Unambiguous Boolean grammars

Boolean grammars are an extension of context-free grammars, in which conjunction and negation may be explicitly used in the rules. In this paper, the notion of ambiguity in Boolean grammars is defined. It is shown that the known transformation of a Boolean grammar to the binary normal form preserves unambiguity, and that every unambiguous Boolean language can be parsed in time O(n2). Linear conjunctive languages are shown to be unambiguous, while the existence of languages inherently ambiguous with respect to Boolean grammars is left open.