@inproceedings{asveld-1995-fuzzy,
title = "A Fuzzy Approach to Erroneous Inputs in Context-Free Language Recognition",
author = "Asveld, Peter R.J.",
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://www.aclweb.org/anthology/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.",
}