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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
Proof Planning: A Practical Approach To Mechanized Reasoning In Mathematics
, 1998
"... INTRODUCTION The attempt to mechanize mathematical reasoning belongs to the first experiments in artificial intelligence in the 1950 (Newell et al., 1957). However, the idea to automate or to support deduction turned out to be harder than originally expected. This can not at least be seen in the mul ..."
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Cited by 8 (3 self)
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INTRODUCTION The attempt to mechanize mathematical reasoning belongs to the first experiments in artificial intelligence in the 1950 (Newell et al., 1957). However, the idea to automate or to support deduction turned out to be harder than originally expected. This can not at least be seen in the multitude of approaches that were pursued to model different aspects of mathematical reasoning. There are different dimension according to which these systems can be classified: input language (e.g., ordersorted firstorder logic), calculus (e.g., resolution), interaction level (e.g., batch mode), proof output (e.g., refutation graph), and the purpose (e.g., automated theorem proving) as well as many more subtle points concerning the fine tuning of the proof search. In this contribution the proof planning approach will be presented. Since it is not the mainstream approach to mechanized reasoning, it seems to be worth to look at it in a more principled way and to contrast it to other appro
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 5 (4 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
A multimodi Proof Planner
 UNIVERSITY OF KOBLENZLANDAU
, 1998
"... Proof planning is a novel knowledgebased approach for proof construction, which supports the incorporation of mathematical knowledge and the common mathematical proof techniques of a particular mathematical field. This paradigm is adopted in the\Omega mega proof development system, to provide supp ..."
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Proof planning is a novel knowledgebased approach for proof construction, which supports the incorporation of mathematical knowledge and the common mathematical proof techniques of a particular mathematical field. This paradigm is adopted in the\Omega mega proof development system, to provide support for the user. A considerable part of the proof construction and even sometimes the whole work can be undertaken by a proof planner. In the \Omega mega project we are investigating the aspect of computation under bounded resources in mathematical theorem proving. The relevant resources are, in addition to time and memory space, user availability as well as the frequency of user interaction. At this issue, the proof planner of\Omega mega is conceived in such a way that it has a resourceadaptive behaviour. This property of the planner is achieved by a planner modus which defines the planner behaviour depending on which and how many resources are available. In this paper, we describe the...
Proof Development with ΩMEGA: √2 Is Irrational
, 2002
"... Freek Wiedijk proposed the wellknown theorem about the irrationality of √2 as a case study and used this theorem for a comparison of fifteen (interactive) theorem proving systems, which were asked to present their solution (see [48]). This represents an important shift of emphasis in the field of a ..."
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Freek Wiedijk proposed the wellknown theorem about the irrationality of √2 as a case study and used this theorem for a comparison of fifteen (interactive) theorem proving systems, which were asked to present their solution (see [48]). This represents an important shift of emphasis in the field of automated deduction away from the somehow artificial problems of the past as represented, for example, in the test set of the TPTP library [45] back to real mathematical challenges. In this paper we present an overview of the Ωmega system as far as it is relevant for the purpose of this paper and show the development of a proof for this theorem.
The Proof Planners of \Omega mega:
, 2004
"... TIK D66123 SAARBRU"CKEN GERMANYWWW: ..."
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ERICA MELIS AND JÖRG H. SIEKMANN CONCEPTS IN PROOF PLANNING
"... Knowledgebased proof planning is a new paradigm in automated theorem proving. Its motivation partly comes from an increasing disillusionment by many researchers in the field of automated deduction, who feel that traditional techniques have been pushed to their limit and – as important as these deve ..."
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Knowledgebased proof planning is a new paradigm in automated theorem proving. Its motivation partly comes from an increasing disillusionment by many researchers in the field of automated deduction, who feel that traditional techniques have been pushed to their limit and – as important as these developments have been in the past
An Interactive Proof Development Environment + Anticipation = A Mathematical Assistant?
, 2000
"... Current semiautomated theorem provers are often advertised as "mathematical assistant systems". However, these tools behave too passively and in a stereotypic way to meet this ambitious goal because they lack the capability to adequately take into account requirements on proof search cont ..."
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Current semiautomated theorem provers are often advertised as "mathematical assistant systems". However, these tools behave too passively and in a stereotypic way to meet this ambitious goal because they lack the capability to adequately take into account requirements on proof search control and user demands for their own actions. Motivated by this deficit, we have incorporated several facilities into the MEGA proof development system that anticipate a number of divergent factors, based on mathematical knowledge, proof search defaults, and expectations about users. The techniques enhance the system's functionality through proof planning by knowledgeintensive methods, proof search guidance by default suggesting agents, and proof presentation by redundancy avoidance measures. The system's behavior suggests that anticipation is without doubt a central driving force in a mathematical assistant. Keywords: Mathematical Assistant System, Automated Theorem Proving, Proof planning, Agents, ...