LACL 2005: Logical Aspects of Computational Linguistics pp 162-176 | Cite as
Strict Deterministic Aspects of Minimalist Grammars
Abstract
The Minimalist Grammars (MGs) proposed by Stabler(1997) have tree-shaped derivations (Harkema, 2001b; Michaelis, 2001a). As in categorial grammars, each lexical item is an association between a vocabulary element and complex of features, and so the ”yields” or ”fringes” of the derivation trees are sequences of these lexical items, and the string parts of these lexical items are reordered in the course of the derivation. This paper shows that while the derived string languages can be ambiguous and non-context-free, the set of yields of the derivation trees is always context-free and unambiguous. In fact, the derivation yield languages are strictly deterministic context-free languages, which implies that they are LR(0), and that the generation of derivation trees from a yield language string can be computed in linear time. This result suggests that the work of MG parsing consists essentially of guessing the lexical entries associated with words and empty categories.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Chomsky, N.: The Minimalist Program. MIT Press, Cambridge (1995)MATHGoogle Scholar
- 2.Ebbinghaus, H.-D., Flum, J., Thomas, W.: Mathematical Logic. Springer, Heidelberg (1994)MATHGoogle Scholar
- 3.Enderton, H.B.: A Mathematical Introduction to Logic. Harcourt (2001)Google Scholar
- 4.Harkema, H.: A characterization of minimalist languages. In: de Groote, P., Morrill, G., Retoré, C. (eds.) LACL 2001. LNCS (LNAI), vol. 2099, p. 193. Springer, Heidelberg (2001a)CrossRefGoogle Scholar
- 5.Harkema, H.: Parsing Minimalist Grammars. Ph.D. thesis, UCLA (2001b)Google Scholar
- 6.Harrison, M.A.: Introduction to Formal Language Theory. Addison-Wesley, Reading (1978)MATHGoogle Scholar
- 7.Harrison, M.A., Havel, I.M.: Strict deterministic grammars. Journal of Computer and System Sciences 7, 237–277 (1973)MATHMathSciNetCrossRefGoogle Scholar
- 8.Keenan, E.L., Stabler, E.P.: Bare Grammar: Lectures on Linguistic Invariants. Stanford Monographs in Linguistics. CSLI Publications (2003)Google Scholar
- 9.Knuth, D.: On the translation of languages from left to right. Information and Control 8(6), 607–639 (1965)CrossRefMathSciNetGoogle Scholar
- 10.Michaelis, Jens. 1998. Derivational minimalism is mildly context-sensitive. In Proceedings, Logical Aspects of Computational Linguistics, LACL’98, Grenoble.CrossRefGoogle Scholar
- 11.Michaelis, J.: On Formal Properties of Minimalist Grammars. Ph.D. thesis, Potsdam University (2001a)Google Scholar
- 12.Michaelis, J.: Transforming linear context free rewriting systems into minimalist grammars. In: de Groote, P., Morrill, G., Retoré, C. (eds.) LACL 2001. LNCS (LNAI), vol. 2099, Springer, Heidelberg (2001b)Google Scholar
- 13.Shoenfield, J.R.: Mathematical Logic. Addison-Wesley, Reading (1967)MATHGoogle Scholar
- 14.Stabler, E., Keenan, E.: Structural similarity. Theoretical Computer Science 293, 345–363 (2003)MATHCrossRefMathSciNetGoogle Scholar
- 15.Stabler, E.P.: Derivational minimalism. In: Retoré, C. (ed.) Logical Aspects of Computational Linguistics, pp. 68–95. Springer, Heidelberg (1997)CrossRefGoogle Scholar