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The Challenges of Multivalued "Functions"


Reference:

Davenport, J., 2010. The Challenges of Multivalued "Functions". Lecture Notes in Computer Science, 6167, pp. 1-12.

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    Official URL:

    http://dx.doi.org/10.1007/978-3-642-14128-7_1

    Abstract

    Although, formally, mathematics is clear that a function is a single-valued object, mathematical practice is looser, particularly with n-th roots and various inverse functions. In this paper, we point out some of the looseness, and ask what the implications are, both for Artifcial Intelligence and Symbolic Computation, of these practices. In doing so, we look at the steps necessary to convert existing texts into (a) rigorous statements (b) rigorously proved statements. In particular we ask whether there might be a constant "de Bruijn factor" [18] as we make these texts more formal, and conclude that the answer depends greatly on the interpretation being placed on the symbols.

    Details

    Item Type Articles
    CreatorsDavenport, J.
    DOI10.1007/978-3-642-14128-7_1
    DepartmentsFaculty of Science > Computer Science
    Publisher StatementAISC2010-submitted.pdf: The original publication is available at www.springerlink.com; Springer-AISC.pdf: The original publication is available at www.springerlink.com
    RefereedNo
    StatusPublished
    ID Code18792
    Additional InformationInvited talk at Artificial Intelligence and Symbolic Computation 2010, part of the Conferences in Intelligent Mathematics 2010, 4-10 July 2010. Paris, France.

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