A Fuzzy Approach to Erroneous Inputs in Context-Free Language Recognition

Peter R.J. Asveld


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.
Anthology ID:
1995.iwpt-1.5
Volume:
Proceedings of the Fourth International Workshop on Parsing Technologies
Month:
September 20-24
Year:
1995
Address:
Prague and Karlovy Vary, Czech Republic
Venues:
IWPT | WS
SIG:
SIGPARSE
Publisher:
Association for Computational Linguistics
Note:
Pages:
14–25
Language:
URL:
https://www.aclweb.org/anthology/1995.iwpt-1.5
DOI:
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PDF:
http://aclanthology.lst.uni-saarland.de/1995.iwpt-1.5.pdf