TY - JOUR

T1 - The Challenges of Multivalued "Functions"

AU - Davenport, James

N1 - Invited talk at Artificial Intelligence and Symbolic Computation 2010, part of the Conferences in Intelligent Mathematics 2010, 4-10 July 2010. Paris, France.

PY - 2010/7

Y1 - 2010/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77954872736&partnerID=8YFLogxK

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

U2 - 10.1007/978-3-642-14128-7_1

DO - 10.1007/978-3-642-14128-7_1

M3 - Article

SN - 0302-9743

VL - 6167

SP - 1

EP - 12

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

ER -