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OMDoc: Towards an Internet Standard for the Administration, Distribution and Teaching of mathematical Knowledge
 IN PROCEEDINGS AISC'2000
, 2000
"... In this paper we present an extension OMDoc to the OpenMath standard that allows to represent the semantics and structure of various kinds of mathematical documents, including articles, textbooks, interactive books, courses. It can serve as the content language for agent communication of mathematic ..."
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Cited by 42 (5 self)
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In this paper we present an extension OMDoc to the OpenMath standard that allows to represent the semantics and structure of various kinds of mathematical documents, including articles, textbooks, interactive books, courses. It can serve as the content language for agent communication of mathematical services on a mathematical software bus.
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,...
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...
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.
Automated Reasoning for Computational Semantics
, 1999
"... This paper discusses inference in computational semantics. We argue that stateoftheart methods in firstorder theorem proving and model building are of direct relevance to inference for natural language processing. We support our claim by discussing the inferential aspects of several higher disco ..."
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This paper discusses inference in computational semantics. We argue that stateoftheart methods in firstorder theorem proving and model building are of direct relevance to inference for natural language processing. We support our claim by discussing the inferential aspects of several higher discourse phenomena and reporting on an experiment where the induced deduction problems are solved by the MathWeb society of theorem proving agents. Keywords: Automated Reasoning, discourse, natural language processing, theorem proving 1 Introduction Semantic analysis  inference on the basis of semantic information and world knowledge  is one of the central cognitive tasks in naturallanguage processing (NLP) and Artificial Intelligence. It is needed for situationdependent disambiguation and for the coherent embedding of utterances into the discourse context. Humans obviously have at their disposal very efficient techniques for semantic analysis, in NLP, similarly powerful techniques have...
Integrating HR and tptp2X into MathWeb to Compare Automated Theorem Provers
 In Proceedings of the CADE'02 Workshop on Problems and Problem sets
, 2002
"... The assessment and comparison of automated theorem proving systems (ATPs) is important for the advancement of the field. At present, the de facto assessment method is to test provers on the TPTP library of nearly 6000 theorems. We describe here a project which aims to complement the TPTP service by ..."
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The assessment and comparison of automated theorem proving systems (ATPs) is important for the advancement of the field. At present, the de facto assessment method is to test provers on the TPTP library of nearly 6000 theorems. We describe here a project which aims to complement the TPTP service by automatically generating theorems of sufficient diculty to provide a significant test for first order provers. This has been achieved by integrating the HR automated theory formation program into the MathWeb Software Bus. HR generates first order conjectures in TPTP format and passes them to a concurrent ATP service in MathWeb. MathWeb then uses the tptp2X utility to translate the conjectures into the input format of a set of provers. In this way, various ATP systems can be compared on their performance over sets of thousands of theorems they have not been previously exposed to. Our purpose here is to describe the integration of various new programs into the MathWeb architecture, rather than to present a full analysis of the performance of theorem provers. However, to demonstrate the potential of the combination of the systems, we describe some preliminary results from experiments in group theory.
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