The Non-associativity of Polarized Tree-Based Grammars
نویسندگان
چکیده
Polarities are used to sanction grammar fragment combination in high level tree-based formalisms such as eXtenssible MetaGrammar (XMG) and polarized unification grammars (PUG). We show that attaching polarities to tree nodes renders the combination operation non-associative, and in practice leads to overgeneration. We first provide some examples of non-associative combination operators in existing polarity-based formalisms. We then prove that there is no other nontrivial polarity system for which grammar combination is associative. This property of polarities casts doubt on the usability of polarity-based grammars for grammar engineering.
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