally unable to cope with even moderately difficult theorems in mainstream mathematics. While there are many reasons for the failure of the classical searchbased paradigm, it is apparent that mathematicians can cope with long and complex proofs and have strategies to avoid less promising proof paths without suffering from the exponential search spaces. Consequently, a combination of the power of automated tools with humanlike capabilities seems necessary to prove mainstream mathematical theorems with the help of a machine. In the following, we shall describe the prototypical system Ωmega that explores proof planning together with highlevel proof tools. Ωmega is a mixedinitiative system with the ultimate goal of supporting theorem proving in mainstream mathematics and mathematics education.
LOmegaUI: Lovely OMEGA User Interface
, 2001
"... The capabilities of a automated theorem prover's interface are essential for the effective use of (interactive) proof systems. ..."
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The capabilities of a automated theorem prover's interface are essential for the effective use of (interactive) proof systems.
An Agentbased Approach to Reasoning
, 2001
"... This paper discusses an agent based approach to automated and interactive reasoning. It 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 ove ..."
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This paper discusses an agent based approach to automated and interactive reasoning. It 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. The approach particularly supports cooperative proofs between reasoning agents which are strong in different applications areas, e.g., higherorder and firstorder theorem provers and computer algebra systems.