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Planning Diagonalization Proofs
 IN PROCEEDINGS OF 8TH INTERNATIONAL CONFERENCE ON ARTI INTELLIGENCE: METHODOLOGY, SYSTEMS, APPLICATIONS (AIMSA'98), LNAI, SOZOPOL
, 1997
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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 6 (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
A proofcentric approach to mathematical assistants
 Journal of Applied Logic: Special Issue on Mathematics Assistance Systems
, 2005
"... We present an approach to mathematical assistants which uses readable, executable proof scripts as the central language for interaction. We examine an implementation that combines the Isar language, the Isabelle theorem prover and the IsaPlanner proof planner. We argue that this synergy provides a f ..."
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Cited by 5 (1 self)
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We present an approach to mathematical assistants which uses readable, executable proof scripts as the central language for interaction. We examine an implementation that combines the Isar language, the Isabelle theorem prover and the IsaPlanner proof planner. We argue that this synergy provides a flexible environment for the exploration, certification, and presentation of mathematical proof.
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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Cited by 3 (3 self)
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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...
The Mechanization of the Diagonalization Proof Strategy
 FACHBEREICH INFORMATIK, UNIVERSITAT DES SAARLANDES, IM STADTWALD
, 1996
"... We present an empirical study of mathematical proofs by diagonalization, the aim is their mechanization based on proof planning techniques. We show that these proofs can be constructed according to a strategy that (i) finds an indexing relation, (ii) constructs a diagonal element, and (iii) makes th ..."
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Cited by 2 (1 self)
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We present an empirical study of mathematical proofs by diagonalization, the aim is their mechanization based on proof planning techniques. We show that these proofs can be constructed according to a strategy that (i) finds an indexing relation, (ii) constructs a diagonal element, and (iii) makes the implicit contradiction of the diagonal element explicit. Moreover we suggest how diagonal elements can be represented.
Generating Effective Constraint Programs: An Application of Automated Reasoning
"... Constraint programming has proven to be successful at solving a wide range of problems including important industrial problems. To solve a problem, one first “models ” it by characterising its solutions by the constraints ..."
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Cited by 1 (0 self)
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Constraint programming has proven to be successful at solving a wide range of problems including important industrial problems. To solve a problem, one first “models ” it by characterising its solutions by the constraints
Towards an Open System for Theorem Proving
, 1998
"... In this contribution I advocate an open system for formalised mathematical reasoning that is able to capture different mathematical formalisms as well as a wide variety of proof formats. This is assumed to be much more adequate since it more closely reflects the situation in mathematics as a whole. ..."
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In this contribution I advocate an open system for formalised mathematical reasoning that is able to capture different mathematical formalisms as well as a wide variety of proof formats. This is assumed to be much more adequate since it more closely reflects the situation in mathematics as a whole. In particular I try to classify different dimension according to which proofs can be classified. 1 Introduction One of the ultimate goals of the mechanisation of proofs is to achieve an increased rigour in proof. Mathematics generally enjoys the prestige of being the correct scientific discipline par excellence. This reputation stems from the requirement that every claim must be justified by a rigorous proof. The ultimate goal of many mechanised reasoning systems is to support mathematicians in the task of constructing such a proof. This is not trivial, since in traditional mathematical practice, proofs are not given in terms of single calculus rules but at a level of abstraction that conv...
Decision Planning Knowledge . . .
 ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
, 2003
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