On the Nature of Economy in Language
言語における経済性をめぐって
福井 直樹
FUKUI Naoki
Vol.3, No.1 (February 1996), pp.51-71.
Received 1994/8/23, accepted 1995/7/11.
ABSTRACT:
This paper argues that there are rather unexpected fundamental connections to
be made between the principles of language and the laws governing the
inorganic world.
After summarizing the major development of economy
principles in physics and the basic results of discrete optimization
problems in combinatorial mathematics, I will argue that the economy
principles which theoretical linguists are currently trying to discover
in the theory of language are something comparable to the Principle of
Least Action in physics.
This provides us with a concrete interpretation
of the point Chomsky has repeatedly made (Chomsky, 1991a,b, passim),
i.e.,
language, despite its biological nature, shares the fundamental property of
the inorganic world; it is designed for ``elegance,'' not for
efficient use.
I will then discuss the nature of two types of economy principles of
language proposed in the literature, ``economy of derivation'' and
``economy of representation,'' from the point of view of the theory of
computational
complexity, and claim that the two economy principles exhibit quite
different properties with respect to their computational complexities:
economy of representation is efficiently solvable and therefore seems to
be in the complexity class P in the sense of the theory of computational
complexity, whereas economy of derivation is fundamentally computationally
intractable and appears to belong to the class NP-P.
How, then, can language be ever used, if its fundamental property
(economy of derivation) poses an intractable optimization problem?
I will suggest that language is equipped with certain mechanisms,
the real-world counterparts of the ``heuristic algorithms''
studied in the theory of optimization, that facilitate its efficient use.
Thus, to the extent that these mechanisms are available, language becomes
usable, despite its fundamental computational intractability.
keywords：
最小作用の原理 Principle of Least Action，
派生の経済性 economy of derivation，
表示の経済性 economy of representation，
離散最適化 discrete optimization，
計算量理論 theory of computational complexity，
近似アルゴリズム heuristic algorithms
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