Associative Grammar Combination Operators for Tree-Based Grammars Yael Sygal Department of Computer Science University of Haifa, Israel yaelc@cs.haifa.ac.il Shuly Wintner Department of Computer Science University of Haifa, Israel shuly@cs.haifa.ac.il 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. 1 Introduction Development of large-scale grammars for natural languages is an active area of research in human language technology. Such grammars are developed not only for purposes of theoretical linguistic research, but also for natural language applications such as machine translation, speech genera- tion, etc. Wide-coverage grammars are being developed for various languages in several theoretical frameworks. Grammar development is a complex enterprise: It is not unusual for a single grammar to be developed by a team including several linguists, computational linguists and computer sci- 1