Abstract
This talk explores issues in the construction of computationally simple grammars. In particular, we investigate the trade-off between simplicity of implementation and expressive power. We begin by developing what appears to be the simplest possible definite clause grammar implementation for a sub-theory in the minimalist program: that of probe-goal case agreement (Chomsky, Lectures in Government and Binding. Dordrecht: Foris; 2001). In computational modeling, there is a simple trade-off between simplicity of mechanism and expressive power, e.g., the Chomsky hierarchy. However, simplicity of implementation need not correlate with limited expressive power. Unification is a simple but powerful mechanism that can be used to implement uninterpretable/interpretable feature matching. We show, using examples from Chomsky (Lectures in Government and Binding. Dordrecht: Foris; 2001), as in (1)–(3), that unification-based derivations result in agree relations with fewer probe-goal steps than predicted. This economy of derivation results because once unified, unvalued features from different heads can be instantiated or valued simultaneously at a parse global level. Therefore, unification trades off fewer probe-goal steps for possibly unbounded agree relations.
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Notes
- 1.
In theory, the generate-and-test paradigm, i.e., generate linguistic descriptions and explicitly rule out illicit cases, can be contrasted with a constraint-based approach, i.e., one that emits only licit linguistic descriptions. From a computational complexity perspective, the constraint-based approach offers the possibility of avoiding the inefficiency inherent in overgenerating linguistic descriptions. Careful comparisons are necessary to verify that the bookkeeping necessary to maintain and manipulate constraint descriptions does not trump the inefficiency introduced by simple overgeneration. (See also footnote 8.) However, the author is not aware of any substantial purely constraint-based implementations of the Principle and Parameters approach.
- 2.
In practice, serial constraint testing can be organized to favor the early elimination of illicit candidates (to reduce implementational inefficiency). Note that most of the candidates in Fig. 10.1 are eliminated early on by the Case and Theta group of constraints. Only one other parse (in addition to the correct parse) makes any significant headway out of the Case and Theta group.
- 3.
Generally, overgeneration could be due to insufficient grammatical constraints or to the implementation itself. Given a sentence with a single licit parse, in the former case, extra parses will be generated. In the latter case, the system will produce multiple candidates, but only the correct parse will survive constraint checking.
- 4.
This is true up to a point. For example, from the same lexical array, one can assemble both John likes Mary and Mary likes John using the same sequence of steps, depending on which nominal, John or Mary, is selected to be the subject and direct object, respectively. See the sequence of operations shown in Fig. 10.3.
- 5.
The term “local” refers to the limits on search extent imposed by Phase theory on the unrestricted c-command domain.
- 6.
Inflectional morphology is not implemented in Fig. 10.3. We assume a procedure that spells out likes from t (tensed) + v* (φ: 3rd-sg-fem)+ V (like).
- 7.
In Fig. 10.4, the !F notation, where F is a feature, as in [n!case …], is used to indicate that a SO has a (currently) unvalued uninterpretable feature. In steps 1 and 3, Mary and John have unvalued Case, respectively. By steps 2 and 4, the uninterpretable Case in each case has been valued by probes v* and t, respectively.
- 8.
PRT is assumed by Chomsky (2001) to have uninterpretable number and gender φ-features.
- 9.
Implementation note: more precisely, an unvalued uninterpretable feature will have an uninstantiated logical variable as its value. Thus, when two unvalued uninterpretable features are unified, their values are represented by the same variable.
- 10.
Chomsky (2001) assumes there is φ-incomplete, containing only a person feature.
- 11.
In this implementation, it is assumed that External Merge is preferred (where available) to Internal Merge.
- 12.
Example pairs (3.a–b) and (4.a–b) differ with respect to the Case assigned to several prizes, nominative and accusative by matrix tense and v*, respectively. This difference is not manifested here. However, cf. we expect him/*her to be nominated.
References
Chomsky, N. A. (1981). Lectures in government and binding. Dordrecht: Foris.
Chomsky, N. A. (2001). Derivation by phase. In M. Kenstowicz (Ed.), Ken Hale: A life in language (pp. 1–52). Cambridge, MA: MIT Press.
Fong, S. (1991). Computational Properties of Principle-Based Grammatical Theories. Ph.D thesis, Artificial Intelligence Laboratory, MIT.
Stabler, E. P. (1997). Derivational minimalism. In C. Retoré (Ed.), Logical aspects of computational linguistics (LACL ’96), Lecture Notes in Artificial Intelligence, 1328 (pp. 68–95). Berlin: Springer.
Vijay-Shanker, K., & Weir, D. J. (1994). The equivalence of four extensions of context-free grammars. Mathematical Systems Theory, 27, 27–51.
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Fong, S. (2014). Unification and Efficient Computation in the Minimalist Program. In: Lowenthal, F., Lefebvre, L. (eds) Language and Recursion. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9414-0_10
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