Semiotic Modeling for De-Duplication

of Text Strings

Using A Word-Stack Approach



J.B. Phillips, R.Wiltshire, P.Prueitt, G.Price

Engineering Development Institute
and
Highland Technologies




Introduction


One of the most fundamental relationships in an algebraic structure is the property of equality. The reflexive property of equality (Selby and Sweet, 1969) states that

(1)      A = A

and the commutative (otherwise referred to as the symmetric) property of equality (Kuratowski and Mostowski, 1968) states that if

(2)      A(operator)B = C

then

(3)      B(operator)A = C

However, these properties assume an altogether different meaning if A or B can change over time. Thus, if

(4)      A|t = 0   A|t = t1

then the entire concept of equality is eroded substantially.

Similarly, the concept of a function hinges on the constancy of values. If

(5)      f(A|t = 0) f(A|t = t1),

which is part of the definition of a function, contingent upon Eq. (4), then the concept of a function also assumes a dramatically different meaning. Moreover, assume that

(6)      A|t = t2 = A|t = t3

Then if

(7)      f(A|t = t2) f(A|t = t3),

it can be concluded that f is not a true function.


Consider the following definition of a function (Michel and Herget, 1981):

Let X and Y be non-void sets. A function f from X into Y is a subset of X Y = {(x, y): x X, y Y} x X a unique y Y (x, y) f. The set X is called the domain of f, and we say that f is defined on X. The set {y Y: (x, y) f for some x X} is called the range of f, and is denoted by (f). (x, y) f, we call y the value of f at x and denote it by f(x). We write f:XY to denote the function f from X into Y, or mapping X into Y.




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AS/SA Nº 6/7, Article 1 : Page 1 / 13

© 1999, AS/SA

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1999.05.31