The Challenges of Multivalued “Functions”

  • James H. Davenport
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6167)


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 Artificial 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.


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • James H. Davenport
    • 1
  1. 1.Department of Computer ScienceUniversity of BathBathUnited Kingdom

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