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History and Future of Implicit and Inductionless Induction: Beware the Old Jade and The Zombie!
, 2005
"... In this survey on implicit induction I recollect some memories on the history of implicit induction as it is relevant for future research on computerassisted theorem proving, esp. memories that significantly differ from the presentation in a recent handbook article on “inductionless induction”. M ..."
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In this survey on implicit induction I recollect some memories on the history of implicit induction as it is relevant for future research on computerassisted theorem proving, esp. memories that significantly differ from the presentation in a recent handbook article on “inductionless induction”. Moreover, the important references excluded there are provided here. In order to clear the fog a little, there is a short introduction to inductive theorem proving and a discussion of connotations of implicit induction like “descente infinie”, “inductionless induction”, “proof by consistency”, implicit induction orderings (term orderings), and refutational completeness.
The use of theorem provers in the teaching and practice of formal methods
 In Proceedings of the Irish Workshop on Formal Methods
, 1997
"... ©Copyright in this paper belongs to the author(s) Published in collaboration with the ..."
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©Copyright in this paper belongs to the author(s) Published in collaboration with the
Computing Presuppositions and Implicatures in Mathematical Discourse
"... In any wellwritten mathematical discourse a certain amount of mathematical and metamathematical knowledge is presupposed and implied. We give an account on presuppositions and implicatures in mathematical discourse and describe an architecture that allows to e ectively interpret them. Our approach ..."
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In any wellwritten mathematical discourse a certain amount of mathematical and metamathematical knowledge is presupposed and implied. We give an account on presuppositions and implicatures in mathematical discourse and describe an architecture that allows to e ectively interpret them. Our approach heavily relies on proof methods that capture common patterns of argumentation in mathematical discourse. This pragmatic information provides a highlevel strategic discourse understanding and allows to compute the presupposed and implied information.
Towards the Mechanical Verification of Textbook Proofs
"... Our goal is to implement a program for the machine verification of textbook proofs. We study the task from both the linguistics and automated reasoning perspective and give an indepth analysis for a sample textbook proof. We propose a framework for natural language proof understanding that extends ..."
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Our goal is to implement a program for the machine verification of textbook proofs. We study the task from both the linguistics and automated reasoning perspective and give an indepth analysis for a sample textbook proof. We propose a framework for natural language proof understanding that extends and integrates stateoftheart technologies from Natural Language Processing (Discourse Representation Theory) and Automated Reasoning (Proof Planning) in a novel and promising way, having the potential to initiate progress in both of these disciplines.
An Intelligent Tutoring System for Induction Proofs
"... interfaces. We will specify and implement abstract interfaces for the student model, the dialogue history and the problem state. 4 Diagnosis and Therapy. We will view the diagnosis task as a plan recognition problem. We will explore the possibilities (i) of using proof plans and Oyster/Clam's proof ..."
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interfaces. We will specify and implement abstract interfaces for the student model, the dialogue history and the problem state. 4 Diagnosis and Therapy. We will view the diagnosis task as a plan recognition problem. We will explore the possibilities (i) of using proof plans and Oyster/Clam's proof planning facility to support the diagnosis and therapy task; (ii) of adapting a probabilistic plan recognition approach using Bayes's belief networks. This is the approach taken in Andes, a physics tutoring system [GCV98] with similar domain properties. Since specifying and implementing the diagnosis and therapy module of Intuition will be a significant project in itself, we will recruit a PhD student who will concentrate his research efforts solely on these components: 4.1 Knowledge acquisition (6pm), literature survey (3pm), and summarisation of intermediate results (1pm). 4.2 Diagnosis module (9pm), and summarisation of intermediate results (1pm). 4.3 Therapy module (9pm), and summar...
Reasoning About Logic Programs Using Definitions And Induction
, 2002
"... In this dissertation, we exhibit work revolving around the FO metalogic. After going over some of the background material on FO , we discuss work about induction, and give induction principles that are richer than mathematical induction, in that they yield shorter, simpler and more elegant pr ..."
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In this dissertation, we exhibit work revolving around the FO metalogic. After going over some of the background material on FO , we discuss work about induction, and give induction principles that are richer than mathematical induction, in that they yield shorter, simpler and more elegant proofs. We then define and study notions of entailment and equivalence between two FO definitions. We make use of these notions by defining a framework, closely related to FO , for performing program transformation on definitions, and proving it correct. Finally, we discuss implementations in Prolog of Iris, a theorem prover based on FO tool based on the framework we built.
Conditionals and PseudoConditionals in Mathematical Texts
"... Conditionals are the basic ingredient of a mathematical argument. We present an analysis of conditionals and pseudoconditional in mathematical discourse, and then propose a computational framework for the (re)construction and semantic representation of conditional dependencies. 1 ..."
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Conditionals are the basic ingredient of a mathematical argument. We present an analysis of conditionals and pseudoconditional in mathematical discourse, and then propose a computational framework for the (re)construction and semantic representation of conditional dependencies. 1