Associative Grammar Combination Operators for Tree-Based Grammars

Authors:
Yael Sygal;Shuly Wintner
Affiliations:
Department of Computer Science, University of Haifa, Haifa, Israel;Department of Computer Science, University of Haifa, Haifa, Israel
Venue:
Journal of Logic, Language and Information
Year:
2009

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Abstract

Polarized unification grammar (PUG) is a linguistic formalism which uses polarities to better control the way grammar fragments interact. The grammar combination operation of PUG was conjectured to be associative. We show that PUG grammar combination is not associative, and even attaching polarities to objects does not make it order-independent. Moreover, we prove that no non-trivial polarity system exists for which grammar combination is associative. We then redefine the grammar combination operator, moving to the powerset domain, in a way that guarantees associativity. The method we propose is general and is applicable to a variety of tree-based grammar formalisms.