In computational linguistics Karlsson has designed a language-independent formalism called Constraint Grammar. It makes possible the automatic morphological disambiguation and syntactic analysis of ordinary running text that has been supplied with all theoretically possible morphological and syntactic interpretations. The basic original reference is Karlsson (1990) which defines Constraint Grammar.
Karlsson has also worked on the history of linguistics where his main contribution is participation in the book Even Hovdhaugen, Fred Karlsson, Carol Henriksen, and Bengt Sigurd, The History of Linguistics in the Nordic Countries, Societas Scientiarum Fennica, Jyväskylä 2000.
Although Karlsson is a Swedish-speaking Finn, his knowledge of his second native language Finnish is exceptionally good, and he is widely considered a de facto authority on the language's rules. His work on the language (e.g. Finnish: An Essential Grammar, Karlsson (2004), originally published in 1983 and republished in 1999) has been used in various Finnish translations of open source projects.
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