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Automatic generation of epsilon-delta proofs of continuity

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Artificial Intelligence and Symbolic Computation (AISC 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1476))

Abstract

As part of a project on automatic generation of proofs involving both logic and computation, we have automated the production of some proofs involving epsilon-delta arguments. These proofs involve two or three quantifiers on the logical side, and on the computational side, they involve algebra, trigonometry, and some calculus. At the border of logic and computation, they involve several types of arguments involving inequalities, including transitivity chaining and several types of bounding arguments, in which bounds are sought that do not depend on certain variables. Control mechanisms have been developed for intermixing logical deduction steps with computational steps and with inequality reasoning. Problems discussed here as examples involve the continuity and uniform continuity of various specific functions.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, San Jose State University, 95192, San Jose, California, USA

    Michael Beeson

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  1. Michael Beeson
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Jacques Calmet Jan Plaza

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© 1998 Springer-Verlag Berlin Heidelberg

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Beeson, M. (1998). Automatic generation of epsilon-delta proofs of continuity. In: Calmet, J., Plaza, J. (eds) Artificial Intelligence and Symbolic Computation. AISC 1998. Lecture Notes in Computer Science, vol 1476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055903

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  • DOI: https://doi.org/10.1007/BFb0055903

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64960-1

  • Online ISBN: 978-3-540-49816-2

  • eBook Packages: Springer Book Archive

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