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    <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.</abstract>
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%0 Conference Proceedings
%T A Fuzzy Approach to Erroneous Inputs in Context-Free Language Recognition
%A Asveld, Peter R.J.
%Y Hajicova, Eva
%Y Lang, Bernard
%Y Berwick, Robert
%Y Bunt, Harry
%Y Carpenter, Bob
%Y Church, Ken
%Y Joshi, Aravind
%Y Kaplan, Ronald
%Y Kay, Martin
%Y Nagao, Makoto
%Y Nijholt, Anton
%Y Steedman, Mark
%Y Thompson, Henry
%Y Tomita, Masaru
%Y Vijay-Shanker, K.
%Y Wilks, Yorick
%Y Wittenburg, Kent
%S Proceedings of the Fourth International Workshop on Parsing Technologies
%D 1995
%8 sep 20 24
%I Association for Computational Linguistics
%C Prague and Karlovy Vary, Czech Republic
%F asveld-1995-fuzzy
%X 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.
%U https://aclanthology.org/1995.iwpt-1.5
%P 14-25

Markdown (Informal)

[A Fuzzy Approach to Erroneous Inputs in Context-Free Language Recognition](https://aclanthology.org/1995.iwpt-1.5) (Asveld, IWPT-WS 1995)

• A Fuzzy Approach to Erroneous Inputs in Context-Free Language Recognition (Asveld, IWPT-WS 1995)

ACL

• Peter R.J. Asveld. 1995. A Fuzzy Approach to Erroneous Inputs in Context-Free Language Recognition. In Proceedings of the Fourth International Workshop on Parsing Technologies, pages 14–25, Prague and Karlovy Vary, Czech Republic. Association for Computational Linguistics.