Further results on syntactic ambiguity of internal contextual grammars

Abstract

Ambiguity plays an important role in checking the relevances of formalism for natural language processing. As contextual grammars were shown to be an appropriate description for natural languages, analyzing syntactic ambiguity of contextual grammars deserves a special attention. The levels of ambiguity of internal contextual grammars are defined depending on the information used for describing a derivation. In this paper, we continue the study on ambiguity of internal contextual grammars which was investigated in [3] and [13]. We achieve solutions to the following open problems addressed in the above papers. For each (i, j) ∈ {(2, 1), (1, 0), (0, 1)}, are there languages which are inherently i-ambiguous with respect to grammars with arbitrary selector, but j-ambiguous with respect to grammars with finite selector?