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A distance function is proposed that maps pairs of strings to the real numbers. It has been shown that given suitable constraints the function is a metric over the free monoid generated from a set of grammatical symbols. The necessary constraints modify the metric so that it maps pairs of strings to a lattice of real numbers. Thus for each string the metric defines a countable set of nested neighbourhoods. This aspect of the space has proved useful for the correction of certain kinds of grammatical errors that occur in English sentences. An English parser was written that used the metric to propose corrections to a variety of ungrammatical sentences. Experience with the program suggests that in many cases the intuitive notion of grammatical similarity corresponds closely to the mathematical definition of nearest neighbour in the space.

A metric space defined on English and its relation to error correction