Fuzzy context-free languages: part 1: Generalized fuzzy context-free grammars

  • Authors:

  • Peter R. J. Asveld

  • Affiliations:

  • Department of Computer Science, Twente University of Technology, AE Enschede, The Netherlands

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2005

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Abstract

Motivated by aspects of robustness in parsing a context-free language, we study generalized fuzzy context-free grammars. These fuzzy context-free K-grammars provide a general framework to describe correctly as well as erroneously derived sentences by a single generating mechanism. They model the situation of making a finite choice out of an infinity of possible grammatical errors during each context-free derivation step. Formally, a fuzzy context-free K-grammar is a fuzzy context-free grammar with a countable rather than a finite number of rules satisfying the following condition: for each symbol α, the set containing all right-hand sides of rules with left-hand side equal to α forms a fuzzy language that belongs to a given family K of fuzzy languages. We investigate the generating power of fuzzy context-free K-grammars, and we show that under minor assumptions on the parameter K, the family of languages generated by fuzzy context-free K-grammars possesses closure properties very similar to those of the family of ordinary context-free languages.