tailieunhanh - Báo cáo khoa học: "A Note on Categorial Grammar, Disharmony and Permutation"

CONCLUSIONS None of the additional characteristics for CatListGram affects the weak capacity of a categorial grammar; .: • exclusive cancellation of primitives does not affect recognition capacity maintaining more than one argument stack does not affect recognition capacity merging argument stacks of primary and secondary category does not affect recognition capacity and it takes more than disharmony to induce permutation closure. | Proceedings of EACL 99 A Note on Categorial Grammar Disharmony and Permutation Crit Cremers Leiden University Department of General Linguistics . box 9515 2300 RA Leiden The Netherlands cremers@ Disharmonious Composition DishComp is definable as X Y Y z x z Y Z X Y x z and is comdemned by Carpenter 1998 202 and Jacobson 1992 139ff Harmonious Composition HarmComp is defined as X Y Y Z x z Y z X Y x z and is generally adored Lambek Calculus Lambek has the following basis axiom X X rules if X Y z if X Z Y ỉf X Z Y then X Z Y and Y z x then X Y z then Y X z Permutation Closure of language L PermL PermL s I s in L and s is a permutation of sj and L c PermL but nice languages are not PermL for any L Fact 1 DishComp is not a theorem of Lambek but HarmComp is as you can easily check Fact 2 DishComp Lambek Lambek Permutation undirected Lambek Moortgat 1988 Van Benthem 1991 Lambek is maximal but contextfree For any assignment A of categorial types to the atoms of language L if Lambek recognizes L under A Lambek DishComp recognizes PermL under A so disharmony is always too much for Lam-bek Generalized Composition GenComp Joshi et al. 1991 Steedman 1990 primary type X Y secondary type Y Zl . Zn secondary type composition . Y Zi . Zn . X Zi . Zn primary type composition X Y . X Z1 . Zn while I is or and is conserved under com- position. Summarizing combinatory categorial grammar Fact 3 GenComp entails DishComp and you need it for the famous crossing dependencies in Dutch but Fact Jj It is not the case that for any assignment A of categorial types to the atoms of language L if GenComp recognizes L with respect to A GenComp recognizes PermL with respect to A as you can see from MIX MIX PermTRIPLE where TRIPLE anbncn n 0 - which is more than mildly context-sensitive Joshi et al. 1991 - and Fact 5 Consider the assignment Ab of categories to the lexicon a b c . Ab a a Ab c c Ab b s a c s a c s 273 Proceedings of EACL 99 . s c s a . s s c a s c a . Ab b s

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• Permutation
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