... up.cat(D a red apple)= LA(cat(D a ), LA(cat(Dred), cat(Dapple)))= LA(LC(cat(D a ), cat(Dred)), cat(Dapple))Based on Theorem 2, it follows that combinatoryoperation of categories has ... International Conference on Acoustics,Speech, and Signal Processing (ICASSP).E. Charniak, K. Knight, and K. Yamada. 2003. Syntax-based language models for statistical machine transla-tion. ... Chiang. 2005. A hierarchical phrase-based model forstatistical machine translation. In Proceedings of the43th Annual Meeting of the Association for Computa-tional Linguistics (ACL).D. Chiang....