@inproceedings{asveld-1995-fuzzy,
title = "A Fuzzy Approach to Erroneous Inputs in Context-Free Language Recognition",
author = "Asveld, Peter R.J.",
editor = "Hajicova, Eva and
Lang, Bernard and
Berwick, Robert and
Bunt, Harry and
Carpenter, Bob and
Church, Ken and
Joshi, Aravind and
Kaplan, Ronald and
Kay, Martin and
Nagao, Makoto and
Nijholt, Anton and
Steedman, Mark and
Thompson, Henry and
Tomita, Masaru and
Vijay-Shanker, K. and
Wilks, Yorick and
Wittenburg, Kent",
booktitle = "Proceedings of the Fourth International Workshop on Parsing Technologies",
month = sep # " 20-24",
year = "1995",
address = "Prague and Karlovy Vary, Czech Republic",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/1995.iwpt-1.5",
pages = "14--25",
abstract = "Using fuzzy context-free grammars one can easily describe a finite number of ways to derive incorrect strings together with their degree of correctness. However, in general there is an infinite number of ways to perform a certain task wrongly. In this paper we introduce a generalization of fuzzy context-free grammars, the so-called fuzzy context-free $K$-grammars, to model the situation of malting a finite choice out of an infinity of possible grammatical errors during each context-free derivation step. Under minor assumptions on the parameter $K$ this model happens to be a very general framework to describe correctly as well as erroneously derived sentences by a single generating mechanism. Our first result characterizes the generating capacity of these fuzzy context-free $K$-grammars. As consequences we obtain: (i) bounds on modeling grammatical errors within the framework of fuzzy context-free grammars, and (ii) the fact that the family of languages generated by fuzzy context-free $K$-grammars shares closure properties very similar to those of the family of ordinary context-free languages. The second part of the paper is devoted to a few algorithms to recognize fuzzy context-free languages: viz. a variant of a functional version of Cocke-Younger-Kasami{'}s algorithm and some recursive descent algorithms. These algorithms tum out to be robust in some very elementary sense and they can easily be extended to corresponding parsing algorithms.",
}