An Elementary Formal Categorization of a Corpus of Spelling Errors

Abstract

If we take the complete mastery of orthography to be the productive knowledge of all spelling rules that exist within a language, then the orthography of an individual word can be identified with some subset of those rules. Accordingly, relations between words’ orthographies can be framed in terms of formal relations between those subsets and partitioned into four categories:

• identity: two words’ subsets contain the same elements, i.e. the two orthographies contain the same spelling rules

• exclusion: two words do not have any rule in common

• inclusion: word a’s orthography contains all the rules of that of word b, plus some more

• overlap: two words have some — but not all — rules in common. This category naturally is accompanied by some measure for the amount of overlap

The paper describes an algorithm to infer this partition from (co)variations of misspellings of words. The need for such an inference arises from (i) the want of a basis for a taxonomy of spelling errors which is less superficial or ad hoc than the common ones, and from (ii) the requirement to have an independent test for the psychological validity of recently developed software that converts ’sounds’ to orthography for Dutch words. Eventually the inference is the first phase of a broad heuristic to detect the underlying cognitive processes that govern the behavior of persons who are in the process of building up the orthography of their mother’s tongue, say children of about ten. These processes are not necessarily homomorph to the ’institutional’ ones, i.e. the rules from textbooks or teachers.

The kernel of the algorithm consists of 3 independent criteria. The first criterion effects a relation between the scope of the deficit as to the orthography of some word and the likelihood of it distribution of spellings. The second one connects the relative commonality (’covariance’) of two spelling distributions to inclusion and overlap. The third criterion, heterogeneity, focuses on the amount of difference between spellings.

Each triple of words effects three pairs; allocation to one of the four categories of two of them puts constraints on the allocation of the third one. For instance: if a includes b and b and c have overlap, then c cannot include a, nor can c and a exclude each other. These ’triple constraints’ are utilized to handle the stochastic aspect of the inference, which in itself is rather opaque: the algorithm has one free ’bias’-parameter which is assumed to be optimal when the number of violations of the ’triple constraints’ is minimal.

The results of the application of the algorithm to real data are given.

It is indicated how this elementary categorization could be a precursor to a taxonomy of spelling errors, how it could reveal differences between ’normals’ and ’dyslectics’, and how it leads towards the notion of ’effective extent of errors’: a way of counting the number of independent sources of error.

As the algorithm is purely formal, in the sense that no assumptions are involved that are specific to spelling processes, it can be generalized to all domains where incorrect cognitive performances can be discretely and finitely differentiated.