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Mathematical proofs at a crossroad?
 THEORY IS FOREVER, LECTURES NOTES IN COMPUT. SCI. 3113
, 2004
"... For more than 2000 years, from Pythagoras and Euclid to Hilbert and Bourbaki, mathematical proofs were essentially based on axiomaticdeductive reasoning. In the last decades, the increasing length and complexity of many mathematical proofs led to the expansion of some empirical, experimental, psy ..."
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Cited by 5 (5 self)
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For more than 2000 years, from Pythagoras and Euclid to Hilbert and Bourbaki, mathematical proofs were essentially based on axiomaticdeductive reasoning. In the last decades, the increasing length and complexity of many mathematical proofs led to the expansion of some empirical, experimental
Tutorial dialogs on mathematical proofs
 In Proceedings of the IJCAI Workshop on Knowledge Representation
, 2003
"... The representation of knowledge for a mathematical proof assistant is generally used exclusively for the purpose of proving theorems. Aiming at a broader scope, we examine the use of mathematical knowledge in a mathematical tutoring system with flexible natural language dialog. Based on an analysis ..."
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Cited by 19 (15 self)
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The representation of knowledge for a mathematical proof assistant is generally used exclusively for the purpose of proving theorems. Aiming at a broader scope, we examine the use of mathematical knowledge in a mathematical tutoring system with flexible natural language dialog. Based on an analysis
The informal logic of mathematical proof
 ASPIC2 Argumentation Service Platform with Integrated Components http://www.argumentation.org
, 2007
"... Paul Erdős famously remarked that ‘a mathematician is a machine for turning coffee into theorems ’ [9, p. 7]. The proof of mathematical theorems is central to mathematical practice and to much recent debate about the nature of mathematics. This paper is an attempt to introduce a new perspective on t ..."
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Cited by 9 (3 self)
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Paul Erdős famously remarked that ‘a mathematician is a machine for turning coffee into theorems ’ [9, p. 7]. The proof of mathematical theorems is central to mathematical practice and to much recent debate about the nature of mathematics. This paper is an attempt to introduce a new perspective
COMPUTER UNDERSTANDING OF MATHEMATICAL PROOFS
, 1977
"... Mathematical proofs constitute a mixture of formulas with a subset of natural language. They can be represented as a sequence of lines expressible in the symbolism of predicate calculus. The transition from step to step may depend on a series of logical manipulations and/or on intricate mathematical ..."
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Cited by 1 (0 self)
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Mathematical proofs constitute a mixture of formulas with a subset of natural language. They can be represented as a sequence of lines expressible in the symbolism of predicate calculus. The transition from step to step may depend on a series of logical manipulations and/or on intricate
IMPS: An Interactive Mathematical Proof System
 Journal of Automated Reasoning
, 1993
"... imps is an Interactive Mathematical Proof System intended as a general purpose tool for formulating and applying mathematics in a familiar fashion. The logic of imps is based on a version of simple type theory with partial functions and subtypes. Mathematical specication and inference are perfor ..."
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Cited by 87 (21 self)
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imps is an Interactive Mathematical Proof System intended as a general purpose tool for formulating and applying mathematics in a familiar fashion. The logic of imps is based on a version of simple type theory with partial functions and subtypes. Mathematical specication and inference
DYNAMICAL ASPECTS OF MATHEMATICAL PROOF
"... Abstract: In regarding mathematical thinking as proceeding via operations involving a small number of ‘items ’ at any one time, an important feature is the phenomenon in which a section of mathematical structure may be mentally held as a single unit, possessing an interiority that can be subsequentl ..."
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be subsequently expanded without loss of detail and trigger connections with other parts of cognitive structure. This article discusses the role of this phenomenon of ‘compression ’ and ‘expansion ’ in the manipulation of statements involved in certain types of mathematical proof. Implications for teaching linked
Institutional and personal meanings of mathematical proof
 Educational Studies in Mathematics, V48
, 2001
"... ABSTRACT. Although studies on students ’ difficulties in producing mathematical proofs have been carried out in different countries, few research workers have focussed their attention on the identification of mathematical proof schemes in university students. This information is potentially useful f ..."
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Cited by 12 (0 self)
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ABSTRACT. Although studies on students ’ difficulties in producing mathematical proofs have been carried out in different countries, few research workers have focussed their attention on the identification of mathematical proof schemes in university students. This information is potentially useful
Planning Mathematical Proofs with Methods
 JOURNAL OF INFORMATION PROCESSING AND CYBERNETICS, EIK
, 1994
"... In this article we formally describe a declarative approach for encoding plan operators in proof planning, the socalled methods. The notion of method evolves from the much studied concept tactic and was first used by Bundy. While significant deductive power has been achieved with the planning appro ..."
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Cited by 16 (5 self)
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In this article we formally describe a declarative approach for encoding plan operators in proof planning, the socalled methods. The notion of method evolves from the much studied concept tactic and was first used by Bundy. While significant deductive power has been achieved with the planning
Towards an Interactive Mathematical Proof Language
, 2003
"... Formalizing mathematical proofs has as aim to represent arbitrary mathematical notions and proofs on a computer in order to construct a database of certified results useful to learn and develop the subject. ..."
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Cited by 7 (0 self)
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Formalizing mathematical proofs has as aim to represent arbitrary mathematical notions and proofs on a computer in order to construct a database of certified results useful to learn and develop the subject.
English summaries of mathematical proofs
 Second International Joint Conference on Automated Reasoning — Workshop on ComputerSupported Mathematical Theory Development
, 2004
"... Automated theorem proving is becoming more important as the volume of applications in industrial and practical research areas increases. Due to the formalism of theorem provers and the massive amount of information included in machineoriented proofs, formal proofs are difficult to understand withou ..."
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Cited by 4 (0 self)
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without specific training. A verbalisation system, ClamNL, was developed to generate English text from formal representations of inductive proofs, as produced by the Clam proof planner. The aim was to generate natural language proofs that resemble the presentation of proofs found in mathematical textbooks
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